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Combat Robotics Capstone Project FINAL CULMINATING REPORT

Jonathan Kettle, James Smykaluk, Travis Turner | ENGI-4969 | 13 April 2018

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Abstract Combat robotics competitions are a form of entertainment that provides an exciting

introduction to engineering for the public. In a combat robotics match, robots are placed inside of

an arena and fight until one robot is incapacitated, or a time limit is reached. Between matches,

teams can repair their robot. Over the history of these competitions, increasingly effective robots

have been designed and can deal spectacular damage for audiences.

For this project, a 30lb combat robot was designed, manufactured, and participated in a

competition at the University of Illinois. The robot was propelled by two drive wheels connected

to gearmotors, with casters used to support the robots weight. The active weapon was a large

rotating steel drum with axially machined “teeth”. As the drum rotates, the teeth contact the

surface of the opposing robot, causing damage. The drum rotated at up to 18650 RPM during

testing, giving a minimum rotational kinetic weapon energy of (9.11 kJ). The drum is spun by a

V-belt connected to a brushless motor. The robot was powered by a lithium polymer (Li-Po)

battery, connected to electronic speed controllers (ESC’s) which regulate the power supplied to

the motors. A radio transmitter-receiver pair was used to send the operator’s instructions to the

ESC’s.

In the Robobrawl 2018 Combat Robotics Tournament, our robot (The Revolver) won one of

its three scheduled matches, and both of its exhibition matches. Problems with the weapon ESC

prevented the effective use of the weapon throughout the competition, giving our robot a

siginificant disadvantage.

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Acknowledgement We would like to acknowledge the support and contributions from the people and

organizations that have made this project possible:

Dr. H. Bai for his unending enthusiasm and professional guidance.

Kailash Bhatia for his patience, tools and expertise.

Bruce Misner, for their electrical supplies and advice

Mr. Rudnicki (Rudnicki Industrial Inc.) for his time, material, and honest criticism.

Jet Welding and Ornamental Ironworks for their welding services.

Alyssa Mueller for her honest efforts.

Lakehead University Makerspace and volunteers, for their tools, storage, and expertise.

Maier Hardware for helping us get the nuts and bolts right.

The students of iRobotics/University of Illinois for the well-run competition,

sportsmanship, and knowledge.

ESS and LUSU for their financial contributions.

Kevin Turner for his tools, especially the ones we lost.

Our families, for their financial and personal support.

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Table of Contents

Abstract ......................................................................................................................................................... ii

Acknowledgement ....................................................................................................................................... iii

List of Figures ............................................................................................................................................. vii

List of Tables ............................................................................................................................................... ix

Nomenclature ................................................................................................................................................ x

Introduction ................................................................................................................................................... 1

Problem Definition ........................................................................................................................................ 2

Constraints and Criteria ................................................................................................................................ 3

Constraints ................................................................................................................................................ 3

Criteria ...................................................................................................................................................... 4

Concept Generation ...................................................................................................................................... 5

Preliminary Design Layouts and Analyses ................................................................................................... 7

Final Design and Analyses ............................................................................................................................ 9

Mechanical Design .................................................................................................................................... 9

Drum Design Robot .............................................................................................................................. 9

Invertible Design ................................................................................................................................. 10

Weight Distribution ............................................................................................................................ 10

Wheel Selection .................................................................................................................................. 14

Wheel Placement ................................................................................................................................ 14

Weapon Shaft Design.......................................................................................................................... 15

Belt Selection ...................................................................................................................................... 15

Bushing Selection ............................................................................................................................... 17

Temperature Simulation ...................................................................................................................... 17

Weapon Design ....................................................................................................................................... 20

Drum Material ..................................................................................................................................... 20

Drum Shape ........................................................................................................................................ 21

Drum Energy ....................................................................................................................................... 23

Drum Teeth Design ............................................................................................................................. 24

Rotating Stress in Weapon .................................................................................................................. 25

Drum Motor Support ........................................................................................................................... 27

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Time for Weapon to Stop ....................................................................... Error! Bookmark not defined.

Drum Weapon Safety .......................................................................................................................... 29

Frame Design .......................................................................................................................................... 29

Frame Material .................................................................................................................................... 29

Welding ............................................................................................................................................... 30

Wheel Guards ...................................................................................................................................... 30

Wedge Design ..................................................................................................................................... 30

Electrical Design ..................................................................................................................................... 30

Transmitter and Receiver .................................................................................................................... 31

Brushless and Brushed Motors and Speed Controllers ....................................................................... 32

Batteries .............................................................................................................................................. 35

Motor Sizing ....................................................................................................................................... 37

Weapon Motor Sizing ......................................................................................................................... 41

Battery Considerations ........................................................................................................................ 43

Operation, Maintenance, Service and Disposal .......................................................................................... 45

Safety Warnings ...................................................................................................................................... 45

Robot Operation ...................................................................................................................................... 45

Robot Assembly Procedure ................................................................................................................. 45

Safe Start-Up Procedure...................................................................................................................... 47

Controlling the robot ........................................................................................................................... 48

Safe Shut-Down Procedure ................................................................................................................. 48

Maintenance ............................................................................................................................................ 49

Costs and Bill of Materials ......................................................................................................................... 51

Validation and Compliance ......................................................................................................................... 53

Competition................................................................................................................................................. 56

Conclusions ................................................................................................................................................. 59

Recommendations for Future Teams .......................................................................................................... 59

Project Management ............................................................................................................................... 60

Procurement ............................................................................................................................................ 60

Testing .................................................................................................................................................... 61

Competition............................................................................................................................................. 61

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Design of Weapon ................................................................................................................................... 62

Weapon Drive Design ............................................................................................................................. 62

Frame Design .......................................................................................................................................... 62

Gyroscopic Effect ................................................................................................................................... 63

Temperature ............................................................................................................................................ 63

Bibliography ............................................................................................................................................... 64

Appendices .................................................................................................................................................. 65

A1: Weapon Shaft Design ...................................................................................................................... 65

A2: Belt Centre to Centre Distance and Tension .................................................................................... 66

A3: Bushing Design ................................................................................................................................ 67

A4: Gyroscopic Force Analysis .............................................................................................................. 67

A5: Heat Transfer FEA Setup ................................................................................................................. 69

A6: Drum Length .................................................................................................................................... 73

A7: Drum Energy .................................................................................................................................... 73

A8: Weapon Tooth Design ..................................................................................................................... 74

A9: Weapon Stop Time .......................................................................................................................... 76

A10: Electromechanical Model Derivations ........................................................................................... 76

Exponential Modelling ........................................................................................................................ 76

Linear Acceleration Approximation: Energy Method ........................................................................ 82

Linear and Non-Linear Model Prediction ........................................................................................... 84

A11: RoboBrawl 2018 Rules .................................................................................................................. 85

A12: Weight and Dimensions List .......................................................................................................... 99

A13: Acceleration Data Analysis .......................................................................................................... 100

A14: CAD Drawings Used During Manufacture .................................................................................. 104

A15: Electrical Schematic ..................................................................................................................... 122

A16: Gantt Chart and List of Deliverables ........................................................................................... 123

A17: ENGI-4969 Degree Project Guideline Policy ................................................................................. 124

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List of Figures

Figure 1: Initial Design ................................................................................................................................. 7

Figure 2: Preliminary Designs ...................................................................................................................... 8

Figure 3: Frame Weight Estimate ............................................................................................................... 11

Figure 4: Secondary Design ........................................................................................................................ 11

Figure 5: Secondary Design w/ Top Cover ................................................................................................. 12

Figure 6: Caster Wheel ............................................................................................................................... 12

Figure 7: Final Design ................................................................................................................................ 13

Figure 8: Final Design w/ Top Cover ......................................................................................................... 13

Figure 9: Wheel Placement [8] ................................................................................................................... 14

Figure 10: Centre of Mass ........................................................................................................................... 15

Figure 11: Solid Drum Design .................................................................................................................... 22

Figure 12: Six-Holed Drum Design ............................................................................................................ 22

Figure 13: Drum Teeth Design [8] .............................................................................................................. 24

Figure 14: Drum FEA Simulation, Final Adaptive Model ......................................................................... 26

Figure 15: Weapon Motor Mount ............................................................................................................... 27

Figure 16: Motor Mount Spacer ................................................................................................................. 28

Figure 17: Weapon Safety Stop .................................................................................................................. 29

Figure 18: Torque - Speed Curve of DC Motor .......................................................................................... 37

Figure 19: Cycle Velocity Plot ................................................................................................................... 39

Figure 20: Cycle Torque Plot ...................................................................................................................... 39

Figure 21: Cycle Power Consumption ........................................................................................................ 40

Figure 22: Bill of Materials ......................................................................................................................... 53

Figure 23: Shaft Force Analysis.................................................................................................................. 65

Figure 24: Gyroscopic Forces ..................................................................................................................... 68

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Figure 25: Components of acceleration .................................................................................................... 102

Figure 26: Resultant Acceleration............................................................................................................. 102

Figure 27: Velocity Components .............................................................................................................. 103

Figure 28: Velocity Resultant ................................................................................................................... 103

Figure 29:Weapon View 1 ........................................................................................................................ 104

Figure 30: Weapon View 2 ....................................................................................................................... 105




Figure 34: Shaft View ............................................................................................................................... 109



Figure 37: Weapon Motor Sheave ........................................................................................................... 112

Figure 38: The Revolver - Top View ...................................................................................................... 113

Figure 39: Frame - Top View ................................................................................................................... 114

Figure 40: Frame - Isometric View ........................................................................................................... 115

Figure 41: Full Robot View ...................................................................................................................... 116

Figure 42: Frame - Exploded View ........................................................................................................... 117

Figure 43: Frame - Isometric View ........................................................................................................... 118

Figure 44: Drive Motor Gearbox Dimensions .......................................................................................... 119

Figure 45: Weapon Mount – Non-Drive Side ........................................................................................... 120

Figure 46: Weapon Mount: Drive Side ..................................................................................................... 121

Figure 47: Electrical Layout ..................................................................................................................... 122

Figure 48: Gantt Chart .............................................................................................................................. 123

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List of Tables

Table 1: Types of Combat Robot Designs .................................................................................................... 1

Table 2: Criteria & Weightings ..................................................................................................................... 4

Table 3: Control of Motion ........................................................................................................................... 6

Table 4: Offensive Capability ....................................................................................................................... 6

Table 5: Robustness ...................................................................................................................................... 6

Table 6: Frame Weight Estimate ................................................................................................................ 11

Table 7: Design Weight .............................................................................................................................. 13

Table 8: Thermal Variables ........................................................................................................................ 18

Table 9: FEA Thermal Results.................................................................................................................... 19

Table 10: AISI 1080 Material Properties .................................................................................................... 20

Table 11: AISI 4340 HT Material Properties .............................................................................................. 21

Table 12: Rotational Drum Kinetic Energy ................................................................................................ 23

Table 13: Weapon Tooth Depth .................................................................................................................. 25

Table 14: FEA Simulation Values .............................................................................................................. 25

Table 15: Aluminum 5053 Material Properties .......................................................................................... 30

Table 16: Linear & Non-Linear Kinematic Models .................................................................................... 37

Table 17: Weapon Design Equations .......................................................................................................... 42

Table 18 Pre-Competition Tests ................................................................................................................. 54

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Nomenclature Symbol (Units) Description 𝑡 (𝑚) Thickness

𝑇 (𝑁𝑚) Torque 𝑎 (𝑚) Dimension of Hole

𝜔 (𝑟𝑎𝑑

𝑠𝑜𝑟 𝑅𝑃𝑀)

Rotational Velocity 𝑏 (𝑚) Outer Dimension

Disk

𝐹 (𝑁) Force 𝜎 (𝑀𝑃𝑎) General Stress

𝑣 (𝑚

𝑠) Velocity 𝐶 (𝑚) Circumference

𝑎 (𝑚

𝑠2) Acceleration 𝐶𝐿 (𝑚) Chord Length

𝑡 (𝑠) Time 𝑟 (𝑚) Radius of Large

Intersecting Circle

𝑟 (𝑚) Radius 𝑟2 (𝑚) Radius of Small

Intersecting Circle

𝑃 (𝑊) Power 𝑑 (𝑚) Distance Between

Hole Centres

𝜂 Efficiency ℎ (𝑚) Intersecting Distance

of two Circles

𝐸 (𝐽) Energy 𝐿 (𝑚) Length of Belt

𝑚 (𝑘𝑔) Mass FHP Fractional Horse

Power

𝐻𝑉𝑠 (𝐽) Energy Capacity of

Battery

𝑇𝑠𝑡 (𝑙𝑏𝑓 𝑜𝑟 𝑁) Belt Tension

𝐼𝑑 (𝑘𝑔 ∗ 𝑚2) Moment of Inertia of

Weapon

𝑃𝑉 Bushing Combined

Pressure Velocity

Rating

𝑑 (𝑚) Distance Rotated

Through

𝜇𝑘 Kinetic Friction

Coefficient

𝑆𝑢𝑡 (𝑀𝑃𝑎) Tensile Strength 𝐺 Gyroscopic Moment

𝑉 (𝑘𝑁) Shear Force 𝑀 Counteracting

Moment

𝐴 (𝑚2) Shaft Area 𝑇 (𝐾 𝑜𝑟 ℃) Temperature

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𝜏𝑚𝑎𝑥 (𝑀𝑃𝑎) Maximum Shear

Stress

𝐶𝑃 Specific Heat

Capacity

𝜌 (𝑘𝑔) Density 𝜌𝐶𝑃 (

J

m3K)

Volumetric Heat

Capacity

𝜈 Poisson’s Ratio 𝑘 (

𝑊

𝑚𝐾)

Thermal Conductivity

𝑄 (

𝑊

𝑚3)

Heat Generation

𝜈 (𝑚2

𝑠)

Kinematic Viscosity

𝐵 (

1

𝐾)

Volume Coefficient

of Expansion

𝐺𝑟 Grashof Number

𝑃𝑟 Prandtl Number

𝑅𝑎 Rayleigh’s Number

ℎ (

𝑊

𝑚2𝐾)

Convection Heat

Transfer Coefficient

𝑅𝑒𝑑 Reynold’s Number

𝑁𝑢𝐷 Nusselt Number

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Introduction The goal of this project was to design, manufacture a robot and participate in a combat

robotics competition. Combat robotics design involves in depth knowledge of mechanical and

electrical concepts, 3D modelling, and finite element analysis. Manufacturing requires

knowledge of procurement, machine shop practices, soldering and wire mounting. Competing

involves masterful robot control, as well as knowledge of repair/maintenance procedures.

Successful application of these skillsets is key to winning combat robotics competitions.

When combat robotics was first popularized (late 1990’s, early 2000’s) there was high

diversity in the types of robots that entered competition. As participants came to understand the

competition and the characteristics of winning robots, robots became more homogenous. Today,

combat robots can be divided into the following common categories:

Table 1: Types of Combat Robot Designs

Type Description

Wedge A wedge which is low to the ground is used to

get underneath opponent

Flipper An arm is placed underneath the opponent,

and is actuated upwards to flip opponent.

Horizontal Shaft Weapon A rotating weapon spins about a horizontal

shaft.

Vertical Shaft Weapon A rotating weapon spins about a vertical

shaft.

Rotary An outer shell or member rotates about the

entire robot.

Walker Various weapons. Walker robots are typically

given much higher weight limits due to their

technical difficulty.

Hammer A large weight is swung horizontally or

vertically at opponent

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Analysing past solutions is important to understanding the types of robots that may be

encountered in competition, and to provide inspiration on possible design elements.

High profile combat robotics competitions like the televised series BattleBots® offer

large cash prizes (up to $25,000 for the champion, and 7 x $10,000 prizes in various categories).

Many competitions offer robotics parts or small cash prizes for the winner. Cash prizes might be

enticing but competing is generally not a financially lucrative endeavour. Combat robotics

should be valued instead for the breadth and depth of experience it provides participants. It is an

excellent practical project to gain experience in design, manufacturing and maintenance. On a

societal level, combat robotics is an excellent tool to get young people interested in science,

engineering and robotics.

The robot itself does not have intellectual property potential, however, the solution to

some of the sub-problems has potential for further research. Table 16: Linear & Non-Linear

Kinematic Models and Table 17: Weapon Design Equations describe the solutions of linear and

non-linear models which were not found in any textbooks or research papers. These equations

give the power consumption as a function of time, the energy consumed in one cycle, and the

expected battery life of a motor – battery pair, for two different types of electric motors.

Problem Definition The goal of this project was to design and manufacture a combat robot and participate in

a combat robotics competition. The competition selected was Robobrawl 2018 hosted by

iRobotics, the student robotics organization at the University of Illinois. In the competition, the

goal was to win matches in the arena while minimizing the damage to our own machine. A

match can be won in 2 ways:

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• By “knock out”, where the opposing robot ceases motion for 10 seconds.

• By “time out”, where the 3-minute time limit is reached, and robots are scored

based on aggression and damage to the opposing robot.

To achieve this, a robot must have offensive capability, robustness to survive matches,

and controlled motion.

Constraints and Criteria

Constraints

iRobotics follows a strict set of rules and regulations that each competing robot must

abide by to be permitted into the competition. The full requirements for the competition are

available in Appendix A11:RoboBrawl 2018 Rules . The ruleset is based on commonly used

rules published by the Robot Fighting League. Key elements of this ruleset are listed below.

The robot must:

• Weigh less than 30lbs.

• Have a manual disconnect switch that fully deactivates weapon and drive train within 60

seconds.

• Have manual weapon stops in a high visibility colour.

• Have an active weapon that comprises at least 20% of the robot’s weight.

• Have controlled motion.

• Have a status light visible from outside of the robot.

• Have a failsafe radio system.

• Have fire proof bags for Li-Po batteries.

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The robot must NOT:

• Be pre-loaded through springs or kinetic motion.

• Use magnets offensively.

• Ground electrical circuits on frame.

• Use flammable gasses.

• Use an internal combustion engine or liquid fuels.

• Cause invisible damage to the other robot (ex. RF jamming).

• Use heat or fire as weapons.

• Use untethered projectiles (nets, ball bearings, liquids)

Criteria

The criteria of the design were chosen and given a numerical rating from 1 to 10, with 1

representing “not relevant to the design”, and 10 being “highly significant”. This weighting

scheme helped the team select a body/weapon style for the robot:

Table 2: Criteria & Weightings

Criteria Weight (out of 10)

Offensive Capability 9

Robustness 6

Control of Motion 7

Affordability 4

Manufacturability 6

Offensive capability is the ability of the robot to damage another. This rating was based

on the energy that the weapon can deliver, and a qualitative assessment of possible performance.

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Robustness is the ability of the robot to take damage. This rating was based on the

strength of the robot’s armor, as well as the presence of components that may be damaged

externally.

Control of Motion is the ability to control the robot in adverse conditions. This rating was

based on the number of powered wheels, design of drivetrain, and interactions between the

weapon and the drivetrain.

Affordability is based on a rough estimation of the cost to build a robot of a given design.

Manufacturability describes the ease of manufacturing the robot. The rating is higher for

designs that use common materials and processes.

Concept Generation Concept generation for this project was based on an initial data acquisition phase. Each

team member watched several hours of combat robotics competitions. Because the popular

televised competitions (BattleBots® and Robot Wars®) have many theatrical elements and focus

on heavyweight (200lb +) robots, the team focused on amateur events in similar weight ranges

(12lb to 30lb). Some of the amateur events watched include (Dragon Con®, Momo Con®, etc.).

The team members took individual notes, on the strengths and weaknesses of various robots,

focusing on the categories of offensive capability, robustness, and control of motion.

Based on this gathered information, team members presented ideas on various overall

designs and specific design elements. Due to the constantly evolving nature of the competitions

it was impossible to decide on an optimal robot type. The group debated several different

possibilities for the function of the robot:

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Table 3: Control of Motion

Propulsion Type Pros Cons

2 wheels Less space, Low weight Low traction

4 wheels Better traction Too many motors or

complicated drive train

6 wheels Better traction, redundancy Heavy, lots of space

Tracked Excellent traction Slow acceleration, cost of

track/belt

Table 4: Offensive Capability

Weapon Type Pros Cons

Flipper Low clearance, effective

against many geometries

Difficult to design, expensive

if using hydraulics or

pneumatics

Horizontal Shaft Weapon High energy Hard to control, gyroscopic

effect

Vertical Shaft Weapon High energy Throws itself when weapon

makes contact

Rotary Weapon also protects robot Can damage itself

Table 5: Robustness

Frame Type Pros Cons

Open Frame Light weight Low protection for electronic

components from

cutting/piercing

Armor-on-Frame Great protection, shock

absorbing

Heavy, bolts may not be

reliable

Armor-as-Frame Good protection, easy to

manufacture, easy to mount

components

Transmits vibrations to

electronic components.

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Although the type of the robot has a large effect on performance, the quality of the design

and manufacture are arguably even more important. The group committed to a general

mechanical design to reduce the design space.

Preliminary Design Layouts and Analyses The initial mechanical design had the following elements:

● 4 wheels,

● 4 gearboxes,

● 5 motors,

● Horizontal axis rotary disc/drum weapon,

● Armor-as-frame design (vs frame only, or frame and armor)

Figure 1: Initial Design

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Figure 2: Preliminary Designs

One major disadvantage of several designs is their inability to function upside down,

which incapacitates the robot if it were to flip over in competition. To avoid this, the geometry of

the robot was designed so that it could operate in either orientation. Gear-motors were chosen as

the propulsion mechanisms because motor-gearbox combinations are compact and come in a

wide range of gear ratios.

Robot design is very open-ended. As such, the group had to reduce the design space to

maximize the amount of time spent on detailed design and manufacture. The first tool used to

reduce the design space was the Weights and Dimensions list (in Appendix A12: Weight and

Dimensions ListA12: Weight and Dimensions List). Knowing some of the basic requirements and

constraints, components like the battery, motors, and speed controllers were chosen. The size and

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weight of these components allowed the team to refine the design. It must be noted that an

iterative process was used to ensure the weight of the robot was as close to 30 lb as reasonably

possible. Based on this analysis the preliminary design was changed in the following ways:

• The number of driven wheels was reduced to 2 to save weight.

• The weapon was made much larger, greatly increasing energy of the weapon.

• The pentagon shaped frame was changed to a rectangular shape. This made

manufacture and design simpler.

• The wheels were placed on the outside of the robot frame with wheel guards

added for protection.

• A wedge was added to the rear end of the robot to improve the centre of gravity,

and give a secondary passive weapon.

Final Design and Analyses

Mechanical Design

The following sections document the various design tasks that were completed to finish

the mechanical design of the robot. Some tasks were performed with incomplete knowledge of

operating conditions or missing manufacturer specifications, or missing specifications of other

robot parts.

Drum Design Robot

Drum robot designs are a spinning drum with teeth, driven by a belt transmission system.

The drum is mounted horizontally in the front of the robot in such a way that it launches

opponents into the air when contact is made, inverting the competitor or causing damage from

the impact with the weapon and the ground. Drum robots are compact versions of the vertical

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spinners, with a low centre of gravity, capable of being invertible, suffering smaller gyroscopic

effects and quick spin up times.

Invertible Design

The robot was designed to take advantage of the low design profile of a drum robot by

being fully invertible. This is an advantage during competition by not suffering the risk of being

flipped by competitor’s robots, or being inadvertently knocked upside down during an impact.

By being mindful during the initial design stages, this design weakness can be reduced.

Weight Distribution

Initial weight distribution was determined through research to roughly have a balanced

weight distribution of 30/30/25/15. Which translates to 30% (4.1 kg) allocated to the drive

system, 30% (4.1 kg) of the weight towards weapons, 25% (3.4 kg) to the structure and armour,

with the remaining 15% (2.1 kg) to electronics and batteries. This weight distribution was only a

starting point for the design of the robot, but offers an excellent starting point of what is required.

The initial design consisted of a four-wheeled robot with a small solid disk. This design

had a very heavy drive system due to the four drive motors. As such, the secondary design

removed two of these motors to reduce weight. The drum was considerably undersized during

these iterations, and was later lengthened once a material for the drum was selected. The design

consisted of a thin outer steel shell with cross braces for mounting. An estimate of frame weight

was also calculated as follows, to determine the material choices available for the frame in terms

of weight restrictions.

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Figure 3: Frame Weight Estimate

Table 6: Frame Weight Estimate

Steel, 1/8” Aluminum ¼”

Thickness of Armor (m) 0.003175 0.00635

Density of Armor (kg/m3) 8050 2700

Height (m) 0.1 0.1

Rear Length (m) 0.15 0.15

Rear Width (m) 0.3 0.3

Front Width (m) 0.1 0.1

Angle 𝜃 (degrees) 45 45

Front Length (m) 0.1 0.1

Surface Area Top/bottom (m2) 0.1300 0.1300

Surface Area Sides(m2) 0.0983 0.0983

Surface Area Total (m2) 0.2283 0.2283

Weight (kg) 5.8437 3.9139

Weight (lb) 12.8363 8.6107

The design choice was made to use an aluminum unibody shell, with a solid bottom for

easier mounting of components. Taking into consideration the weight distributions as discussed

on the previous page, a secondary design was produced, and may be seen below.

Figure 4: Secondary Design

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This design featured a two-wheeled decision for weight savings, as well as a second LiPo

battery and properly sized drum. This design also featured a top thinner cover for the robot for

protection from attacks from above the robot.

Figure 5: Secondary Design w/ Top Cover

Because the design was changed from four driving wheels, to two driving wheels, the

robot’s front was supported by two casters. The casters provide support for the drum while

maintaining a low friction coefficient; reducing strains on the drive motors and battery.

Figure 6: Caster Wheel

The design was then further optimized, the drum motor was remodelled, with sheaves,

and proper mounts for several components were implemented. The wheel guards and a rear

wedge were added to the design as seen below.

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Figure 7: Final Design

The design in figure 7 above proved to be the final design for the combat robot. The

design with the top cover included can be seen in figure 8 below.

Figure 8: Final Design w/ Top Cover

The weight of each component was estimated in Appendix A12: Weight and Dimensions List.

With a comparison to the allowable weight in competition, the current design is under weight.

Table 7: Design Weight

Total Design Weight (kg) 11.00

Weight limit (kg) 13.61

Unused Weight Room (kg) 2.61

This remaining weight allows for unexpected design challenges during manufacturing of the

robot.

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Wheel Selection

An ideal wheel choice would be robust and offer good protection against damage and

punctures. For this reason, a solid plastic wheel was selected, with a rubberized surface was

used. The coefficient of friction between the floor (metal) and rubber is much greater than the

coefficient for plastic on metal, leaving rubber to be the obvious choice to attain high traction.

Wheel Placement

Figure 9: Wheel Placement [8]

The combat robot only has two active wheels. Placement of the wheel is critical to ensure

proper traction of the robot, for driving control in the arena. Pictured above is a drum design with

the centre of mass 𝐶1, and centre of the wheel 𝐶. The distance between the centre of mass and

the wheel is important; too close and the robot would “buck” upwards when accelerating, too far

away and the wheel would lose traction while accelerating. It won’t tilt during acceleration

because of the forward torque with respect to the wheel axis 𝐹 ∗ 𝑎 = 𝑇𝑜𝑟𝑞𝑢𝑒, counteracts the

force from the wheels 𝜇 ∗ 𝐹 ∗ 𝑟. The ideal distance for the wheels to be back from the centre of

mass can be calculated by 𝐹 ∗ 𝑎 ≥ 𝜇 ∗ 𝐹 ∗ ℎ 𝑜𝑟 𝑎 = 𝜇 ∗ ℎ. Where 𝜇 is the coefficient of friction

between the wheels and the ground, and 𝐹 is the robot weight.

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Figure 10: Centre of Mass

Figure 10 illustrates the robot’s centre of mass for two different situations; the right mass

centre pertains to the robot with the wheel guards and wedge removed, and the left mass centre

corresponds to the robot with the wheel guards and wedge in place. This is important to note, as

the centre of mass is very forward on the robot due to the weight of the drum without the guard

and wedge. The second centre of mass was designed to be much further back to aid in the

traction of the wheels. The previous equations were used to determine how the added weight

would provide an improved weight distribution while adding to the structural strength of the

robot.

Weapon Shaft Design

The stationary shaft which the weapon rotates about is a possible point of failure for our

design. Failure due to bending is very unlikely, as both the shaft, bushings and weapon would

need to deflect by a large amount. The shaft will most likely fail due to shear stress. It is

impossible to know the amount of force that the shaft will experience in combat, due to a number

of unknown factors. A detailed design of the shaft is given in Appendix A1: Weapon Shaft

Design, with the result implying that the shaft should be no smaller than 13 mm in diameter. A

shaft 18 𝑚𝑚 in diameter, with a small step reduction to 16 𝑚𝑚 was chosen. Exceeding the

minimum diameter will improve rigidity, safety, and longevity.

Belt Selection

A V-belt drive was selected over gear or chain drives for its ability to slip, and ease of

manufacture and alignment. Slip was desired, as a rigid connection between the weapon and

16 | P A G E

motor could cause significant damage to the motor or transmission system if the weapon were to

instantaneously stop rotating during competition.

Research

V-belts consist of rubber and internal steel cables. The cables and rubber are only able to

bend to a certain radius before the steel cables permanently deform. The belt specified will be

rated with a minimum sheave diameter.

Belts in automotive and industrial applications are selected to have a very long life, from

2 to 5 years. In a controlled environment, with properly aligned sheaves, these belts fail due to

fatigue of either the rubber or the steel cables within.

In this application, a very short belt life is acceptable (a match lasts a maximum of 3

minutes). According to our initial research, belts typically fail due to melting/heat damage in

combat robotics, meaning typical rating and design procedures are not applicable.

Geometrically, there are goals of minimizing the centre-to-centre distance between the

sheaves, and the constraint of having the maximum sheave diameter smaller than that of the

weapon (~90mm). Minimizing the centre-to-centre distance reduces material cost and weight

needed for armor.

Based on these constraints, a Fractional Horse Power (light duty) belt type was selected,

which have low minimum sheave diameters and come in small lengths. All sizes of these belts

are designed for “drive systems operating at 1HP or less”. Cross sectional sizes range from 2L to

5L. A 3L120 belt was selected, giving one of the smallest possible centre-to-centre distances

between sheaves of 3.64 in.

17 | P A G E

Belt Tension

Most textbooks have procedures for specifying tension for larger belts, and do not present

factors for FHP belt sizes. An alternate guide to belt tension was found, [3] which provided a

general formula and factors for calculating the required static belt tension. This belt tension is

used in the design of bushings and to calculate friction. When building the robot, the belt will be

tensioned to 140 N.

Bushing Selection

Rolling element bearings could have been specified, but there is a high risk of

catastrophic failure due to high impact loads. For this reason, bushings were selected, which

instead fail by abrasion or slowly wearing out. Using a bushing ensured a gradual failure over

time, which is preferable to the abrupt failure expected in rolling element bearings.

Bushings are rated based on 3 variables, Pressure (P) Velocity (V) and a combined PV

rating. The pressure on the bushing is calculated over the projected internal area, considering

both the belt tension and the weight of the drum. Our design requires bushings with a rating of

approximately 7.92 𝑀𝑃𝑎 ∙ 𝑚/𝑠. Knowing these parameters, the most suitable bushing was

selected, with a PV rating range of 2.1~ 5.0 𝑀𝑃𝑎 ∙ 𝑚/𝑠, with a velocity rating much lower than

necessary, and a pressure rating much higher than necessary. There were no off-the-shelf

products that fit the needed specifications, as most products are designed for lower speeds over

much longer time spans, so this “off-spec” bushing had to be purchased.

Temperature Simulation

To estimate the maximum temperature reached inside of the robot, thermal FEA was

performed on the two motor types. Worst-case scenario assumptions were made in to produce

conservative (high) temperature estimates.

The general PDE solved by MATLAB’s solvepde function is:

18 | P A G E

𝑚𝜕2𝑢

𝜕𝑡2+ 𝑑

𝜕𝑢

𝜕𝑡− ∇ ∙ (𝑐∇𝑢) + 𝑎𝑢 = 𝑓

For transient analysis, the parabolic heat equation is used:

𝜌𝐶𝑝𝜕𝑇

𝜕𝑡− 𝑘

𝜕2𝑇

𝜕𝑥2 = 𝑄

Comparing these equations, the following variables need to be specified:

Table 8: Thermal Variables

General PDE Variable Thermal Variable

Symbol Description Units

u T Temperature ℃ , 𝐾

m N/A N/A N/A

d 𝜌𝐶𝑃 Volumetric heat

capacity

J

m3K

c k Thermal conductivity 𝑊

𝑚𝐾

a N/A N/A N/A

f Q Heat generation 𝑊

𝑚3

Results of the FEA are shown in

Table 9: FEA Thermal Results. Three trials of the simulation were run, at 25%, 50% and

75% of the average cycle power according to the non-linear motor design models to be discussed

later. It is possible that high motor temperatures will interfere with the operation of other parts

within the robot. However, it is likely that the motors have been designed to dissipate heat far

better than these models suggest. The technical setup of this FEA may be found in Appendix A5:

Heat Transfer FEA Setup.

Table 9: FEA Thermal Results

19 | P A G E

Drive Motor Weapon Motor

25% 𝑃𝑙𝑜𝑠𝑠

36 to 44 °C

44.5 to 48 °C


52 to 68 °C

71 to 76 °C


70 to 90 °C

97 to 104°C

20 | P A G E

Weapon Design

Drum Material

The material selected for the drum is critical for the success of an impact weapon. The

ideal material would require a high yield strength, hardness, impact toughness and fracture

toughness. The impact toughness is a measure of the materials resistance to impacts, and how

much impact energy the material absorbs before breaking. Hardness of the material is the

resistance to penetration by other harder materials. Hardness is important when designing drum

weapons because the tooth of the drum must remain sharp to properly “catch” other combat

robots to inflict significant damage. The fracture toughness is the resistance of the material to the

propagation of cracks; the higher the fracture toughness, the higher the stresses it can withstand

before fracturing.

When considering the criteria for the drum material, many materials do appear to satisfy

the above requirements; in particular, medium and high carbon steels. Both steels offer good

strength characteristics, however, some more exotic alloys will be considered too expensive for

this project.

Initially, AISI 1080 steel was selected for initial design purposes. AISI 1080 has the following

properties:

Table 10: AISI 1080 Material Properties

Property Magnitude

Modulus of Elasticity (GPa) 205

Tensile Strength, Yield (MPa) 420

Tensile Strength, Ultimate (MPa) 770

Rockwell C Hardness 31

Density (g/cm3) 7.85

21 | P A G E

AISI 1080 is a high carbon steel that offers a great balance between strength, hardness

and impact toughness. Ultimately, a piece of AISI 4340 HT steel was donated to the capstone

team from a local machine shop. AISI 4340 HT has the following properties:

Table 11: AISI 4340 HT Material Properties

Property Magnitude




Rockwell C Hardness 43


AISI 4340 HT is a high carbon steel with even higher strength and impact toughness due

to the heat treatment process. With a hardness of 43 Rockwell C, AISI 4340 HT steel is reaching

the upper limit of hardness before becoming too brittle, breaking under severe impact instead of

yielding.

Drum Shape

The drum shape was designed to optimize the rotational kinetic energy available. As a

drum bot design, the initial starting shape was a cylinder. A hole for the shaft was of course

necessary, so a 20 𝑚𝑚 bore was implemented to accommodate the 18 𝑚𝑚 shaft with bushings.

Next, following teeth depth designs two 10 mm teeth mill cuts were modeled. Drum symmetry

was paramount, as even the smallest asymmetries have the potential to cause fatal vibration

issues at high speeds.

22 | P A G E

Figure 11: Solid Drum Design

Lastly, the remaining cylinder material was optimized to move material weight towards

the outside of the drum to increase the mass moment of inertia. To achieve this, six 15 mm holes

were bored out of the drum; removing inner material while maintaining drum integrity.

Figure 12: Six-Holed Drum Design

As mentioned above, the drum was to be designed with the weapon comprising 30% (4.1

kg) of the total robot’s mass. To ensure that the drum does not go over this weight limit, the

length was determined such that the mass of the drum would be 100 g less than the allotted

amount. Knowing the density of steel from Table 11: AISI 4340 HT Material Properties, and using

23 | P A G E

3D modelling to determine the cross sectional area of the drum (0.004600888 𝑚2), the

maximum length was easily determined to be 110.4 mm.

Drum Energy

The rotational drum energy was calculated using the moment of inertia of the cylinder

with the rotating speed and a standard weight when comparing designs.

This kinetic energy by using the six-holed design results in a 20% larger rotational kinetic

energy capability than the non-holed design discussed above. Its theorized that further material

removal past 6 holes would compromise the integrity of the drum at high rotational velocities.

Not only are impacts a concern for failure, but the hoop stress would begin to tear the drum apart

at high speeds. This design challenge can be seen later in the hoop stress calculations.

However, it is important to account for the issue during combat that the drum may not

always be up to full speed, and thus it is important to understand the effects of lower drum

speeds, such as the minimum drum speed of 6,000 𝑟𝑝𝑚 design for the drum teeth. The reduction

in speed has an non-linear reduction in kinetic energy, emphasizing the importance of the speed

of the drum during impact contact. An overview of different drum designs with respect to the

stored rotational kinetic energy is as follows. The “Disk Design” column refers to the diameter of

the main shaft hole and any other weight reallocation holes. A constant drum mass of 4 kg, a

drum radius of 0.045 m, and angular speed of 21000 rpm were used to generate Table 12:

Rotational Drum Kinetic Energy.

Table 12: Rotational Drum Kinetic Energy

Disk Design Mass Moment of Inertia (kgm2) Kinetic Energy (kJ)

½” shaft, 0 holes 0.003996 9.65

½” shaft, 4 holes 0.004503 10.88

½” shaft, 6 holes 0.004755 11.49

¾” shaft, 0 holes 0.004532 10.95

24 | P A G E

¾” shaft, 4 holes 0.004693 11.34

¾” shaft, 6 holes C 0.005011 12.10

¾” shaft, 6 holes F 0.004786 11.56

18 mm shaft, 0 holes 0.004530 10.94

18 mm shaft, 6 holes 0.004783 11.55

This overview helped when choosing the final drum design, seeing as the choice was a

balance between structural strength and kinetic energy trade offs.

Drum Teeth Design

Two drum teeth designs were considered; a single material-single-piece design, and a

multi-part design with a softer material for the main drum and a harder material insert for the

teeth. A single piece design was selected to maximize rigidity and manufacturability, while

minimizing the number of parts.

Figure 13: Drum Teeth Design [8]

The smallest theoretical depth of the drum teeth may be determined used elementary

dynamics. The summary of the minimum tooth depth required at several rotational speeds may

be seen in Table 13: Weapon Tooth Depth.

25 | P A G E

Table 13: Weapon Tooth Depth

Weapon Speed (rpm) Required Tooth Depth (mm)

6000 10

10000 6

21000 3

Rotating Stress in Weapon

Finite Element Analysis was completed using the Autodesk Fusion 360 program to determine the

maximum stresses in the rotating drum. The simulations were completed with refining mesh

sizes until a convergence occurred.

The simulation used a rotating angular speed of 2093 𝑟𝑎𝑑/𝑠, with a pin constraint along the

model’s inner diameter. An adaptive mesh method was used for speed and accuracy, which

resulted in a maximum Von Mises stress of 148.1 MPa, with a convergence rate of 2.59967%.

The convergence rate of 2.59967% was deemed unacceptable for this simulation, so another

more precise simulation was done.

Using an adaptive refining mesh method with an exit criterion based on the Von Mises stress and

refining the mesh further, the following simulation occurred:

Table 14: FEA Simulation Values

Element Type Tetrahedra

Maximum Stress 190.4 𝑀𝑃𝑎

Minimum Stress 0.3178 𝑀𝑃𝑎

Number of Elements 2,228,738

Number of Nodes 3,123,093

Convergence Rate 0.539795%

26 | P A G E

Figure 14: Drum FEA Simulation, Final Adaptive Model

This simulation’s mesh was refined six times, and terminated when the convergence rate

achieved the result of 0.539795%. By using 2,228,738 elements the model is very precise, and

accepted as the final result.

The standard overall mesh refinements proved computationally complicated and not efficient.

Although refining the mesh did show signs of convergence, 2,413,493 nodes spread out equally

over the model was very inefficient. The adaptive mesh used a similar number of nodes but

27 | P A G E

focused more elements in critical locations proving to be more efficient to achieve convergence.

The convergence rate of 0.539795% is acceptable for this simulation.

From the results we achieved a maximum Von Mises stress of 190.4 MPa, which is well below

the 1371 MPa yield strength of the material. This means the rotational speeds will not damage

the drum model, and the AISI 4340 HT steel is appropriate for use.

Drum Motor Support

A custom drum motor support was created and used in competition. Originally, the motor

was supported by a pair of plastic brackets with PLA (polylactic acid) plastic inserts. Although

these supports were functional, it proved challenging to properly tension and line up the motor

with the drum. Thus, a simpler “single” piece design was designed and 3D printed to simplify the

assembly/robot setup.

Figure 15: Weapon Motor Mount

Two of these PLA mounts reduced the amount of parts needed by half, providing

excellent support and reduction in support size. The process was even further simplified by

implementing a simple spacer that connects the mounts into one rigid support body.

28 | P A G E

Figure 16: Motor Mount Spacer

Weapon Stop Time

Competition rules state that any rotating parts must come to a complete stop within 60

seconds of the robot’s power being shut off. Without a braking mechanism, the robot depends on

friction to stop the weapon within the time limit.

Friction will come from 2 areas of contact, the bushing, and the belt/sheave. Belt/sheave

friction is difficult to predict because the nature of contact is unknown. The belt can either slip

about either sheave, or the belt may continue to spin the sheaves, making the frictional loadings

uncertain (kinetic vs static friction).

The amount of time to stop the weapon was determined to be 69.44 seconds. This calculation

solely considered the bushing friction, and did not account for the belt friction and friction with

the air. Belt friction was thought to be just as, if not more significant, than the bushing friction.

Due to the complexities in calculating belt friction, but knowing it to be significant in slowing

down the weapon, it had to be assumed that the weapon would stop in the required 60 seconds

timeframe. After building the system and turning it off from full speed, it was found that the

drum came to a rest in under 10 seconds.

29 | P A G E

Drum Weapon Safety

A simple removable design safety was required for the robot due to competition rules. An

insert was designed to be inserted into the drum bore holes from the outside of the robot,

preventing rotation of the drum when not in combat.

Figure 17: Weapon Safety Stop

Frame Design

Frame Material

If cost was not a factor, a titanium alloy would have been an ideal choice due to is low

density and high density. High grade titanium alloys are an excellent choice due to there strength

to weight ratios, where weight is a hard constraint for competition.

Aluminum is a very light metal with a fraction of the density of steel, which makes it a

good alternative choice for the frame material as a weight saving design decision. Ideally a 6000

series aluminum alloy would have been chosen due to its medium strength, being a reasonable

choice for a steel substitute in frame design for combat robotics.

A local machine shop donated pieces of aluminum 5053 checker plate to the team for the

frame . The 5000 series aluminum is low in strength, and resistant to sea corrosion, which is not

useful in combat robotics. Even though it’s not the ideal frame material, it did have the ideal

price of $0, which was perfect for this project. Aluminum 5053 has the following properties:

30 | P A G E

Table 15: Aluminum 5053 Material Properties

Property Magnitude




Brinell Hardness 60


Welding

A welded frame was selected due to its rigid connections and minimal misalignment

risks. Welded frames may be easily repaired with JB weld. It is important to recognize the

disadvantages due to heat affected areas becoming brittle and prone to cracking due on impact

during competition. To compensate for this unwanted heat treatment, a lot of weld filler is used

to strengthen the welded connections. The added filler in contributes significant weight to the

workpiece.

Wheel Guards

The wheel guards were made from steel plate, while simultaneously improving the

robot’s weight distribution and protection of the wheels. Damage to the wheels would

immediately disable the robots motion, resulting in a technical knock during competition. These

wheel guards serve to protect the bot from this type of failure.

Wedge Design

The wedge was designed as a secondary weapon for use during combat. Additionally, the

wedge serves as a counter weight for the drum, offering better traction for the wheels. The wedge

offers protection against other spinning weapon designs. Spinning weapons have difficulties

properly hitting wedge designs.

Electrical Design

The following section gives an in-depth discussion of each electrical component group of

the combat robot.

31 | P A G E

Transmitter and Receiver

The transmitter/receiver pair acts as the user-interface for the robot controls and the

information receiving hub inside the robot.

The transmitter reads the user input (position of toggle/switch/knob) and bundles the

information in discrete quantities in preparation of sending the data to the receiver. The

transmitter then encodes the information digitally while supplementing the message with error-

checking code. The signal then gets sent to the receiver, and if there is substantial noise in the

environment where the signal is being transmitted, the transmitter and receiver will automatically

search for a clear channel (frequency) that has less noise. This makes it very easy for modern

transmitters and receivers to communicate in noisy environments with absolutely no

troubleshooting by the user.

The signal from the transmitter is sent to the receiver at approximately 2.4 GHz.

Different manufacturers send signals in different languages while still at the 2.4 GHz frequency,

but due to the language difference, not all transmitters are compatible with all receivers. To

eliminate compatibility problems, most transmitters come with a paired receiver.

When connecting motors and servos to the receiver, it's important to ensure that they are

plugged in correctly. Each motor/servo has three wires; a signal, +5 V, and ground wire. There

is usually a marker somewhere on the receiver that will indicate which pin corresponds to each

wire.

The receiver communicates to the servos and speed controller by sending out a series of

pulses that directly correspond to the input of the transmitter. The duration of these pulses is

measured in milliseconds, with longer pulse durations corresponding to higher levels of input

32 | P A G E

from the transmitter. These pulses are usually square waves. This style of motor/servo input is

called pulse-width modulation, or PWM.

In summary, transmitters usually come with their own receivers. The receiver gets its

power by taking 5 V from the battery. Each component is plugged into the receiver by using a

signal, +5 V, and ground wire. Receivers communicate to motors/servos by using PWM signals.

It will be discussed later that the battery voltage used for this project was a nominal 11.1

V, which is much greater than the 5V required for the receiver. If the receiver was wired directly

to the main line of the battery, it would fail due to voltage overload. This problem was solved by

including a standalone battery eliminator circuit (UBEC) in the design. There are multiple types

of BECs, but this project utilized a switching UBEC. Switching UBECs receive power directly

from the battery and have an automated switching mechanism that turns on and off thousands of

times per second. When combined with a capacitor, the result is an output from the UBEC at a

consistent 5V; precisely what the receiver requires. Switching UBECs are approximately 94%

efficient. Most ESCs come equipped with linear BECs wired into them, but these BECs

essentially operate like a resistor, resulting in additional heat build up and drastically reduced

efficiency. For this reason, the switching UBEC was specified.

Brushless and Brushed Motors and Speed Controllers

All brushless motors have numerical designations that indicate their characteristics. An

example of this would be a D2822/12 1450 KV motor. The first two digits signify the motor or

rotor diameter in mm. For example, the motor listed above has either a 28 mm outer shell

(known as a "can") or a 28 mm rotor inside the can. The reason that this measurement may be

either for rotor or can width is because there really aren't any standards in the RC industry

33 | P A G E

relating to brushless motor dimensions. In general, larger diameter motors generate more torque

because they have a longer moment arm at which the EMF acts.

The second two-digit number is the height of the rotor or motor, in mm. For the same

reasons as listed above, it varies between manufacturers whether this number corresponds to the

rotor or can height.

The third number, preceded by a "/" corresponds to the number of wire turns around each

pole inside the motor. In general, the smaller the number, the faster the rotation, and the larger

the number, the more torque that gets produced. It's important to note that the power to the motor

is constant (when at steady state), and two motors with the same power consumption can have

different torques and speeds by changing the number of coils surrounding each pole.

The last number corresponds to the number of revolutions per volt. This number

represents the number of revolutions the motor would turn for every volt it received in a no-load

scenario. For example, if the above motor was fed an input of 3 V, the motor would have a no-

load speed of 3*1450 = 4350 revolutions per minute, in theory.

Brushless motors work very similar to an AC motor. At any given time, two of the three

poles of the brushless motor are energized; one pole with a positive charge, the other with a

negative charge. It is known that like charges repel and opposite charges attract. The positive

charged pole attracts a point on the surface of the rotor (shaft), causing the shaft to rotate. The

negatively charged pole would strategically be powered such that it “pushes” said point on the

rod towards the positively charged pole. To maintain motion, the charge of the poles is

constantly being changed. This results in a smooth, fast, and consistent rotation of the shaft.

34 | P A G E

Brushed motors are subject to many of the same nomenclatures as discussed above, but

work on a different premise than their brushless equivalents. A permanent magnet surrounds a

conductor with a current flowing through it. This conductor is connected to a commutator

through a set of brushes. As current passes through the conductor, a change in the magnetic field

surrounding the conductor occurs. This interacts with the permanent magnet surrounding the

conductor, and causes the conductor to rotate. Brushed motors are inherently simpler than

brushless motors, but the brushes on the commutators tend to wear down overtime, requiring

more maintenance than a brushless motor.

It's important to be aware of the wattage, amperage, weight, and voltage ratings of

motors. The amperage rating of the speed controller must be a minimum of 20% more than that

of the motor to ensure the controller isn't destroyed by overloading.

Brushless motors are all three phase motors, and the speed controller ensures that the

correct two phases are firing at any given time. If it is desired for the motor to be turning in the

opposite direction, simply switch the connection of any two of the three wires leading from the

motor to the ESC. The direction of rotation of a DC brushed motor can be obtained by swapping

the + and – connections to the motor.

In Summary, the numeric code on the motor is used to specify its diameter, height,

number of coils, and no-load rotation speed per volt of input. Speed controllers (ESC) must be

able to handle at least 20% more current than the maximum current draw of the motor. Brushless

motors are three phase, and may have their direction switched by switching the connections of

any two of the wire motors with the ESC, whereas the rotational direction of brushed motors can

be changed by simply reversing the polarity.

35 | P A G E

Batteries

Power supplies typically come with a series of numbers that describe their performance.

Most commonly, lithium polymer batteries (LiPo) are used in RC vehicles due to their ability to

discharge power rapidly and their high charge to weight ratio.

Each cell of a LiPo battery is rated for a nominal 3.7 V. Based on the battery charge,

internal resistance, and temperature, the instantaneous voltage may be anywhere within 3 V to

4.2 V. All calculations involving voltage from the battery should be calculated using the nominal

voltage to ensure a good "average" voltage is used. Many batteries come with multiple LiPo cells

built in to them, with the number of cells denoted on the battery as "2S", or "3S" or "6S", etc.

This project utilized a 3S battery.

The mA*hr (milliamp - hour) rating is a measure of the total amount of energy stored

within the battery. Higher capacity batteries increase the longevity of the system between

charges. For example, a 2000 mAi*hr battery can draw 2 amps for one hour before running out

of electricity. Competitive robotics competitions usually last under 3 minutes, so our battery will

need to be chosen to last a minimum of 3 minutes with all weapons and motors operating at

maximum capacity. The 3S battery used for our robot had a capacity of 6000 mAh.

The next important rating is the discharge rating, which is otherwise known as the "C"

rating. This indicates the maximum safe rate that power can be drawn from the battery. Let's

assume the 2000 mA*hr battery discussed above had a discharge rating of 10 C. This means that

the battery could be discharged at a maximum amperage of 10 C*2000 mA*hr = 20000 mA = 20

Amps. Drawing current at a rate faster than this could cause severe battery damage in the form of

sparking or fire. There is usually a charge rating on the battery as well, which is usually between

1 C and 3 C. The safest charge rate for LiPo batteries is 1 C.

36 | P A G E

The internal resistance of the power supply is the amount of resistance the battery faces

when it tries to send power to the speed controller. The larger this resistance, the less power can

be expelled from the source in a usable form as electricity. It is interesting to note that the battery

still expels the same amount of energy, but at larger internal resistances, more of this energy goes

to heat. Internal resistance data is not published with batteries because it tends to change over

time, and even with temperature. It must be measured using a specific device. There is a

correlation between the discharge rating the internal resistance of the battery which implies that

as the discharge rating increases, the internal resistance decreases. To simplify the design

calculations, the internal resistance will not be considered. The robot will still be functional if it's

translational speed or weapon rotation speed changes by a few percent gradually over time.

For our purposes, the following information is critical regarding LiPo batteries:

• Significant attention to safety must be taken while charging, storing, and discharging

LiPo supplies.

• Maximum possible discharge rate is calculated as "C" rating * storage.

• Maximum amount of charge that may be stored in the battery is the mA*hr rating.

• Each cell of the battery contains a nominal 3.7 V.

The following paragraph briefly summarizes how the electronic components of our robot

operate:

A radio transmitter (AKA "Remote controller") is used to send a signal to a receiver. The

receiver is powered from the main power supply, which also powers the speed controllers and

motors. The receiver will send a pulse-width-modulated (PWM) signal to the speed controller,

which will translate the signal to variable voltage that is fed to each motor.

37 | P A G E

Motor Sizing

Drive Motors

Determining specs of the motors need to be to provide adequate acceleration and speed of

the robot was accomplished using multiple mathematical models to ensure that the finished

product achieves desirable motion. Full derivations for the models in Table 16: Linear & Non-

Linear Kinematic Models may be observed in A10: Electromechanical Model Derivations.

Figure 18: Torque - Speed Curve of DC Motor

Table 16: Linear & Non-Linear Kinematic Models

Non-Linear Model Linear Model

Cycle Time (sec) −𝑚𝑟2𝜔𝑛

′

𝑇0′ ln(0.05)

19 𝑚𝑟2𝜔𝑛′

10 𝑇0′

Translational

Speed (function of

𝑡) 𝑟𝜔𝑛

′ (1 − 𝑒−𝑡

𝑇0′

𝑚𝑟2𝜔𝑛′)

𝑇0′

2𝑚𝑟𝑡

Rotational Speed

(function of 𝑡) 𝜔𝑛′ (1 − 𝑒

−𝑡𝑇0′


𝑇0′

2𝑚𝑟2𝑡

Power

Consumption

(function of 𝑡)

𝑇0′𝜔𝑛′

𝜂(𝑒

−𝑡𝑇0′

𝑚𝑟2𝜔𝑛′− 𝑒

−𝑡2𝑇0

′


𝑇0′2

2𝜂𝑚𝑟2( 𝑡 −

𝑇0′

2𝜂𝜔𝑛𝑚𝑟2𝑡2)

Startup Cycle

Energy (J) 361

800 𝑚𝑟2𝜔𝑛

′ 2

𝜂 (

361

400)𝑚𝑟2𝜔′𝑛

2

𝜂(1 −

19

30𝜂)

Estimated

Lifespan (sec) −800𝐻𝑉𝑠𝜂 ln(0.05)

361 𝜔𝑛′𝑇0′

1600𝐻𝑉𝑠𝜂

361 𝜔𝑛′𝑇0′

38 | P A G E

It is easy to observe the differences between the non-linear and linear models in Table 16:

Linear & Non-Linear Kinematic Models. A MATLAB code was compiled to graphically

illustrate the differences between both models for cycle velocity, torque, and power

consumption. The program also provides other key metrics from Table 16: Linear & Non-Linear

Kinematic Models that will be used to assess the performance of the motors.

Running the program with input parameters from a standard household cordless drill and

power supply provides the following outputs:

***NONLINEAR ALGORITHM***

From rest to full speed, 4.14 m/s, takes approximately 0.27 seconds

Energy consumed per cycle is 259.1250 Joules

Maximum current consumption is 142.9608 Amps

A true lifespan of over 250.76 seconds or 4.18 minutes is predicted

***LINEAR APPROXIMATION***

From rest to full speed, 4.14 m/s, takes approximately 0.17 seconds

Energy consumed per cycle is -211.1389 Joules

A true lifespan of over -195.19 seconds or -3.25 minutes is predicted

39 | P A G E

Figure 19: Cycle Velocity Plot

Figure 20: Cycle Torque Plot

40 | P A G E

Figure 21: Cycle Power Consumption

Nonlinear and Linear Model Analysis

By examining Figure 19: Cycle Velocity Plot and Figure 20: Cycle Torque Plot, it is

evident that there are discrepancies between the linear and non-linear models. Through personal

experience working with DC motors, it is known that true motors do not behave particularly

linearly over their entire operating domain, and that linear approximations are best applied over a

small segment of their operating domain. The velocity and torque linear approximations do,

however, provide crude but reasonable approximations for a start up cycle from 0 to 95%

throttle.

The linear approximation does not hold well with regards to power consumption in Figure

21: Cycle Power Consumption. The inaccuracies of the torque and angular speed curves multiply,

producing a model that predicts negative power consumption for a significant portion of the

motor’s start up phase. The physical meaning of negative power consumption requires the motor

41 | P A G E

to release energy as it accelerates, which is a blatant violation of the laws of thermodynamics.

This is a fatal error of the model.

Over the first 0.04 seconds of Figure 21: Cycle Power Consumption, it is interesting that

both models predict similar shaped power consumption curves. This helps provide validity to the

non-linear model, and further enforces that the linearized model should not be used for design

purposes.

In all three figures, the non-linearized equations provide smooth, intuitive curves that

involve very few assumptions. In general, reducing the number of assumptions during the

derivation of an equation improves the accuracy of the model. For these reasons, the non-linear

equations are superior to the linear approximations, and will be used for the remainder of the

design process.

Weapon Motor Sizing

The nonlinearized equations above were derived from the conservation of energy

principle. The linearized equations were based on linear approximations of the angular

acceleration of the drive motors. As discussed immediately above, the non-linear approaches will

be used for the remainder of this report, including the sizing of the weapon motor.

Although the weapon motor will be spinning a drum and not propelling the robot, these

equations may still be used with some slight modification. It may be observed that the term

𝑚𝑟2appears frequently in these equations. It is also known that 𝑚𝑟2 is the moment of inertia for

a point mass, not a disk, rotating about an axis. By replacing this term with the mass moment of

inertia of the weapon drum 𝐼𝑑, Eq. 2-15 may be reused throughout the design phase for the

weapon motor.

42 | P A G E

Weapon Motor Design Equations

By making the substitution of 𝑚𝑟2 for 𝐼𝑑 in the nonlinear equations in Table 16: Linear & Non-

Linear Kinematic Models above, the following weapon design equations may be realized

Table 17: Weapon Design Equations

Model Description

𝑡𝑐𝑦𝑐𝑙𝑒𝑤𝑒𝑎𝑝𝑜𝑛 = −𝐼𝑑𝜔𝑛

′

𝑇0′ ln(0.05)

Time required for weapon to

accelerate to max speed, starting from

rest

𝑣𝑤𝑒𝑎𝑝𝑜𝑛(𝑡) = 𝑟𝑑𝜔𝑛′ (1 − 𝑒

−𝑡𝑇0′

𝐼𝑑𝜔𝑛′)

Maximum speed of the cutting edge of

the weapon

𝜔𝑤𝑒𝑎𝑝𝑜𝑛(𝑡) = 𝜔𝑛′ (1 − 𝑒

−𝑡𝑇0′


Maximum rotational velocity of the

weapon

𝑃𝑐𝑤𝑒𝑎𝑝𝑜𝑛(𝑡) =𝑇0′𝜔𝑛

′

𝜂(𝑒

−𝑡𝑇0′

𝐼𝑑𝜔𝑛′− 𝑒

−𝑡2𝑇0′


Instantaneous power consumed in

bringing the weapon up to speed,

starting from rest

𝐸𝑐𝑦𝑐𝑙𝑒𝑤𝑒𝑎𝑝𝑜𝑛 = (361

800)𝐼𝑑𝜔

′𝑛2

𝜂

Energy used in bringing the weapon

up to speed, starting from rest

𝑡𝑙𝑖𝑓𝑒𝑤𝑒𝑎𝑝𝑜𝑛= −

800𝐻𝑉𝑠𝜂 ln(0.05)

361 𝜔𝑛′ 𝑇0′

Estimated battery life of the weapon

(worst case scenario)

As discussed in the equipment section, there are two main types of continuous rotation

motors; brushed and brushless. Due to the high-speed nature of the weapon, it will need to be

driven by a brushless motor. Brushless motors are not only more efficient, but undergo

significantly less wear at elevated speeds due to the absence of brushes.

One of the challenges of working with brushless motors is that they are usually

manufactured for recreational users in mind. This means that they do not come with all the

published data necessary to perform an engineering design analysis; more specifically, the torque

ratings are not published.

The torque rating (stall torque) may be determined through use of the torque-speed curve

as shown in Figure 18: Torque - Speed Curve of DC Motor. Through knowledge of electric

43 | P A G E

motors and as confirmed using our own MATLAB program, maximum power consumption

occurs when the motor is operating at 50% of its maximum rated speed. Fortunately, most

brushless motors do come with the published peak power output value. Knowing the peak power,

and the speed at which it occurs to be 1

2𝜔0, the corresponding torque would be: 𝑇1/2 =

𝑃𝑟𝑎𝑡𝑒𝑑1

2𝜔0

.

Because this peak output occurs at the half-speed mark, and the torque-speed curve is linear, the

stall torque would be twice that of the peak power, such that 𝑇0 = 4𝑃𝑟𝑎𝑡𝑒𝑑/𝜔0 .

The approach of calculating the maximum torque by using the power rating 𝑃𝑟𝑎𝑡𝑒𝑑 has

not be observed elsewhere, and may be original to this report. A means of supporting the

methodology is by inserting the above equation for 𝑇0 and corresponding values into the existing

MATLAB program for motor sizing and comparing the peak power consumption to the rated

power output. The power consumption curve, which does not take into consideration the rated

power of the motor, shows that the power consumption peak calculated here is within a few

percent of the rated peak power. This strongly supports the methodology used herein.

Battery Considerations

Lifespan

It should be noted that the estimated system lifespan 𝑡𝑙𝑖𝑓𝑒 for both the weapon and drive

motor does not take into consideration that the drive motors and weapon motors will likely be

running simultaneously, meaning that the battery would need to be sized large enough to power

both weapon and drive motors simultaneously. The equations for 𝑡𝑠𝑝𝑎𝑛 above are the relative

lifespans if solely the drive or weapon motors are activated, which will not be truly

representative of a combat scenario.

44 | P A G E

An estimate of the total lifespan of the battery may be attained by dividing the energy

capacity of the battery by the summation of the quotient of cycle energies and cycle times for

each set of mothers. Expressing this mathematically looks like:

𝑡𝑆𝑦𝑠𝑡𝑒𝑚 𝐿𝑖𝑓𝑒 =𝐻𝑉𝑠

∑𝐸𝑐𝑦𝑐𝑙𝑒𝑖1

𝑡𝑐𝑦𝑐𝑙𝑒𝑖

𝑡𝑆𝑦𝑠𝑡𝑒𝑚 𝐿𝑖𝑓𝑒 =𝐻𝑉𝑠

[𝐸𝑐𝑦𝑐𝑙𝑒𝑡𝑐𝑦𝑐𝑙𝑒

]𝑑𝑟𝑖𝑣𝑒

+ [𝐸𝑐𝑦𝑐𝑙𝑒𝑡𝑐𝑦𝑐𝑙𝑒

]𝑤𝑒𝑎𝑝𝑜𝑛

Electrical Current Availability

Up until now, there has been no discussion of the ability of the power supply to provide

adequate current. The power supply acts as a voltage source, meaning that the voltage delivered

to the system by the battery will consistently be the source’s nominal voltage rating. The current,

however, will vary as the motors’ electromotive resistances are altered with throttle position and

motor response during operation.

The maximum safe discharge rate of power supplies may be determined by multiplying

the supply’s discharge rating by its storage capacity. This discharge rate will be the highest

possible amperage that the battery can release without risking permanent damage to the battery.

To avoid battery damage and ensure the robot performs as anticipated, the maximum

amperage draw of both the propulsion and weapon motors must be determined. Conveniently,

the power consumption curves for both the drive and weapon motors (Eq. 13 and 29) can be

graphed as in figure 4, allowing the peak power consumption to be determined for each set of

motors. Dividing this peak power by the power supply voltage 𝑉𝑠 will provide an estimate to the

maximum current drawn by the motors.

45 | P A G E

The drive motors and weapon motors will be wired in parallel, meaning that the sum of

currents drawn from each motor will represent the total maximum current draw to be compared

with the maximum allowable discharge rate of the battery. The maximum allowable discharge

rate should be at least 20% higher than the anticipated peak current draw rate.

Taking the derivative of the power consumption curve, setting it equal to zero, solving,

and back-substituting the result into the power consumption equation would be an acceptable

means of accomplishing this. However, due to the highly non-linear power consumption

equations, numerical methods will be employed to determine the maximum of these curves.

Operation, Maintenance, Service and Disposal

Safety Warnings

Li-Po batteries can explode or catch fire. Whenever a Li-Po battery is charging, or not in

use, it should be in a fire-safe bag. Weapon safeties should be in place unless the robot is in an

intrinsically safe area, like an arena. The robot is never to be operated near people. Safe power-

up and power-down procedures are described later.

Robot Operation

Robot Assembly Procedure

From the fully disassembled state, the robot can be mechanically assembled by the following

procedure:

1. Drive Train

a. Screw in the gearmotors through the bottom of the frame.

b. Slide the wheel collars onto the gearmotor shaft and tighten set screws.

c. Slide wheels onto collars.

d. Use snap-ring tool to attach snap ring on wheel collar, in front of wheel.

e. Tighten retaining screw and washers into end of gearmotor shaft.

46 | P A G E

2. Weapon

a. Insert the brushless motor into the one-piece motor mount.

b. Lightly bolt the motor mount to the frame.

c. Grease the weapon and weapon shaft.

d. Insert the weapon shaft (flat side first) through the side of the robot and through

the first shaft mount.

e. Place Belleville washers on shaft.

f. Wrap the V-belt around weapon sheave and line up the other side of the weapon

with the weapon shaft.

g. Slide shaft through weapon.

h. Place Belleville washers between weapon and the second shaft mount.

i. Ensure alignment of shaft flats with the second shaft mount and insert the shaft.

Use of a hammer may be necessary.

j. Line up the end of the shaft with the end of the second shaft mount.

k. Insert and tighten shaft set screws.

l. Place motor sheave on motor shaft and tighten set screw.

m. Wrap V-belt around motor sheave.

n. Align motor mount so that sheaves and belt are properly aligned.

o. Pull motor mount backwards to put a small amount of tension on the belt.

p. Fully tighten motor mount

3. Screw casters into place.

4. Wheel guard and wedge.

a. Place wheel guard around robot.

47 | P A G E

b. Insert bolts through wheel guard and frame, 2 on each side at the front of the

robot, and tighten nuts.

c. Place wedge at back of robot, and insert 4 bolts through the inside of the robot,

through the frame, wheel guard and wedge.

d. Place nuts on bolts on the interior of the wedge. Tighten each nut.

e. Examine the ground clearance of the wedge. Tighten bottom bolts to decrease

clearance, tighten top bolts to increase clearance. This is due to a “spring” effect

between the 3 clamped layers.

5. Electrical components.

a. Place drive ESC in frame and tighten bolts and nuts.

b. Place battery, weapon ESC on the Velcro inside the robot.

c. Connect the motors, battery, ESC’s, receiver, light, battery eliminator circuit, and

manual switch according to the electrical diagram.

d. Mount the wires (using tape, adhesives, zip-ties) to avoid the motors and moving

components.

e. Secure light and manual switch to frame using adhesives.

6. Dust cover.

a. Place dust cover on top of robot, ensuring that wires maintain their location and

are not clamped between the dust cover and other components.

b. Insert 6 bolts through frame and dust cover and tighten nuts.

7. Place adhesive (such as JB Weld SteelStik®, thread locker, or Super Glue ®) onto

exterior bolts.

Safe Start-Up Procedure

1. In an intrinsically safe area, such as an arena, flip the manual switch to the “on” position.

48 | P A G E

2. Remove weapon safeties.

3. Exit arena.

4. Turn on transmitter.

5. Test controls.

Controlling the robot

The left joystick controls the throttle of the weapon motor, allowing the weapon to spin

up. This throttle should be moved very gently, as quick motions have the potential to cause over-

heating in the weapon ESC. The right joystick controls the drive, with front/back and left/right

control. Control of the drive is not limited; going from full throttle in one direction to full throttle

in the other direction does not cause any electrical issues. There may be traction issues as the

wheels tend to slip under high speed and acceleration.

The internal components of the robot reach high temperatures during operation. This may

affect the operation of several components, and for this reason it is not recommended to use high

throttles for long periods of time.

The robot has a limited battery life (although much longer than the competition

maximum of 3 minutes). When the battery is approaching the end of its charge, the drive system

will slow down as the voltage to the motors decreases. The ESCs utilized in this project have

automatic cut-offs when the battery voltage drops to a certain, low amount. Robot operation

should be stopped to avoid completely consuming the battery charge, which may damage the

battery.

Safe Shut-Down Procedure

1. Turn off transmitter, and ensure robot motion has ceased.

2. Enter arena.

49 | P A G E

3. Flip manual switch to the “off” position.

4. Insert weapon safeties.

The robot will reach high temperatures during operation. Caution must be exercised when

opening the robot and performing repairs.

Maintenance

The robot has only received limited use, so the following maintenance issues are based

on the wear and tear experienced during the project.

The shaft and weapon should be greased whenever practical. Slight wear is already

visible on the shaft at the location of the bushings. Consistently greasing the shaft and bushings

should prolong their life.

The bushings (located inside the weapon) and shaft should be inspected periodically.

Scratches, indentations or discolouring of the shaft could indicate the bushings are reaching the

end of their life and need replacement.

The V-Belt will likely need to be replaced after several matches. Belt wear was expected

to be much higher than experienced. The belt should be examined for heat and wear damage

after every match, and changed if significant changes in shape, texture, or colour are found.

The wheels will experience gradual wear in regular operation and should be considered a

replaceable, rather than permanent, component.

Casters will also experience wear. Dust and metal shavings are likely to get inside the

caster and quickly ruin its internal rolling elements. If the rolling resistance of the caster

dramatically increases, it should be replaced.

50 | P A G E

Bolts and nuts will become damaged due to impacts, and will wear out as the threads are

tightened and loosened during assembly. If bolts or nuts become difficult to thread, they should

be replaced.

A significant part of combat robotics competitions is the maintenance and repair that is

performed in “the pits” between matches. Due to financial constraints, it was not possible to have

a full set of spare parts. It was also not possible to have every tool that may have been useful. In

general, spares of inexpensive parts were procured and common hand and power tools were

brought to the competition.

Spare parts brought (in addition to parts on robot):

• 2 wheels and wheel hubs

• 4 belts

• 2 bushings

• Belleville washers

• Several packages of bolts, nuts and washers

• Various set screws

• 2 motor sheaves

• Motor mounts and motor spacers

• Velcro

• Wires

• Connectors

• Battery

• Super glue

51 | P A G E

• JB Weld SteelStik

Tools brought:

• Grinder + disks

• Dremel + heads

• Metal file

• Soldering iron + solder

• Drill + bits

• 2 battery chargers

• Wrenches

• Pliers

• Hammer

• Screwdrivers

• Snap ring tool

• Allen keys

Costs and Bill of Materials The bill of materials (BOM) was created with several sections, with the first section

showing the cost of building the final design. The second section is for parts purchased but not

used in the final design. The third section is the travel costs of attending the competition. Most

values include extra costs like duties, fees, shipping and currency conversion.

A reasonable effort was made to estimate the value of donated material and time,

although these values may not be accurate.

52 | P A G E

Combat Robot

Part Count : 33

Design Cost : $1,717.03

Additional Costs: $156.54

Travel Costs: $651.46

Total Cost: $2,525.03

Part # Part Category Part Name Qty Supplier Unit Cost Actual Cost Estimated Donated Value

1 Frame Frame 1Rudinicki Industrial,

Jet Welding and

Ornamental

Ironworks

200.00$

2 Frame Wheel Guard 1

Lakehead University

Steel Bridge Team

40.00$

3 Frame Wedge 1

Lakehead University

Steel Bridge Team

80.00$

4 Weapon Weapon 1Rudinicki Industrial,

Lakehead University

Machine Shop

40.00$ 180.00$

5 Mechanical Shaft,

Linear Shaft SFJ18-200-

SC01 Misumi

35.50$ 35.50$

6 Mechanical Bushings,

Oil Free Bushing

MDZB18-254 Misumi

10.26$ 41.04$

7 Mechanical Belleville Washers,

Disc Spring MDS18-2

4 Misumi

2.46$ 9.84$

8 Mechanical Weapon Shaft Set

Screws

2

Lakehead University

Machine Shop

1.00$

9 Mechanical Motor Sheaves, V-Belt

Pulley: 3L/4L/A Belt

Section Size, For 3L-

Section & A-Section (4L,

A & AX), 1/2 in Bore

Dia, Solid, 1 1/2 in OD

2 Gamut

12.61$ 25.22$

10 Mechanical V Belts, Single V-Belt:

Inch, 3L Belt, 3L120

Industry, 12 in Outside

Lg, 1 1/2 in Min Pulley

Dia, 3/8 in Top Wd 5 Gamut

9.22$ 46.10$

11 Mechanical Machined Motor Sheave

1

Lakehead University

Machine Shop

20.00$

12 Mechanical Wheels 4 Bane Bots 7.33$ 29.32$

13 Mechanical Wheel Hubs, Set

Screws, Snap Rings 4 Bane Bots

7.33$ 29.32$

14 Mechanical Bolts Maier Hardware,

Canadian Tire

10.00$ 4.00$

15 Mechanical Nuts Maier Hardware,

Canadian Tire

5.00$ 2.00$

16 Mechanical Washers Canadian Tire 5.00$

17 Mechanical 3D Printed Parts Lakehead University

Makerspace

5.00$

18 Electrical Brushless Motor 1 1 Turnigy / HobbyKing 89.87$ 89.87$

53 | P A G E

Figure 22: Bill of Materials

Validation and Compliance The operation of the robot was validated through several tests, and of course, the

competition. It was difficult to gather reliable data on robot performance, although several

attempts were made. The pre-competition tests are listed below:

19 Electrical Weapon Electronic

Speed Controller 1

101.19$ 101.19$

20 Electrical PDX Gearmotors

2

Bane Bots /

Robot Marketplace

117.79$ 235.57$

21 Electrical Drive Electronic Speed

Controller 1

Sabertooth /

Robot Marketplace

175.40$ 175.40$

22 Electrical Li-Po Battery, 11.1V

6000mAh 1 Amazon

59.99$ 59.99$

23 Electrical Good Li-Po Charger 1 Amazon 25.00$

24 Electrical Li-Po Safe Bag Amazon 9.99$

25 Electrical Wiring 5.98$

26 Electrical Battery Eliminator

Circuit

24.84$

27 Electrical RC Transmitter and

Reciever Amazon

90.38$

28 Electrical Connectors 6.20$

29 Electrical Solder 9.03$

30 Misc. Packaging Michael's 20.09$

31 Misc. JB Weld, JB Weld Steel

Stik, Snap Ring Pliars Home Depot

40.00$

32 Misc. Grease Canadian Bearings 5.00$

33 Misc. Transmitter Batteries 10.16$

1,185.03$ 532.00$

THINGS THAT WERE BOUGHT BUT NOT IN FINAL DESIGN

34 Mechanical 3D Printed Parts Lakehead University

Makerspace

20.00$

35 Mechanical Motor Mounts 2 Home Depot 3.80$ 7.60$

36 Mechanical 3L Vbelt 1 Northern Turf Equipment 22.18$ 22.18$

37 Electrical Extra Brushless Motor 1 Shop in Urbana/Champagne 40.00$

38 Electrical 2nd Li-Po 1 Amazon 50.00$

39 Electrical Cheap Battery Charger 1 Amazon 16.76$ 16.76$

156.54$

EVENT COSTS

40 Accomodation 301.46$

41 Fuel 150.00$

42 Food 200.00$

651.46$

Total

Actual Cost

Total

Estimated Donated Value

1,993.03$ 532.00$

Total Project Cost

2,525.03$

54 | P A G E

Table 18 Pre-Competition Tests

Test Date Location Results

Propulsion Test #1 March 3rd CB Hallway Slow movement, high

slip, difficult control.

Propulsion Test #2 March 6th North End Community

Centre

Faster movement, lower

slip, improved control.

Possible max speed of 4

m/s (14.4 km/h)

Weapon Test #1 March 7th LU Makerspace Weapon speed of 18650

RPM, minor vibrations.

Weapon stopped within

60s of cutting power.

Weigh-in March 7th LU Print Shop 26.95 lb

Combined Propulsion

and Weapon Test

March 7th Bora Laskin Gymnasium Weapon and Drive

functional

simultaneously. No

gyroscopic tipping at low

speeds

The weapon speed was measured using a photo tachometer and reflective marker, giving a

rotational velocity of over 18650 RPM. In this test, the weapon likely had not yet reached

maximum speed. The max linear speed was measured using an acceleration logging smart phone

app, and processing data in MATLAB. It is possible that the robot achieved a max speed of

about 4 m/s (14.4 km/h), meaning that the theoretical non-linear speed model predicted the same

maximum speed as that achieved in testing. This data is available in Appendix A13: Acceleration

Data Analysis

The design was manufactured with some minor difficulties. Some of the issues were noticed

during manufacturing, or in testing. Manufacturing issues include:

55 | P A G E

• Not all mounting holes were included in the original design. These had to be added

manually, with low precision compared to the laser cutter.

• The original motor sheaves were off the shelf, unbalanced, and relied on a 3D printed

insert. After testing, this component was changed to a custom machined sheave.

• There was significant centre of gravity issues after the first build. The weapon was so

heavy that the rear driven wheels did not have traction. The wheel guards and rear wedge

were partially added to solve centre of gravity issues.

• No mount was designed for the manual switch. It was fixed in place using adhesives.

There were some minor safety issues that were discovered during testing and competition:

• Bolts can become loose due to vibrations caused by the weapon system. This was solved

by applying adhesives to bolts.

• The first adhesive applied to secure the manual switch was superglue, which did not

withstand the forces of regular competition. This was remedied by using a much stronger

adhesive (JB Weld SteelStik).

Some issues affecting usability were also discovered:

• Steering of the robot was not reliable. At high acceleration/speed there was a significant

difference in slip rates between the two driving wheels, causing the robot to turn or spin

when trying to drive forward. This was partially solved by applying different signal gains

to the wheels, increasing the signal to the wheel experiencing higher slip.

• The weapon motor would stall if too much current was passed through the speed

controller. The weapon throttle would have to be increased very slowly to prevent

stalling. Eventually, the weapon ESC was damaged and became unusable. This can be

56 | P A G E

remedied by using higher quality (and expensive) weapon ESCs, and a higher voltage

battery coupled with a geared transmission system for the weapon.

After the competition, the robot had sustained some minor damage including:

• A small chip out of the corner of the weapon tooth.

• Small grind marks against the wedge, wheel guards and front aluminum welds.

Competition The RoboBrawl Combat Robotics Tournament is an annual varsity robotics competition hosted

by the University of Illinois in the city of Champaign, Illinois, USA, and was hosted March 9th-

10th , 2018. The Lakehead University team departed Thunder Bay around 6 AM on March 8th to

arrive in Champaign at 8 PM, EST. The remainder of the night was spent unpacking and picking

up last-minute supplies from a local Amazon ® pickup.

The following morning was spent checking the robot’s control systems and re-programming the

speed controllers during the commute to the event. The team paid the safety deposit upon

arriving and setup their workstation in the “pits”. The team then did elementary system checks in

the “safe-spin up” area, and the robot appeared to be fully functional.

Upon commencing the match against Absaluki (a robot put forth by a sophomore team from

Southern Illinois State University), it was clear that a connection inside the bot wasn’t fully

operating. The Revolver wasn’t fully responsive to user inputs, and received cosmetic damage by

Absaluki in the arena until the connection was knocked back in place; allowing The Revolver to

regain its control. While attempting to power up the weapon to full speed, it appeared to stop

accelerating once it reached approximately 200 RPM. With the weapon not fully functional, The

Revolver was repeatedly positioned its weapon directly impacting the auger-style weapon of

57 | P A G E

Absaluki. This appeared to cause minor damage to Absaluki, but failed to incapacitate the

opponent. Attempts to flip Absaluki using The Revolver’s wedge also failed. After both robots

had survived the maximum allotted time of 3 minutes in the arena, the match was ended and the

judges conferred, with Absaluki being declared the winner. The double-elimination style of the

tournament states that a robot is eliminated from the tournament after it loses two matches; The

Revolver still had a chance to place well in the competition.

After the match, the team re-soldered the fragile connection, and began to troubleshoot the

weapon speed issue. It was determined that the weapon had to be accelerated up to speed very

slowly to avoid current/thermal overload to the weapon speed controller. The team planned to

use this technique in its second match.

The second match, against a robot called Space Jam, was abruptly won by Lakehead University

when Space Jam forfeited the match mere seconds after it commenced. Electrical failures

plagued many teams and prevented multiple schools from participating in their allotted matches.

With no damage to repair, Lakehead University’s team awaited its final match against Wall-F,

from the University of Illinois. Wall-F was a flipper-style robot, and did not feature a rotating

weapon. Immediately after the match began, Wall-F charged The Revolver and lifted it about 6

inches off the floor, held onto it for 27 seconds, and then dropped The Revolver outside of the

arena; winning the match in a technical knock-out, and eliminating The Revolver from the

competition.

The Lakehead team then commuted back to the Airbnb®. To resolve the weapon speed issue, the

team stayed up late into the night to rewire the robot with a second battery in efforts to double

the voltage delivered to the robot (increasing to a nominal voltage of 22.2 V). When this new

configuration was tested, all systems of the robot appeared to be receiving power, indicating that

58 | P A G E

the electrical rewiring had been a success. When making a first attempt to spin the weapon up to

speed, the weapon made several rotations before the ESC began spewing heavy smoke and failed

to operate. The robot was then rewired to the original 11.1 V DC configuration, and the team

ceased operations for the night.

The following morning, the team made attempts to improve the drive control before driving back

to the competition. The remainder of the day was spent in exhibition matches and speaking with

other teams to try and determine a solution to the weapon problem. After purchasing another

motor and being donated a spare ESC, it was found that there was no easy solution to this

problem. The two exhibition matches against Botcepts and Absaluki were both won by The

Revolver in a technical knock-out.

The team then packed up it’s area, spectated a separate robotics tournament occurring on

campus, and had dinner with the team from Southern Illinois State University. The following

morning, the Lakehead Team packed up and drove back to Thunder Bay.

The Revolver was impressive to all competitors, especially those who were unaware of what to

expect from RoboBrawl’s first ever entry from a Canadian university (making RoboBrawl 2018

an international competition). It was determined on the drive back that the small size of the

weapon sheave was to blame for the consistent overheating of the ESCs. The small-diameter

sheave on the weapon was designed to achieve high-speed. However, the high torque required to

get the weapon up to speed would stall the weapon motor, resulting in huge current draws that

were damaging to the weapon ESC. A higher-torque design (accomplished using a gearbox,

different sized sheaves, etc) would resolve this critical issue for future teams.

59 | P A G E

Conclusions This robot performed well in competition and won three matches. Many technical challenges

were solved to produce a working product. The combination of a robust drive system, high power

weapon, and a passive weapon proved useful. This design could make an excellent combat robot with a

few minor improvements.

Although the performance of the robot was hard to quantify due to time constraints, the weapon

achieved a speed of 18650 RPM during a weapon test. This is close to the no-load output of 21 000 RPM,

and even closer to the assumed maximum speed of 19950 RPM. Performance could likely be improved if

further testing was performed.

The design used resources effectively by using scrap and donated material, and choosing pre-

engineered solutions (such as the gearmotors) where possible. The robot was fully manufactured, proving

that the design (with minor modifications) is manufacturable and operable. Drawings and calculations

have not been re-done for the as-built robot, but this task would only require minor changes to layouts and

component specifications. Due to the custom, individualized nature of the robot, mass-manufacturing has

not been considered.

There were great benefits to doing this project as a student team affiliated with Lakehead

University. This helped the team receive donations of materials and time, which would likely have to be

paid for if competing as an unaffiliated team. Access to manufacturing tools in LU’s machine shop and

makerspace also greatly reduced cost.

In the future, the robot will require some maintenance to components like belts and bushings.

Over time, the battery will degrade and will require replacement.

Recommendations for Future Teams This team has solved several problems in combat robotics design, manufacture and

administration. Even though much has been accomplished, this team acknowledges areas for

60 | P A G E

improvement. The following section provides project management advice, improvements to the

design/analysis process, and specific technical recommendations for future combat robotics teams.

Project Management One of the hard constraints in this project is available funds. Seeking monetary sponsorships and

establishing a budget early during the project will make design decisions easier. A higher budget will

allow the team to design and purchase high-quality materials and components. It is recommended that the

next team request sponsorships from personal contacts, local companies as well as non-local and robotics

related companies.

Managing robot weight is also important. The current team had a large amount of the weight

budget left (approximately 3 lbs) to solve remaining technical problems near the end of the manufacturing

phase. To ensure that the weight limit is met, it is recommended to carefully track the weight of all

components as they are specified/procured. By knowing what components can be made lighter, and where

extra weight might be used to improve the design, the burden of design optimization can be reduced.

Procurement Many specifications for off-the-shelf components were not openly available. Additional

specifications can be found by contacting manufacturers. Custom manufacturing is an option but can

increase costs.

Low-cost suppliers should generally be avoided. There are many parts available online that

promise good specifications at a great price, and this is typically a sign that the quality of these

components is low. Parts from Canadian, American and Japanese companies were generally of higher

quality than those from China and Taiwan.

Canadian manufacturers may not make all required components, and international shipping can

be prohibitively expensive. Shipping components made by US companies to a nearby US location

(Ryden’s Border Store) and picking them up was economical, as the number of trips was minimized.

61 | P A G E

Testing It was not possible to perform a large number of tests due to time constraints in this project.

Components and subsystems could be tested in controlled conditions to gather information on the

performance of various components. Test data may be more reliable and usable than manufacturer data or

applying theoretical relationships. This team focussed on theoretical solutions due to budget and time

constraints.

Some test information that may help improve the design include:

• Maximum acceleration and speed

• Maximum power consumption of motors

• Waste heat generated by motors, belt, and bushings

• Bushing and belt life under high speed conditions

• Rotational velocities and accelerations for drive systems

• Maximum temperatures reached in operation

• Impact forces / impact energy

• Reliability of components under shock loading

Collecting test data such as this will also allow future teams to quantify their performance and allow

for year to year improvements in designs at Lakehead University.

Competition It is very important to be prepared for the competition. The current group brought many tools and

extra supplies to prepare for unknown events. It is important to be skilled at taking apart and rebuilding

the robot especially if later stages of the competition are reached, where repair time becomes a limiting

factor.

Other teams are generally sportsman-like, but this cannot be expected. There is a chance that the

robot will be destroyed during competition, and the team should be prepared for this possibility.

62 | P A G E

Design of Weapon Weapon geometry can be improved in two major ways: increasing radius of the weapon, and

using an unsymmetrical tooth design. A larger radius will give the weapon higher energy for a given

rotational velocity. A single tooth design would allow the weapon to make contact once per revolution, at

a deeper depth compared to the two-tooth design. This unsymmetrical design would have to be carefully

designed and manufactured to maintain rotational balance.

Increasing the rotational inertia of the weapon increases the energy that the weapon can output in

competition. The weapon could be designed using multiple materials. By using a light material in the

inner portion of the weapon, and a dense material on the outer portion, a much higher rotational inertia

could be achieved within the same weight and size.

Rotating stresses were approximated in this design by performing FEA to determine rotating

stresses. By modelling the weapon as a rotating body with two sources of stress (rotating stress and

impact stress simultaneously) accuracy can be greatly improved.

Weapon Drive Design The weapon drive (motor sheave, belt, weapon sheave, bushings and shaft) could be improved.

Many design procedures will not apply to combat robot design, due to the high intensity applications and

“random” impacts, each varying in severity. It is recommended that the next team investigate using a flat

or timing belt design. V-Belts are difficult to tension and are potentially much stronger than necessary.

A larger weapon sheave will reduce the start-up torque needed by the motor. Other options to

improve weapon drive design include using multiple motors, multiple belts and adding a belt tensioner.

Frame Design Aluminum was used for the frame/armor of this design, due to availability and weight. Aluminum

welds are especially brittle, and should be avoided. In future designs titanium would be a technically

superior choice, although cost and machinability are downsides. Steel and steel alloys would also be an

improvement.

63 | P A G E

The frame could also be manufactured differently. Using a block of metal and a CNC machine,

very customized geometry could be achieved; improving strength and the internal layout of components.

Gyroscopic Effect Gyroscopic tipping could be mitigated in several ways. Although it did not prove to be an issue,

the robot was not tested extensively at high speed while driving.

By using a cross belt drive, weapon and motor sheaves will be rotating in opposite directions;

slightly reducing the net gyroscopic moment. It is possible that the gyroscopic moment could be

completely counteracted by using another weapon, or an internally rotating body which rotate in the

opposite direction from the original weapon.

Limiting the rotational velocity of the robot so that the “tip factor” of the robot is always less than

1 could eliminate the issue. This could be accomplished by setting the maximum difference in drive

motor speeds (hence the rotational velocity of the robot), as a function of weapon speed, although this

requires extensive programming and microcontroller knowledge. This approach is likely to provide the

best balance between the competing goals of manoeuverability and high weapon speed.

Temperature The internal components of the robot reached high temperatures, which may be able to cause

damage. It may be difficult to improve the efficiency (and therefore heat generation) of the electrical

design, but there are several ways to improve heat rejection within the robot. One way is by putting holes

or slots in the frame/armor, allowing more convection as the robot drives and the weapon rotates. An

auxiliary fan could be added, forcing convection over the hot internal components. These solutions have

obvious disadvantages of reducing strength and increasing power consumption

An innovative solution could involve machining custom sheaves or weapon with a fanned design,

forcing convection over components while delivering power to the weapon. In addition, fins could be

added to internal components, increasing the area available for heat transfer.

64 | P A G E

Bibliography

[1] N. Budynas, Shigley's Mechanical Engineering Design (10th Edition), New York: McGraw Hill

Eduction, 2015.

[2] A. P. Boresi, Advanced Mechanics of Materials, John Wiley & Sons, 2003.

[3] Calculation of V-Belt Tensions and Shaft Loads, Mechanical Power Transmission Association, 2013,

http://mpta.org/wp-content/uploads/2016/05/MPTA-B7i-2013.pdf

[4] Engineering ToolBox, (2004). Friction and Friction Coefficients. [online]

https://www.engineeringtoolbox.com/friction-coefficients-d_778.html

[5] [Churchill and chu, Churchill, Stuart W.; Chu, Humbert H.S. (November 1975). "Correlating

equations for laminar and turbulent free convection from a vertical plate". International Journal of Heat

and Mass Transfer. 18 (11): 1323–1329. doi:10.1016/0017-9310(75)90243-4. Retrieved 18

September 2015.]

[6] Engineering ToolBox, (2005). Dry Air Properties. [online] Available at:

https://www.engineeringtoolbox.com/dry-air-properties-d_973.html [Accessed 12 December 2018]

[7] Cairo University Faculty of Engineering. MPE 635: Electronics Cooling: 9. Forced Convection

Correlations. http://www.pathways.cu.edu.eg/ec/Text-PDF/Part%20B-9.pdf

[8] M. Meggiolaro, RioBotz Combot Tutorial, (2009). [Online PDF]. www.riobotz.com.br

[9] The Robot Marketplace (2018). PDX16 – 16:1 Gearmotor.

http://www.robotmarketplace.com/products/0-pdx16.html

[10] Lakehead University. Department of Mechanical Engineering, ENGI 4969 – Degree Project. Last

updated March 2012.

[11]Tor Shephard (2018). Combatics RoboBrawl 2018. Web, Retrieved 1 January 2018.

http://irobotics.illinois.edu/teams/robobrawl/

http://mpta.org/wp-content/uploads/2016/05/MPTA-B7i-2013.pdf

http://www.sciencedirect.com/science/article/pii/0017931075902434

http://www.sciencedirect.com/science/article/pii/0017931075902434

https://en.wikipedia.org/wiki/Digital_object_identifier

https://doi.org/10.1016%2F0017-9310%2875%2990243-4

http://www.pathways.cu.edu.eg/ec/Text-PDF/Part%20B-9.pdf

http://www.riobotz.com.br/

http://www.robotmarketplace.com/products/0-pdx16.html

65 | P A G E

Appendices

A1: Weapon Shaft Design

The maximum force on the shaft (exerted by its own weapon) can be estimated knowing

the drum radius to be 45 mm, and by using a few conservative assumptions:

• The weapon rotates with peak rotational kinetic energy of 10 𝑘𝐽.

• The angle of impact against a competing bot is 45 degrees.

• The weapon stops rotating completely within 1/8th of a rotation.

Figure 23: Shaft Force Analysis

In this scenario, 𝐹𝐴 represents the force applied to the weapon, and 𝐹𝑅 represents the

resultant force on the shaft. Using the definition of work 𝐸 = 𝐹𝑑, where 𝐸 is energy, and 𝑑 is the

distance over which the force is applied, the force 𝐹 may be determined as:

𝐹 =𝐸

𝑑=𝐸 cos(𝜃)

2𝜋𝑟8

=10 𝑘𝐽 ∗ 𝑐𝑜𝑠45

2𝜋 ∗ 0.045 𝑚8

≅ 200 𝑘𝑁

Because of symmetry along the weapon shaft, and assuming this 200 𝑘𝑁 load occurs at

the midway point between the two supports, the dynamic loading at each support would be

66 | P A G E

100 𝑘𝑁. Using the tensile strength 𝑆𝑢𝑡 = 2015 𝑀𝑃𝑎 for of 52100 Bearing steel [1] and making

the conservative approximation that shear strength as ½ of yield strength (maximum shear stress

theory), and that the shaft is a solid cylinder:

𝜏𝑚𝑎𝑥 =4𝑉

3𝐴=4𝑉

3𝜋𝑟2∴ 𝑟𝑚𝑖𝑛 = √

4𝑉

3𝜋𝜏𝑚𝑎𝑥= √

4 ∗ 100 𝑘𝑁

3𝜋 ∗2015 𝑀𝑃𝑎

2

= 6.49 𝑚𝑚

A2: Belt Centre to Centre Distance and Tension

The selected weapon motor will output a maximum of 1665 W or 2.23 HP. This

maximum power will only be transmitted for a short period of time during acceleration. The

average power over 1 acceleration cycle is 13862 𝐽 13.82 𝑠⁄ = 1003 𝑊 or 1.34 𝐻𝑃, where

13.82 seconds is the spin-up time for the weapon. Although the maximum and average power

exceeds the rated power of the belt, this is justified due to the short-expected lifespan.

𝐿𝑖𝑛𝑒𝑎𝑟 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 𝜔𝑟 = (2200 𝑟𝑎𝑑 𝑠⁄ ) ∗ 0.75 𝑖𝑛 ∗ (1 𝑓𝑡

12 𝑖𝑛) ∗ (

60 𝑠

min) = 8250 𝑓𝑡/𝑚𝑖𝑛

𝐶𝑒𝑛𝑡𝑟𝑒 − 𝑡𝑜 − 𝐶𝑒𝑛𝑡𝑟𝑒 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 =𝐿 − 𝜋𝑑

2=12 𝑖𝑛 − 𝜋 ∗ 1.5 𝑖𝑛

2= 3.64 𝑖𝑛

Required Belt tension

𝑇𝑠𝑡(𝑙𝑏) = 15 (2.5 − 𝐾𝜃𝐾𝜃

) (𝑃𝑑10

3

𝑁𝑏𝑉) + [0.9 𝑊 (

𝑉

60)2

(1

𝑔𝑐)] = 31.68 𝑙𝑏𝑓 = 140.1 𝑁

Where;

𝑃𝑑 = 𝐷𝑒𝑠𝑖𝑔𝑛 𝑃𝑜𝑤𝑒𝑟 = 2.32 𝐻𝑃,

𝑊 = 𝐵𝑒𝑙𝑡 𝑊𝑒𝑖𝑔ℎ𝑡 𝑝𝑒𝑟 𝐹𝑜𝑜𝑡 𝑜𝑓 𝐿𝑒𝑛𝑔𝑡ℎ = 0.04 𝑙𝑏/𝑓𝑡

𝑉 = 𝐵𝑒𝑙𝑡 𝑆𝑝𝑒𝑒𝑑 = 8250 𝑓𝑡/𝑚𝑖𝑛

67 | P A G E

𝑔𝑐 = 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑑𝑢𝑒 𝑡𝑜 𝐺𝑟𝑎𝑣𝑖𝑡𝑦 = 32.2 𝑓𝑡/𝑠2,

𝑁𝑏 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐵𝑒𝑙𝑡𝑠 = 1

𝐾𝜃 = 𝐴𝑟𝑐 − 𝑜𝑓 − 𝐶𝑜𝑛𝑡𝑎𝑐𝑡 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝐹𝑎𝑐𝑡𝑜𝑟 = 0

A3: Bushing Design

This bushing will travel at 𝑉 = 𝑟𝜔 = 9 𝑚𝑚 ∗ 2200 𝑟𝑎𝑑 s⁄ = 19.8 𝑚 𝑠⁄ . The pressure

on the bushing is calculated over the projected internal area, considering both the belt tension

and the weight of the drum.

𝐹 = √140.12 + (9.81 ∗ 4)2 = 145.5 𝑁

Assuming a bearing length of 20mm,

𝑃 =𝐹

𝐴=

145.5𝑁

0.02𝑚 ∗ 0.018𝑚= 0.40 𝑀𝑃𝑎

giving a combined rating of 𝑃𝑉 = 7.92 𝑀𝑃𝑎 ∗ 𝑚/𝑠.

A4: Gyroscopic Force Analysis

Due to very high weapon and robot rotation speeds, there was a risk that the robot will tip

over due to a gyroscopic moment. A gyroscopic moment occurs when a body is rotating about a

shaft, and the shaft is rotating in a perpendicular direction. The formula for a gyroscopic moment

(G) is:

𝐺 = 𝐼𝑑𝜔𝑊𝜔𝐵

𝐼𝑑 = 𝑀𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝑖𝑛𝑒𝑟𝑡𝑖𝑎 𝑜𝑓 𝑟𝑜𝑡𝑎𝑡𝑖𝑛𝑔 𝑏𝑜𝑑𝑦 (𝑊𝑒𝑎𝑝𝑜𝑛)

𝜔𝑊 = 𝑅𝑜𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑟𝑜𝑡𝑎𝑡𝑖𝑛𝑔 𝑏𝑜𝑑𝑦 (𝑊𝑒𝑎𝑝𝑜𝑛)

𝜔𝑅 = 𝑅𝑜𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑠ℎ𝑎𝑓𝑡 (𝑅𝑜𝑏𝑜𝑡)

68 | P A G E

Counteracting the gyroscopic moment is the moment of the robot’s mass, about the edge

of the robot’s wheels. This moment is:

𝑀 =𝑚𝑔𝑙

2

𝑙 = 𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑟𝑜𝑏𝑜𝑡 (𝑖𝑛 𝑡ℎ𝑒 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑠ℎ𝑎𝑓𝑡)

Figure 24: Gyroscopic Forces

If the Gyroscopic moment exceeds the moment of the robot’s mass, then there will be an

angular acceleration, causing the robot to begin tipping.

𝐼𝑓𝐺

𝑀=2𝐼𝑑𝜔𝑊𝜔𝐵𝑚𝑔𝑙

> 1, 𝑟𝑜𝑏𝑜𝑡 𝑤𝑖𝑙𝑙 𝑡𝑖𝑝

Once tipping has begun the moment of the mass will decrease as the angle θ increases.

With other variables held constant, once tipping has initiated, the robot will completely flip over.

𝜔𝐵 = 2 ∗𝑚𝑎𝑥 𝑤ℎ𝑒𝑒𝑙 𝑠𝑝𝑒𝑒𝑑

𝑟𝑎𝑑𝑖𝑢𝑠=2 ∗ 4.14

𝑚𝑠

0.115 𝑚= 72 𝑟𝑎𝑑/𝑠

Based on theoretical values,

𝐺

𝑀=2 ∗ (0.004783

𝑘𝑔𝑚2) ∗ 2200

𝑟𝑎𝑑𝑠 ∗ 72

𝑟𝑎𝑑𝑠

13.6 𝑘𝑔 ∗ 9.81 𝑚𝑠2∗ (0.23) 𝑚

= 49.38 > 1

69 | P A G E

This analysis means that if the robot and weapon were to rotate at their maximum speed, it

will tip over. This can be mitigated by a few different methods.

1) Limit rotational speed of weapon

2) Limit rotational speed of the robot

3) Very carefully control robot during competition

The effectiveness of method 3 depends on the driver reaction time.

A5: Heat Transfer FEA Setup

The material of the motors will have a large effect of the results of any analysis. Because

the precise material composition of the motors are unknown, it is assumed that they are 50%

copper and 50% steel, and use properties that are a mean average of steel and copper thermal

properties:

𝜌𝑚𝑜𝑡𝑜𝑟 =𝜌𝑐𝑜𝑝𝑝𝑒𝑟

2+𝜌𝑠𝑡𝑒𝑒𝑙2

=8960 + 7850

2(𝑘𝑔

𝑚3) = 8405

𝑘𝑔𝑚3⁄

𝐶𝑃 =𝐶𝑃𝑐𝑜𝑝𝑝𝑒𝑟2

+𝐶𝑃𝑠𝑡𝑒𝑒𝑙2

=385 + 500

2(J

kg ∙ K) = 442.5

Jkg ∙ K⁄

𝑘𝑚𝑜𝑡𝑜𝑟 =𝑘𝑐𝑜𝑝𝑝𝑒𝑟

2+𝑘𝑠𝑡𝑒𝑒𝑙2

=401 + 60.5

2(𝑊

𝑚𝐾) = 230.75 𝑊 𝑚 ∙ 𝐾⁄

A convection heat transfer coefficient was calculated using an equation for natural

convection over a horizontal cylinder [5][6]

Further, it is assumed that:

• 30 degrees Celsius air temperature 𝑇𝑏.

• 60 degrees Celsius surface temperature 𝑇𝑠.

70 | P A G E

• Air speed of 2 m/s, due to weapon and belt velocity, and movement of robot.

Kinematic viscosity of air at 30 degrees Celsius is: 𝜈 = 1.568 ∗ 10−5 𝑚2

𝑠⁄

Volume coefficient of expansion of the air:

Β =1

𝑇𝑓=

1

273.15 +302 +

602

= 0.003143 𝐾−1

Diameter of the cylinder, use average of both:

𝑑 =0.04 𝑚 + 0.0381 𝑚

2= 0.03905 𝑚

The Grashof number:

𝐺𝑟 =𝑔Β𝑓(𝑇𝑠 − 𝑇𝑏)𝑑

3

𝜈2=9.81 (

𝑚𝑠2) ∗ 0.003143 𝐾−1 ∗ (60 − 30) 𝐾 ∗ 0.039053 𝑚3

(1.9 ∗ 10−5)2 (𝑚2

𝑠 )2

= 152577.5

With a Prandtl number:

Pr = 0.7

Rayleigh’s number:

𝑅𝑎 = 𝑃𝑟𝐺𝑟 = 0.7 ∗ 152577.5 = 106804

Thermal conductivity of air:

𝑘 = 0.024𝑊 𝑚 ∙ 𝐾⁄

Using Churchill and Chu’s equation:

71 | P A G E

ℎ =𝑘

𝑑

(

0.6 +0.387𝑅𝑎

16

(1 + (0.559Pr )

916)

827

)

2

=0.024

0.03905

(

0.6 +0.387 ∗ 106804

16

(1 + (0.5590.7 )

916)

827

)

2

= 4.855 𝑊 𝑚2 ∙ 𝐾⁄

This heat convection coefficient is too low and produces abnormal results. A convection

coefficient for forced convection is calculated instead, using the Empirical Hilpert relation for

forced convection over a cylinder. [7]

Reynold’s number, assuming a velocity of 2 m/s.

𝑅𝑒𝐷 =𝑣𝐷

𝜈=2 𝑚𝑠 ∗ 0.03905 𝑚

1.568 ∗ 10−5 𝑚2

𝑠

= 4981

ℎ = 𝑁𝑢𝐷 ∗𝑘

𝑑= 𝑐𝑅𝑒𝐷

𝑚Pr13 = 0.193 ∗ 4981(0.618)0.7

13 ∗ 0.024/0.03905 = 20.3 𝑊 𝑚2 ∙ 𝐾⁄

Where the coefficients 𝑐 and 𝑚 depend on Reynold’s number.

This convection heat transfer coefficient produces more accurate results.

Three trials of the simulation were run, at 25%, 50% and 75% of the average cycle power

according to the non-linear motor models. The following 𝑃𝑙𝑜𝑠𝑠 values give the heat generation

within the motors at 100% average cycle power.

The PDX 16 Gearmotor drive motor was modelled as a cylinder with a rectangular prism

with two distinct regions, the motor and the gearbox. Assuming motor efficiency to be 85%, and

using the total efficiency specification, the efficiency of the gearbox can be determined.

72 | P A G E

𝜂𝑔𝑒𝑎𝑟𝑏𝑜𝑥 =𝜂𝑡𝑜𝑡𝑎𝑙𝜂𝑚𝑜𝑡𝑜𝑟

=45.33%

85%= 53.33%

Assuming all efficiency losses are converted to heat within the gearmotor, the heat

generation for the FEA model can be determined:

𝑃𝑎𝑣𝑔 =259.125 𝐽

0.25𝑠= 1036.5 𝑊

𝑃𝑙𝑜𝑠𝑠𝑚𝑜𝑡𝑜𝑟 = 𝑃𝑎𝑣𝑔(1 − 𝜂𝑚𝑜𝑡𝑜𝑟) = 1036.5(1 − 0.85) = 155.5 𝑊

𝑃𝑙𝑜𝑠𝑠𝑔𝑒𝑎𝑟𝑏𝑜𝑥 = (𝑃𝑎𝑣𝑔 − 𝑃𝑙𝑜𝑠𝑠𝑚𝑜𝑡𝑜𝑟) ∗ (1 − 𝜂𝑔𝑒𝑎𝑟𝑏𝑜𝑥) = (1036.5 − 155.5) ∗ (1 − 0.5333)

= 411.2 𝑊

The Turnigy XK-4074 2000KV was modelled as a one region cylinder. With a motor efficiency

of 80%;

𝑃𝑎𝑣𝑔 =13 861 𝐽

13.82𝑠= 1003 𝑊

𝑃𝑙𝑜𝑠𝑠𝑚𝑜𝑡𝑜𝑟 = 𝑃𝑎𝑣𝑔(1 − 𝜂𝑚𝑜𝑡𝑜𝑟) = 1003(1 − 0.8) = 200.6 𝑊

Now that the PDE terms have been specified for both models, boundary conditions are

needed. For both motors, the face attached to the shaft is given a higher convective heat transfer

value.

For the weapon motor, shaft face has an h of 10ℎ = 203 𝑊 𝑚2 ∙ 𝐾⁄

For the drive motor, the shaft face is given an h of 5ℎ = 101.5 𝑊 𝑚2 ∙ 𝐾⁄

With all other faces having the calculated ℎ = 20.3 𝑊 𝑚2 ∙ 𝐾⁄

73 | P A G E

A6: Drum Length

It is known from elementary mathematics that:

𝑚 = 𝑉𝜌

With;

𝑉 = 𝐴𝑐𝐿

Thus;

𝐿 =𝑚

𝜌𝐴𝑐

For the 6 Holed disk designs, made from AISI 4340 HT steel we have;

𝐷𝑒𝑛𝑠𝑖𝑡𝑦 = 𝜌 = 7870 𝑘𝑔 𝑚3⁄

𝐴𝑟𝑒𝑎 = 𝐴𝑐 = 0.004600888 𝑚2

𝑀𝑎𝑠𝑠 = 𝑚 = 4 𝑘𝑔

Therefore;

∴ 𝐿 =𝑚

𝜌𝐴𝑐=

4

7870 ∗ 0.004600888= 0.11047 𝑚 𝑜𝑟 110.4 𝑚𝑚

A7: Drum Energy

The rotational kinetic energy of the drum was modeled in the following manner;

𝐾𝐸 =1

2𝐼 ∗ 𝜔𝑑

2

Where;

74 | P A G E

𝐼 = 𝑀𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝐼𝑛𝑒𝑟𝑡𝑖𝑎

𝜔𝑑 = 𝐴𝑛𝑔𝑢𝑙𝑎𝑟 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦

The moment of inertia was first modelled as a solid cylinder with a moment of inertia calculated

by;

𝐼 = 𝑚𝑎𝑠𝑠 ∗ 𝑟𝑎𝑑𝑖𝑢𝑠2

With more complicated moment of inertia determined using modelling software. The

18 𝑚𝑚 6 𝐻𝑜𝑙𝑒𝑑 𝐷𝑖𝑠𝑘 𝐷𝑒𝑠𝑖𝑔𝑛 has a 𝑚𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝑖𝑛𝑒𝑟𝑡𝑖𝑎 = 0.004783. When considering the

maximum 𝑟𝑝𝑚 𝑜𝑓 20,000 the cylinder has a stored kinetic energy;

𝐾𝐸 =1

2𝐼 ∗ 𝜔𝑑

2 =1

2∗ 0.004783 ∗ 200002 = 10.48 𝑘𝐽

A8: Weapon Tooth Design

If we define the tooth depth as 𝑑, and angular speed of the weapon as 𝜔𝑏, with velocity

of the colliding robots as 𝑣𝑥1 & 𝑣𝑥2 respectively. We can define the tooth depth as;

𝑑 =(𝑣𝑥1 + 𝑣𝑥2)𝜋

𝜔𝑏

Because;

∆𝑡 =𝜋

𝜔𝑏

𝑑 = (𝑣𝑥1 + 𝑣𝑥2)∆𝑡

75 | P A G E

If we assume that both robots are moving toward each other at 1 𝑚/𝑠 and the drum is

spinning at it’s maximum speed of 20,000 𝑟𝑝𝑚 𝑜𝑟 2093.33 𝑟𝑎𝑑/𝑠. We can calculate the

minimum required drum depth by;

𝑑min =(𝑣𝑥1 + 𝑣𝑥2)𝜋

𝜔𝑏=(1 + 1)𝜋

2093.33= 0.003 𝑚 𝑜𝑟 3 𝑚𝑚

However, we must consider that the drum will not be operating at full speed all the time,

so we will also consider a speed less than maximum, that also would be considered as a

midrange energy impact that the drum would be effective at. This speed is a more flexible

choice, so we will begin with 10,000 𝑟𝑝𝑚 𝑜𝑟 1046.67 𝑟𝑎𝑑/𝑠;

𝑑10000 =(𝑣𝑥1 + 𝑣𝑥2)𝜋

𝜔𝑏=(1 + 1)𝜋

1046.67= 0.006 𝑚 𝑜𝑟 6 𝑚𝑚

This change in tooth depth gives us an idea of how the depth of the tooth changes with

drum speed. For design factor considerations, machining of the drum was simplified for the

project, and a standard 10 𝑚𝑚 depth was chosen. The 10 𝑚𝑚 depth will be effective at even

lower speeds;

𝜔𝑙𝑜𝑤 =(𝑣𝑥1 + 𝑣𝑥2)𝜋

𝑑max =(1 + 1)𝜋

0.01= 628.38 𝑟𝑎𝑑 𝑠⁄ 𝑜𝑟 6000 𝑟𝑝𝑚

This lower speed is important, because it is the minimum speed the drum is effective

before contact between the robots could happen at another then tooth section of the drum. This is

particularly important because at these lower speeds a competitor’s weapon would be able to

contact the drum first. This is more a matter of chance depending on where in the rotation the

drum is during the contact.

76 | P A G E

A9: Weapon Stop Time

𝑃𝑜𝑤𝑒𝑟 =𝐸

𝑡=𝐼𝑑𝜔

2

2𝑡= 𝑇𝜔 = 𝐹𝜇𝑘𝑟𝜔

𝑡 =𝐼𝑑𝜔

2

2𝐹𝜇𝑘𝑟𝜔=𝐼𝑑𝜔𝑎𝑣𝑔

𝐹𝜇𝑘𝑟=

𝐸

𝐹𝜇𝑘𝑟𝜔

The force on the bushing is 145.5 N, and the friction coefficient between PTFE and steel

ranges from 0.05 – 0.2, [4]. Choosing the worst-case scenario, a coefficient of friction of 0.05:

𝑡 =10 𝑘𝐽

145.5 𝑁 ∗ 0.05 ∗ 0.009 𝑚 ∗ 2200 𝑟𝑎𝑑/𝑠= 69.44 𝑠

A10: Electromechanical Model Derivations

Exponential Modelling

Let the motor have a stall torque of 𝑇0 (Nm) and a no-load speed of 𝜔𝑛 (rad/s). If the

drive wheels of the robot have a diameter of D that spin at an instantaneous rate of 𝜔 (rad/s), and

the robot accelerates over time 𝑡, then it may be shown that, due to linearity of torque and speed

of DC motors, the torque as a function of 𝜔 is:

𝑇(𝜔) = 𝑇0 (1 −𝜔

𝜔𝑛) Eq. 1

By equating the power equations for that of a linear and angular system through

conservation of energy, and applying Newton’s Second law, it is observed that:

𝐹𝑣 = 𝑇𝜔 = 𝑃𝑜𝑤𝑒𝑟

𝑚𝑎𝑣 = 𝑇(𝜔)𝜔

𝑎 =𝑇(𝜔)𝜔

𝑚𝑣

77 | P A G E

From elementary dynamics, it may be shown that the time 𝑡 required to accelerate to

linear velocity 𝑣 with linear acceleration 𝑎 from rest is:

𝑡 = ∫1

𝑎𝑑𝑣

𝑣

0

𝑡 = ∫𝑚𝑣

𝑇(𝜔)𝜔𝑑𝑣

𝑣

0

Combining with the expression above for torque as a function of angular velocity:

𝑡 = ∫𝑚𝜔𝑟

𝑇0 (1 −𝜔𝜔𝑛)𝜔

𝑑(𝜔𝑟)𝜔

0

= ∫𝑚𝑟2

𝑇0 (1 −𝜔𝜔𝑛)𝑑𝜔

𝜔

0

Recognizing this as an integrand that may be simplified through u-substitution by setting 1 −

𝜔

𝜔𝑛= 𝑢, such that −𝜔𝑛𝑑𝑢 = 𝑑𝜔, it appears that:

𝑡 = ∫−𝜔𝑛𝑚𝑟

2

𝑇0(𝑢)𝑑𝑢

1−𝜔/𝜔𝑛

1

𝑡 = −𝑚𝑟2𝜔𝑛

𝑇0ln (1 −

𝜔

𝜔𝑛) Eq. 2

Performing a logarithmic rearrangement of this expression yields the linear and angular

velocities of the robot as a function of time, respectively, to be:

𝑣(𝑡) = 𝑟𝜔𝑛(1 − 𝑒−𝑡

𝑇0𝑚𝑟2𝜔𝑛) Eq. 3

𝜔(𝑡) = 𝜔𝑛(1 − 𝑒−𝑡

𝑇0𝑚𝑟2𝜔𝑛)

Eq. 4

78 | P A G E

Now that an expression for the speed of the robot has been developed as a function of

time, this expression may be reintroduced to the torque-speed graph to generate a function for

torque in terms of time.

𝑇(𝜔) = 𝑇0 (1 −𝜔

𝜔𝑛)

𝑇(𝑡) = 𝑇0𝑒−𝑡

𝑇0𝑚𝑟2𝜔𝑛 Eq. 5

Knowing that the mechanical power of a rotating system is the product of torque and

angular velocity, the motor output power as a function of time becomes:

𝑃𝑚𝑒𝑐ℎ(𝑡) = 𝑇(𝑡) 𝜔(𝑡)

𝑃𝑚𝑒𝑐ℎ(𝑡) = 𝑇0𝑒−𝑡

𝑇0𝑚𝑟2𝜔𝑛𝜔𝑛 (1 − 𝑒

−𝑡𝑇0

𝑚𝑟2𝜔𝑛)

𝑃𝑚𝑒𝑐ℎ(𝑡) = 𝑇0𝜔𝑛 (𝑒−𝑡

𝑇0𝑚𝑟2𝜔𝑛 − 𝑒

−𝑡2𝑇0

𝑚𝑟2𝜔𝑛) Eq. 6

To adequately size the power supply to ensure the robot achieves adequate run time, the

average power consumption of the robot is required. It is known that the mechanical efficiency

of brushed DC motors is nonlinear, and usually peaks when the motors are operated at

approximately 80% of their no-load speed. This peak efficiency is usually around 0.8. As of this

date, no mathematical expressions for efficiency could be found. Simplifying the analysis to

assume a constant efficiency of 𝜂 = 0.7 should provide an adequate approximation of the

average operational efficiency to be encountered during operation.

𝑃𝑐(𝑡) =𝑇0𝜔𝑛

𝜂(𝑒−𝑡

𝑇0𝑚𝑟2𝜔𝑛 − 𝑒

−𝑡2𝑇0

𝑚𝑟2𝜔𝑛)

Eq. 7

79 | P A G E

At this point it should be noted that efficiency losses generally result in a reduction of

torque, not speed. Seeing as the equations above involve inverse exponential functions, the motor

will never reach no-load speed. For the purposes of this investigation, full speed is defined as the

robot reaching 95% of the theoretical maximum speed, that is, 𝜔 = 0.95𝜔𝑛

The instantaneous power consumption of each motor is necessary to ensure the power

supply can provide enough power when the motors are operating at their maximum consumption

rates. Beyond this, the total energy consumption over a given time can be useful in ensuring the

power supply has enough stored energy to power the device for an entire match.

The total energy required for one cycle (starting from rest and accelerating to 𝜔 =

0.95𝜔𝑛), may be attained by integrating the power consumption equation with respect to time as

follows:

𝐸𝑐𝑦𝑐𝑙𝑒 = ∫𝑇0𝜔𝑛𝜂(𝑒

−𝑡𝑇0

𝑚𝑟2𝜔𝑛 − 𝑒−𝑡

2𝑇0𝑚𝑟2𝜔𝑛)𝑑𝑡

−𝑚𝑟2𝜔𝑛𝑇0

ln(1−0.95𝜔𝑛𝜔𝑛

)7

0

𝐸𝑐𝑦𝑐𝑙𝑒 = 𝑇0𝜔𝑛𝑚𝑟2𝜔𝑛𝜂𝑇0

[1

2𝑒−𝑡

2𝑇0𝑚𝑟2𝜔𝑛 − 𝑒

−𝑡𝑇0

𝑚𝑟2𝜔𝑛]𝑡=0

𝑡=−𝑚𝑟2𝜔𝑛𝑇0

ln (0.05)

𝐸𝑐𝑦𝑐𝑙𝑒 = 𝜔𝑛𝑚𝑟2𝜔𝑛𝜂

{[1

2𝑒2 ln(0.05) − 𝑒ln(0.05)] − [

1

2− 1]}

𝐸𝑐𝑦𝑐𝑙𝑒 = (361

800)𝑚𝑟2𝜔𝑛

2

𝜂 Eq. 8

Opposed from integrating this power consumption curve as used above to derive Eq. 8,

the cycle energy may be found by multiplying the change in kinetic energy by the motor

efficiency:

80 | P A G E

𝐸𝑐𝑦𝑐𝑙𝑒,𝑙𝑖𝑛𝑒𝑎𝑟 = (1

𝜂)1

2𝑚∆𝑣2 =

1

2𝜂𝑚(𝑟(0.95𝜔𝑛))

2

𝐸𝑐𝑦𝑐𝑙𝑒,𝑙𝑖𝑛𝑒𝑎𝑟 =361

800𝜂𝑚𝑟2𝜔𝑛

2

As expected, the cycle energy expression derived from a kinetic energy approach

provided an identical result as obtained above in Eq. 8. This is because kinetic energy is not path

dependent; it is scalar. Generating the same expression using two different methods greatly

increases the validity of the result.

The number of cycles that may be achieved by a given power supply unit until it requires

recharging may be approximated by diving the energy capacity of the battery 𝐻𝑉𝑠 by 𝐸𝑐𝑦𝑐𝑙𝑒.

Knowing that the time required to complete one cycle to be 𝑡 = −𝑚𝑟2𝜔𝑛

𝑇0ln (0.05), the lifetime of

the battery may be approximated as:

𝑡𝑙𝑖𝑓𝑒 = −(𝐻𝑉𝑠𝐸 𝑐𝑦𝑐𝑙𝑒

)𝑚𝑟2𝜔𝑛𝑇0

ln (0.05)

𝑡𝑙𝑖𝑓𝑒 = −(𝐻𝑉𝑠

(361800)

𝑚𝑟2𝜔𝑛2

𝜂

)𝑚𝑟2𝜔𝑛𝑇0

ln(0.05)

𝑡𝑙𝑖𝑓𝑒 = −800𝐻𝑉𝑠𝜂 ln(0.05)

361 𝜔𝑛𝑇0 Eq. 9

The equations generated above will be instrumental in selecting motor and power supply

combinations. It must be noted that none of these equations took into considerations the

limitation of the power supply. For instance, if a motor is rated for use at 16 V and the power

supply can only provide 11 volts, then the maximum speed of the robot will be approximately

81 | P A G E

11/16ths of the rated speed. This linear relationship may be incorporated into the above equations

by the ratio of rated voltage to available voltage as 𝜔𝑛′ = 𝜔𝑛

𝑉𝑠

𝑉𝑟𝑎𝑡𝑒𝑑

The above analysis also only considers the use of one motor at a time. To allow for the

assessment of the machine using multiple drive motors simultaneously, the simple adjustment of

setting 𝑇0′ = 𝑇0𝑁𝑑, where 𝑁𝑑is the number of drive motors being used.

Going back to the significant equations from above and substituting yields the final equations:

𝑡𝑐𝑦𝑐𝑙𝑒 = −𝑚𝑟2𝜔𝑛

′

𝑇0′ ln(0.05) Eq. 10

𝑣(𝑡) = 𝑟𝜔𝑛′ (1 − 𝑒

−𝑡𝑇0′

𝑚𝑟2𝜔𝑛′) Eq. 11

𝜔(𝑡) = 𝜔𝑛′ (1 − 𝑒

−𝑡𝑇0′


𝑃𝑐(𝑡) =𝑇0′𝜔𝑛′

𝜂(𝑒

−𝑡𝑇0′

𝑚𝑟2𝜔𝑛′− 𝑒

−𝑡2𝑇0′




2

𝜂 Eq. 14

𝑡𝑙𝑖𝑓𝑒 = −800𝐻𝑉𝑠𝜂 ln(0.05)

361 𝜔𝑛′ 𝑇0

′ Eq. 15

𝜔𝑛′ = 𝜔𝑛

𝑉𝑠

𝑉𝑟𝑎𝑡𝑒𝑑

Eq. 16

𝑇0′ = 𝑇0𝑁𝑑 Eq. 17

It should be stated that Eq.13-15, or their derivations, could not be found in any textbooks

or research papers. It is likely that these equations are original to this report.

82 | P A G E

Before carrying on to the next section, it’s interesting to note that Eq. 3-4, and

subsequently Eq. 11-12, may be derived from Eq. 5; the expression for motor torque as a

function of time. By setting 𝑇(𝑡) = 𝐹𝑟, and substituting Newton’s Second Law and rearranging,

it is shown that

𝑇(𝑡)

𝑟𝑚=𝑇0𝑒

−𝑡𝑇0

𝑚𝑟2𝜔𝑛

𝑟𝑚= 𝑎(𝑡)

∫𝑇0𝑒

−𝑡𝑇0

𝑚𝑟2𝜔𝑛

𝑟𝑚𝑑𝑡

𝑡

0

= ∫ 𝑎(𝑡)𝑑𝑡𝑣(𝑡)

0

Working through these integrals yields Eq. 3, which is a simply a scalar multiple of Eq. 4.

Linear Acceleration Approximation: Energy Method

Assuming linear acceleration greatly simplifies the analysis of the performance

characteristics of the machine. It’s important to reiterate that some of the equations derived

above have never been observed in other sources. It is a worthwhile endeavor to generate similar

equations using alternative methods to provide a thorough means of analysis and support the

equations from above.

The average value of the torque-speed curve in figure 1 is 𝑇𝑎𝑣𝑔 = 𝑇0′/2. Combining this

with Newton’s second law yields:

𝑇𝑎𝑣𝑔 = 𝑟(𝑚𝑎𝑎𝑣𝑔)

𝑇0′

2𝑚𝑟= 𝑎𝑎𝑣𝑔 Eq. 18

From a finite divided difference approximation of acceleration, it may be stated that

𝑎𝑎𝑣𝑔 = ∆𝑣/∆𝑡, which may be rearranged to form ∆𝑡 = ∆𝑣/𝑎𝑎𝑣𝑔. Assuming the robot to start

83 | P A G E

from rest and accelerate to a speed of 𝑟𝜔0, and substituting Eq. 18 into this expression for time

yields:

∆𝑡𝑐𝑦𝑐𝑙𝑒 = 𝑟(0.95)𝜔𝑛

′

𝑇0′

2𝑚𝑟

=19 𝑚𝑟2𝜔𝑛

′

10 𝑇0′ Eq. 19

Using the expression for average acceleration, Eq.18, the velocity function of the robot

may be determined using basic kinematic equations, where the initial velocity is 0:

𝑣(𝑡) = 𝑎𝑎𝑣𝑔𝑡 =𝑇0′

2𝑚𝑟𝑡 Eq. 20

𝜔(𝑡) = 𝑇0′

2𝑚𝑟2𝑡 Eq. 21

From Figure 18: Torque - Speed Curve of DC Motor above, it is again seen that the

torque as a function of speed is 𝑇(𝜔) = 𝑇0′ (1 −

𝜔

𝜔𝑛), implying that;

𝑇(𝑡) = 𝑇0′ (1 −

𝜔(𝑡)

𝜔𝑛) = 𝑇0

′(1 − 𝑇0′

2𝜔𝑛𝑚𝑟2𝑡) Eq. 22

The power consumption function of the motors may again be determined by multiplying

the motor efficiency with the speed and torque functions, such that 𝑃𝑐(𝑡) =1

𝜂𝑇(𝑡) 𝜔(𝑡).

Performing the substitutions with Eq. 21-22 yields the parabolic relation:

𝑃𝑐(𝑡) =𝑇0′2

2𝜂𝑚𝑟2( 𝑡 −

𝑇0′

2𝜂𝜔𝑛′𝑚𝑟2

𝑡2) Eq. 23

The linearized equivalent to the cyclic energy expression of Eq. 14 may be derived by

integrating Eq. 23 from 𝑡 = 0 to 𝑡 = ∆𝑡𝑐𝑦𝑐𝑙𝑒 =19 𝑚𝑟2𝜔𝑛

′

10 𝑇0′ . Completing this integration yields:

𝐸𝑐𝑦𝑐𝑙𝑒 =𝑚𝑟2(0.95𝜔𝑛

′ )2

𝜂(1 −

2 ∗ 0.95𝜔𝑛′

3𝜂𝜔𝑛′)

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𝐸𝑐𝑦𝑐𝑙𝑒 =𝑚𝑟2(0.95𝜔𝑛

′ )2

𝜂(1 −

2 ∗ 0.95𝜔𝑛′

3𝜂𝜔𝑛′)



2

𝜂(1 −

19

30𝜂) Eq. 24

To determine the linear approximation to 𝑡𝑙𝑖𝑓𝑒, it is useful to again to divide the power

supply energy by the cycle energy, and multiply the result by the cycle time. Performing these

operations leads to:

𝑡𝑙𝑖𝑓𝑒 =1600𝐻𝑉𝑠𝜂

361 𝜔𝑛′ 𝑇0

′ Eq. 25

Linear and Non-Linear Model Prediction

It must be re-iterated that the linear models were generated as an exercise in kinematics

in hope of supplementing the non-linear formulations of equations 10 through 15. These

equations are compared in Table 16: Linear & Non-Linear Kinematic Models above.

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A11: RoboBrawl 2018 Rules

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A12: Weight and Dimensions List

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A13: Acceleration Data Analysis

gFxms = gFx*9.81;

gFyms = gFy*9.81;

figure()

plot(time,gFxms, time,gFyms)

title('Components of Acceleration')

legend('Acceleration in x' , 'Acceleration in y')

xlabel('s')

ylabel('m/s^2')

j=1;

for i = 5587:1:6500

xa(j) = gFxms(i);

ya(j) = gFyms(i);

timea(j) = time(i);

j = j+1;

end

figure()

plot(timea,xa, timea,ya)

title('Components of Acceleration')

legend('Acceleration in x' , 'Acceleration in y')

xlabel('s')

ylabel('m/s^2')

a = sqrt(xa.^2 + ya.^2);

figure()

plot(timea,a)

title('Resultant of Acceleration')

legend('Acceleration')

xlabel('s'); ylabel('m/s^2')

xv = cumtrapz(timea, xa);

yv = cumtrapz(timea, ya);

figure()

plot(timea,xv, timea,yv)

title('Components of Velocity')

legend('Velocity in x' , 'Velocity in y')

xlabel('s'); ylabel('m/s')

v = sqrt(xv.^2 + yv.^2);

figure()

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plot(timea,v)

title('Resultant of Velocity')

legend('Velocity')

xlabel('s')

ylabel('m/s')

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Figure 25: Components of acceleration

Figure 26: Resultant Acceleration

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Figure 27: Velocity Components

Figure 28: Velocity Resultant

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A14: CAD Drawings Used During Manufacture

Figure 29:Weapon View 1

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Figure 30: Weapon View 2

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Figure 34: Shaft View

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Figure 37: Weapon Motor Sheave

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Figure 38: The Revolver - Top View

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Figure 39: Frame - Top View

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Figure 40: Frame - Isometric View

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Figure 41: Full Robot View

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Figure 42: Frame - Exploded View

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Figure 43: Frame - Isometric View

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Figure 44: Drive Motor Gearbox Dimensions

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Figure 45: Weapon Mount – Non-Drive Side

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Figure 46: Weapon Mount: Drive Side

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A15: Electrical Schematic

Figure 47: Electrical Layout

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A16: Gantt Chart and List of Deliverables

Figure 48: Gantt Chart

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A17: ENGI-4969 Degree Project Guideline Policy

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