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Electronic Theses, Treatises and Dissertations The Graduate School

2006

Design of a Wearable CobotJason Yap Chua

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THE FLORIDA STATE UNIVERSITY

FAMU – FSU COLLEGE OF ENGINEERING

DESIGN OF A WEARABLE COBOT

By

JASON YAP CHUA

A Thesis submitted to the Department of Mechanical Engineering

in partial fulfillment of the requirements for the degree of

Master of Science

Degree Awarded: Spring Semester, 2006

ii

The members of the Committee approve the Thesis of Jason Yap Chua defended on February 23, 2006.

___________________________ Carl A. Moore

Professor Directing Thesis ___________________________ Rodney Roberts Outside Committee Member

___________________________ Patrick Hollis Committee Member

Approved: ____________________________________ Chiang Shih, Chair, Mechanical Engineering ____________________________________ Ching-Jen Chen, Dean, FAMU-FSU College of Engineering The Office of Graduate Studies has verified and approved the above named committee members.

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For all my ancestors who worked so hard to give me a better life and for all those that come after me to continue our ancestors’ legacy.

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ACKNOWLEDGEMENTS

I would like to express my gratitude to Dr. Carl Moore for his guidance and assistance in my

research. I would also like to express my appreciation to my committee members, Dr. Patrick

Hollis and Dr. Rodney Roberts for serving on my committee and providing additional guidance.

I must thank Dr. Hollis again for instilling an interest in mechanical design in me through classes

I took with him. Thanks go out to NASA for funding my research. I would also like to thank all

my colleagues in the Center for Intelligent Systems, Control and Robotics Lab for their

friendship and support. A big thanks goes out to Dan Baxter and the FSU Physics Lab for

machining the parts designed. I am indebted to William Kincannon for culturing the art of

engineering in me through machining. I must thank Dr. David Cartes for being a voice of

experience and wisdom. Thank you to Alicia Fontaine for support from an understanding peer.

Thanks also go out to Keith Larson for advice and consultation on engineering and problems

beyond. I cannot thank my family enough for all that they have done for me. Special thanks

must be given to my Grandfathers Chua Yap Chek and Cheng Phi as well as my Father Yap

Siong Chua for having the courage to cross oceans and the skill and determination to succeed in

foreign lands. I am forever indebted to them.

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TABLE OF CONTENTS

List of Tables ................................................................................................ vii List of Figures ................................................................................................ viii Abstract ...................................................................................................... x 1. INTRODUCTION ......................................................................................... 1 1.1 Cobot History........................................................................................ 1 1.2 Telerobotics and Telepresence ............................................................. 7 1.2.1 Telerobotics ................................................................................ 7 1.2.2 Telepresence ............................................................................... 7 1.2.3 Virtual Constraints ...................................................................... 8 1.2.4 Powered Cobot ............................................................................ 9 1.3 Application ........................................................................................... 11 2. MECHANICAL DESIGN ............................................................................. 15 2.1 Arm Cobot ........................................................................................... 15 2.2 Transmission Ratio Design .................................................................. 16 2.2.1 Cable Transmissions ................................................................... 16 2.2.2 Design Parameters ...................................................................... 17 2.3 Capstan Design and Cable Selection ................................................... 19 2.3.1 Design Considerations ................................................................ 19 2.3.2 Loading Design Calculations ...................................................... 22 2.3.3 Loading Design Results .............................................................. 25 2.4 Cable Wrapping Design ....................................................................... 27 2.5 Cable Tensioning Design ..................................................................... 29 3. Results and Conclusions ................................................................................ 31 3.1 Cable Mounting and Tensioning .......................................................... 31 3.2 Results ................................................................................................ 34 3.3 Conclusions .......................................................................................... 35 3.4 Future Work ......................................................................................... 36 APPENDICES ................................................................................................ 38

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A Sava Cable Catalog .............................................................................. 38 B MathCAD Calculations ........................................................................ 51 C Engineering Drawings .......................................................................... 58 REFERENCES ................................................................................................ 105 BIOGRAPHICAL SKETCH .............................................................................. 107

vii

LIST OF TABLES Table 1: Joint Force (Col. 1-8, lb)/Torques (Col. 9-10, lb-in)............................. 18 Table 2: Cable Breaking Strength Adjustment ................................................... 21 Table 3: Sample Listing of Cables for Use in Transmissions ............................. 23 Table 4: Specification of Shoulder Reduction Stages ......................................... 25 Table 5: Specification of Elbow Reduction Stages ............................................. 25 Table 6: Specification of Forearm Reduction Stages .......................................... 26

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LIST OF FIGURES Figure 1: Virtual walls created by actuated steering .......................................... 1 Figure 2: Unicycle Cobot .................................................................................... 2 Figure 3: Unicycle Two-Link Cobot ................................................................... 3 Figure 4: Scooter Cobot ...................................................................................... 3 Figure 5: The scooter cobot guides the car door assembly ................................. 4 Figure 6: The Arm Cobot ................................................................................... 5 Figure 7: The Spherical CVT .............................................................................. 6 Figure 8: Telerobotic System With Visual and Position Feedback .................... 7 Figure 9: Telerobotic System with Virtual Constraints ...................................... 8 Figure 10: Traditional Robotic System ............................................................... 9 Figure 11: Multi-Degree of Freedom Cobotic System ....................................... 10 Figure 12: The DAWP Platform ......................................................................... 11 Figure 13: 6-DOF Cobot Master Controller ....................................................... 12 Figure 14: NASA’s Robonaut ............................................................................. 13 Figure 15: Force Reflecting Hand Controllers ................................................... 13 Figure 16: Wearable Arm Cobot ......................................................................... 15 Figure 17: Capstan Pair with Positive and Negative Torque Cables .................. 16 Figure 18: Experiment Configurations ............................................................... 17 Figure 19: Cobot Arm CG Location and Endpoint Loading for Shoulder Joint 19

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Figure 20: Multi-Stage Transmission and Equation for Adding Stiffnesses ...... 20 Figure 21: Pretensioning in Capstan Pairs .......................................................... 21 Figure 22: Wearable Arm Cobot ......................................................................... 26 Figure 23: Cable Travel in a Spooling Capstan .................................................. 27 Figure 24: Uneven Cable Travel in Capstan Pairs .............................................. 28 Figure 25: Sandwiched Capstan Tensioning Scheme ......................................... 30 Figure 26: Capstan Tensioning Scheme ............................................................. 31 Figure 27: Wearable Cobot Shoulder Transmission ........................................... 32 Figure 28: Cable Mounting Points ...................................................................... 33 Figure 29: Cables Spooling into Capstan Grooves ............................................. 34

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ABSTRACT

Cobots are specially designed robots that use continuously variable transmissions (CVTs)

instead of traditional motor driven joints. Cobots are an attractive choice for telerobotic master

controllers because they are safe in contact with humans and are able to produce stable, high

quality virtual surfaces that can constrain the motion of the master to directions suitable for

telerobotic task completion. This thesis describes the design of a 3-DOF, cable driven, wearable

arm master controller and provides the details on the construction and assembly of the shoulder

joint. Solidworks CAD was used to design the wearable cobot. After shoulder capstans and

shafts were machined the device was assembled and tested. The rotational stiffness for the

shoulder joint was found to be 1.58*105 lb-in/rad and the start torque was found to be 16.5 lb-in.

Improvements and future work are also discussed.

1

CHAPTER 1

INTRODUCTION

1.1 Cobot History

Cobots, or ‘COllaborative roBOTs’ are robots designed to present high quality

constraints safely to human users [1]. The initial driving force behind the invention of

cobots was to meet the need for a robot that could interact safely with automobile

assemblers. There are presently several different cobots, but the defining feature

common to all cobots is the continuously variable transmission (CVT) used in place of

traditional robot joints. The CVTs kinematically separates the cobot’s speed and

direction. For example, the unicycle cobot [1] has one steered wheel rolling on a flat

plane. The steered wheel is a CVT that controls the x and y-axis translational velocity

ratio as a continuous function of the wheel’s heading angle. The actuator, instead of

controlling the rotational velocity of the wheel, is used to steer the wheel.

Fig. 1. Virtual Walls Created by Actuated Steering

2

Fig. 1 shows this virtual wall created by actuated steering where upon reaching the

virtual wall the wheel is steered to roll along the line of the virtual wall. The downward

force and coefficient of friction determines the strength of the virtual wall.

The unicycle cobot, shown below in fig. 2, was created for research purposes and is a

purely passive device.

Fig. 2. Unicycle Cobot [1]

The Unicycle Two-Link Arm (UTLA) in fig. 3 was created for rehabilitation

research. The UTLA is spring loaded at the second rotational joint to provide a constant

down-force at the unicycle. The UTLA operates in 3 different modes. A virtual caster

mode senses the user’s intended motion direction and steers the wheel to accommodate.

The virtual path mode constrains the user to a specified path. The third mode, virtual

wall mode, is a combination of the first 2 modes in which the user may move freely in

certain areas but will be met with a virtual wall upon moving to the edge of the free

movement area.

3

Fig. 3. Unicycle Two-Link Cobot [2]

The scooter cobot in fig. 4 was designed for industrial material handling. It uses three

steered wheels to guide the platform.

Fig. 4. Scooter Cobot [3]

In free mode the scooter operates similarly to a chair on casters. In constrained mode

it follows a specified path but retains the ability to turn on its central axis. The Scooter

cobot was originally designed to assist in automobile assembly by allowing fewer

workers to place and remove parts, like a car door, accurately and easily as shown in fig.

5.

4

Fig. 5. The Scooter Cobot Guiding Car Door Assembly [3]

The arm cobot in fig. 6 was created for industrial design research and is able to create

a 3 dimensional virtual surface in the traditional x, y, z space. The user can qualitatively

determine car ergonomics such as door opening, from interaction with the arm cobot’s

end-effector. For example, the arm cobot can constrain the motion of the end effector to

simulate a sliding path of a door handle when opened by an occupant. The simulation

allows the user to experience the height and path of the door handle without creating a

physical prototype.

5

Fig. 6. The Arm Cobot [4]

The arm cobot’s revolute joints are connected to spherical CVT’s that allow for these

virtual constraints to be formed. The spherical CVT is shown below in fig. 7. In the arm

cobot, the input shafts of the three spherical CVT’s are connected to each revolute joint.

Each output shaft of the spherical CVT’s are connected to each other linking the CVT’s

mechanically. The spherical CVT creates a speed ratio between the input and output

shafts using a transmission sphere. Actuated steering wheels control the spinning axis of

the sphere allowing for different rolling speeds of the input and output shafts. The

actuated steered wheels in the spherical CVT are analogous to the steered wheel in the

unicycle cobot.

6

Fig. 7. The Spherical CVT [4]

As shown, previous cobots were created mainly for research, rehabilitative and

industrial uses. However, the unique qualities of intrinsic safety in contact with humans

and ability to create stable, high quality constraints make cobots ideal for telerobotics

implementation. The following sections will discuss telerobotics and the application of

cobots in telerobotics.

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1.2 Telerobotics and Telepresence

1.2.1 Telerobotics

A typical telerobotic system consists of two robots. The follower, or slave robot,

performs a task at the direction of a human controlled master robot at a remote location.

This system is typically used when human presence at the task site is either impossible or

poses too great a danger to the human.

The first telerobotic systems typically consisted of a robotic manipulator at a remote

site controlled by a control panel or joystick. A user would manipulate the control panel

or joystick while observing the robot on a monitor. Since this type of system has only

visual and position feedback it is difficult to complete tasks.

1.2.2 Telepresence

Telepresence is a property of telerobotic systems that describes the amount and

quality of feedback from the slave robot and its surroundings [5]. The telerobotic system

shown in fig. 6 is indicative of many early telerobotic systems and consists of a master

robot controlling a manipulator with a pencil at a remote site. These systems exhibited a

minimal amount of telepresence using only position control and visual feedback control.

In the case of fig. 8 is would be relatively easy for the user to accidentally commence a

motion causing the slave to break the pencil. Without increased telepresence it would be

nearly impossible to handle unstable materials or perform surgery via a telerobotic

system.

Fig. 8. Telerobotic System With Visual and Position Feedback

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1.2.3 Virtual Constraints

Greater bandwidth in electronic communication and advances in force transducer

technology have allowed the integration of effective force feedback in telerobotic

systems. With force feedback the user can prevent breaking the pencil tip in the fig. 8 by

detecting the amount of downward force applied by the slave on the pencil.

Pictured below in fig. 9 is an example of a telerobotic system equipped with virtual

constraints.

Fig. 9. Telerobotic System with Virtual Constraints

The objective is to draw a straight line at the remote site. The user controlling the

master robot cannot easily draw a straight line without the aid of a straight edge. If the

master controller could be programmed with a straight edge virtual constraint the user

could very easily complete the task. In this situation virtual guides help constrain the

user motion to a straight path and the user determines the speed at which the line is

drawn. This can be easily applied to creating constraints in a multi-dimensional

workspace [6].

For a virtual constraint to be useful it must be firm enough to resist forces against it

and smooth enough that is does not increase frictional drag on the master controller. It is

difficult to implement this control concept safely on traditionally actuator driven robot

systems. For example, when the human user applies a force perpendicular to the virtual

9

ruler constraint in fig. 9, the master robot should respond with an equal and opposite

constraint force to counter that of the human user. The actuators used in a traditional

robot setup are capable of creating large and unpredictable joint velocities that could be

life threatening to the human user [4]. Furthermore, the control structure in a traditional

robot system employs a zero order hold. The zero order hold and sampling of the robots

real-time sensor data creates a situation in which the user can extract energy from a

virtual constraint that is supposed to feel passive [7, 8]. As the user repeatedly uses the

constraint, the repeated energy addition and subtraction could cause the manipulator to

become unstable. Creating high quality virtual constraints for traditional robot systems is

still difficult despite maximized sensor resolution and sampling rates. The use of

powered CVT’s in place of traditional actuators can yield firm, high quality constraints.

1.2.4 Powered Cobot

In a traditional robotic system the actuator is placed directly on each joint shown in

fig. 10. These actuators act as power level and signal level actuators, which requires

actuators of relatively high torque production to maintain rigid virtual constraints. With

large actuators maintaining safety is problematic. Safety and smoothness of the system

can be increased by separating the power level and signal level duties among an increased

number of actuators [1]. A powered cobot can fulfill this requirement.

Fig. 10. Traditional Robotic System

10

A powered cobot with ‘n’ DOF requires ‘n + 1’ actuators, one more than a

conventionally actuated robot of the same dimensionality [1]. In a cobot, ‘n’ number of

actuators are used to adjust the transmission ratios or ‘steer’ each CVT. This steering

angle is denoted by “γ” in fig. 11. The CVT steering actuators are signal level actuators

that cannot affect the speed of the cobot’s endpoint. This is tantamount to a driver in a

parked car turning the steering wheel; while the proposed heading is changed there is no

motive force to realize that change in direction.

The remaining actuator is the power level actuator, denoted by “τ0”, used to amplify

the user’s motions. In the arm cobot each joint is coupled to a CVT. Each CVT is joined

in parallel by a common shaft driven by the power assist actuator, shown in fig. 11. This

powered cobot architecture relies on only one power level actuator which allows for a

more manageable system in terms of control as compared to a system with three power

level actuators.

Fig. 11. Multi-Degree of Freedom Cobotic System

11

1.3 Application

Agencies such as NASA and Argonne National Laboratories are calling for more

sophisticated master robot systems that can provide increased telepresence through the

use of cobot created virtual constraints. The Dual Arm Work Platform (DAWP), shown

with a control station in fig. 12, at the Argonne National Laboratory is used for

disassembly in nuclear reactor cores [9]. The platform has strategically placed cameras

that allow remote control via a series of joysticks and monitors. This particular setup in

fig. 8, provides a limited amount of telepresence, as discussed previously.

Fig. 12. The DAWP Platform [10]

On the DAWP platform, tools are often broken in the middle of performing an

operation. After replacing the tool, 90% of the operation time is spent repositioning the

tool at the original worksite [9].

The time spent repositioning the tool could be greatly reduced if a greater

telepresence at the remote site could be established. This can be achieved by using force

feedback coupled with virtual fixtures [6]. Force feedback would allow the user to sense

the amount of force imposed on the tool, thereby aiding the user in the prevention of tool

breakage. Should a tool break, virtual constraints could be created based on the position

12

of the previous tool worksite to guide the user back to the exact site of the work quickly

and accurately.

A 6-DOF cobot master controller, shown below in fig. 13, has been created to replace

the outdated position feedback joystick controllers that were formerly in use [9]. This

controller employs force feedback and virtual constraints in a joystick interface to aid the

user in task completion.

Fig. 13. 6-DOF Cobot Master Controller [9]

NASA’s Robonaut project intends to aid and even replace the need for manned space

walks by teleoperation of a robot possessing the same configuration and dexterity as a

human, shown in fig. 14 [11]. It is possible that Robonaut could exhibit the same

problems in operation as the DAWP.

13

Fig. 14. NASA’s Robonaut [12]

Currently, Robonaut can function as an anthropometric tool in simple task completion

such as picking up and carrying items, inserting bolts into holes and carrying out other

simple instructions via hand signals. Remote control of Robonaut includes the use of two

Force Reflection Hand Controllers (FRHC). These controllers, shown in fig. 15, can

provide force feedback for the user at the hands.

Fig. 15. Force Reflection Hand Controllers [12]

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While this control setup provides more telepresence than a simple joystick, creating

an even more intuitive device that yields a 1-to-1 correlation in motion between the user

and master robot can increase telepresence even further. A wearable master cobot would

allow for expansion of force feedback to include individual joints of the user’s arm

instead of only imposing forces at the user’s hand. Furthermore, the presence of virtual

constraints via-powered CVT, could help guide Robonaut’s tools.

The author’s design proposed in this thesis will be used in the development of a

master controller for Robonaut. While Robonaut is fully anthropometric in its arm

design, a 3-DOF wearable cobot design will be explored in lieu of a more complex 7-

DOF cobot design.

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CHAPTER 2

Mechanical Design

2.1 Arm Cobot

The arm cobot design created by Dr. Carl Moore, not to be confused with the

wearable arm cobot design discussed in this paper, integrated 3 spherical CVTs with a 3-

DOF manipulator, but suffered problems with backlash and compliance. The wearable

arm cobot design aims to eliminate backlash through the use of cable transmissions while

minimizing device weight and maintaining joint stiffness.

Fig. 16. Wearable Arm Cobot

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The wearable arm cobot design, shown above in fig. 16, will be mated to a new

spherical CVT design currently in development. The previous spherical CVT design

employed polyurethane in-line skate wheels. These softer rubber-like wheels allowed

compliance and creep during CVT operation. This compliance at the CVT is propagated

out to the endpoint of the manipulator and is contraindicative to forming hard, high

quality virtual constraints. The new spherical CVT design will employ metal-to-metal

contact yielding a more controllable system with a compact design and a maximum

sustainable input torque of 5 lb-in.

In the opinion of the writer, the literature concerning cable transmission design is

limited and shallow in exposition. In the following sections the design of a cable

transmission will be discussed in depth including figures and calculations.

2.2 Transmission Ratio Design

2.2.1 Cable Transmissions

Cable and belt transmissions have been widely used in power transmission in which

the belt or cable is run in only one direction. In robotic applications it becomes necessary

to accommodate for both positive and negative torques created at the joint of a

manipulator. In this paper, the cable transmission design will consist of multiple pairs of

capstans and complimentary pairs of cables for positive and negative torque as shown in

the figure below.

Fig. 17. Capstan Pair with Positive and Negative Torque Cables

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Cable transmission design in this paper is approached from 2 directions using an

iterative method. At one end of the transmission is the CVT, which has a maximum slip

torque of 5 lb-in. At the other end of the transmission, the end-effector of the wearable

cobot, is a maximum loading requirement reflecting that of the maximum torque a human

can sustain. After initial calculations from one end of the device the calculations are

iterated back and forth to find a set of variables that satisfy the requirements of a

telerobotic master controller.

2.2.2 Design Parameters

In order to maintain safety in the wearable cobot design the maximum torque a

human can sustain must be reduced to accommodate the 5 lb-in maximum input torque of

the CVT. Only a very general range of maximum sustainable torques is needed as the

CVT can be adjusted to accommodate the user. The transmission ratio for each DOF is

determined by dividing the maximum sustainable user torque by the maximum

sustainable CVT input torque (5 lb-in).

Fig. 18. Experiment Configurations

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In-lab tests were conducted to determine the maximum sustainable joint torques of a

human-male for the shoulder and elbow joints including forearm rotation. Fig. 18 depicts

the experiments performed. The grey dots represent the joint axis that was tested and the

accompanying arrows depict the direction the arm was exerting force or torque.

Experiments 9 and 10 tested forearm torque and are depicted in fig. 18 by a head-on view

of the test subject’s right fist. All test subjects were male graduate students 22-29 years

of age. The experimental data in fig. 18 coincide with the numbers in table 1.

Table 1. Joint Force (Col. 1-8, lb)/Torques (Col. 9-10, lb-in)

Subject

Forearm

Length

Upper

Arm

Length

1

2

3

4

5

6

7

8

9

10

1 13.5” 12” 10 15 18 22 12 15 18 11 21.25 20

2 11.5” 11” 11.5 15 25 25 15 9.5 23 20 16.25 17.5

3 11.75” 11.5” 21 25 25 30 14 18 24 13 15 22.5

4 11.5” 10.75” 12 16 15 25 14.5 11 15 12 17.5 20

To maintain safety for a more generalized range of users, an average was taken for

the maximum sustainable joint torques at the weakest arm orientation. These values are

14 lbs (column 8), 13.62 lbs (Column 1) and 17.5 lb-in (column 9) for the shoulder,

elbow and forearm rotation joints, respectively. When these values are added to the

design target weight of 13 lbs at 12.6 inches from the shoulder, when arm is fully

extended, and divided by the maximum sustainable input torque of the CVT, the

transmission ratio can be found.

The center of gravity for the lower arm is 3.5 lbs at 5 inches from the elbow. The

forces exerted on the end-effector are at 24 inches from the shoulder and 12 inches from

the elbow. The target weight and maximum loadings can be seen in fig. 19 below. The

diameter of the wrist sleeve is 5 in. The transmission ratios for the shoulder, elbow and

forearm rotation are 100:1, 36:1 and 5:1 respectively. Note that the transmission ratio for

the forearm rotation is necessary to maintain joint stiffness rather than to reduce the

forearm torque, this will be further explained in later sections.

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Fig. 19. Cobot Arm CG Location and Endpoint Loading for Shoulder Joint

2.3 Capstan Design and Cable Selection

2.3.1 Design Considerations

Joint stiffness and cobot arm weight are the main considerations during capstan

design and cable selection to create a highly controllable master manipulator. It is

kinematically advantageous to have a very light but very rigid mechanism to maintain the

integrity of virtual constraints.

In the development of the Whole Arm Manipulator (WAM) the equation for

mechanical torsional stiffness was derived [13]. Mechanical torsional stiffness k for a

cable transmission is given by:

2 21*

2 (1 )

N R AEk

NL x N=

+ − (2.1)

The variables in eqn. 2.1 are defined as follows. The cable manufacturer, Carl Stahl

Sava Cable (See App. A), sells cable with a Young’s modulus (E) of 6.3 Mpsi. ‘A’ is the

cross sectional area of the particular cable chosen. The reduction site location ‘x’ and the

transmission length ‘L’ are set equal to each other since speed reduction is done at the

joint. The capstan size ratio (N) is the larger capstan diameter divided by the smaller

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capstan diameter and the driven capstan radius (R) is usually the radius of the larger

capstan in the pair.

For multi-stage transmissions, successive values of torsional stiffness k can be added

similarly to resistors in parallel to find the effective stiffness keff as shown in fig. 20.

Fig. 20. Multi-Stage Transmission and Equation for Adding Stiffnesses

To preserve the integrity of the cables, a few manufacturer suggested guidelines must

be followed. The capstan diameter should generally be at least 25 times the cable

diameter and the maximum dynamic operating load should be no more than 10% of the

cable breaking strength. The design guidelines give a strength percentage according to

variation of capstan diameter to cable diameter ratio as seen in table 2 below. More in-

depth design guidelines regarding mounting procedure and cable selection can be found

in appendix A. Furthermore, to preserve the stability and uniformity of cable

performance there should be a relatively consistent cable line stress for each

transmission.

21

Table 2. Cable Breaking Strength Adjustment

To eliminate backlash the cable transmissions must be pretensioned. The WAM

manipulator uses a pretension of the added static and dynamic cable loadings to prevent

the complimenting cable from going slack under high loading. For example, if a total

maximum torque is 100 lb-in and the capstan it is working on has a 5 in radius, the line

load in the cable will be 20 lbs. This requires that the pretension on each cable (positive

and negative torque) be at least 20 lbs to prevent cable slack as one cable line load will go

to 40 lbs and the other cable’s load will go to 0 lbs as illustrated below in fig. 20. It is

advantageous to set the cable pretension at higher than that of the loading.

Fig. 21. Pretensioning in Capstan Pairs

22

Keeping these guidelines in consideration, only the variables of cable size, capstan

size and transmission ratio remain. Capstan size is chosen based on readily available

material and number of reduction stages as well as aesthetics. The cable transmissions

and their housing were created to be hidden somewhat by the user’s body when viewed

from the front. Cable size is chosen to fulfill the above guidelines and to give an

appropriate stiffness. These calculations are then further iterated to give a reasonable

agreement among the different guidelines.

2.3.2 Loading Design Calculations

The calculations discussed in this section include the calculations for one pair of

capstans and are taken from the final iteration of the shoulder transmission design for the

wearable cobot. The complete calculations for the shoulder, elbow and forearm rotation

joints can be found in appendix B.

In section 2.2.2 the maximum user joint torque was found to be 14 lbs at 24 inches, or

336 lb-in. The target arm weight was 13 lbs at 12.6 inches creating the design target

torque of 163.8 lb-in. When the maximum user torque and the design target torque are

added the total maximum torque T at the shoulder joint is just under 500 lb-in. A 100:1

reduction is necessary to accommodate the CVT input torque of 5 lb-in. This reduction

will be divided among three stages of 2:1, 5:1 and 10:1. Only the first stage reduction of

2:1 will be discussed in detail.

The shoulder capstan diameter was chosen to be 6.25 in. and the complimenting

smaller capstan would have a diameter of 3.125 in. In eqn. 2.1, the capstan size ratio ‘N’

is given by the larger capstan diameter divided by the smaller capstan diameter.

6.25

23.125

inN

in= = (2.2)

23

Now that a shoulder capstan size has been chosen a cable can be chosen. Shoulder

torque ‘T’ is divided by the shoulder capstan radius to determine the cable line loading

‘CL’.

500160

3.125

lb inCL lb

in

−= = (2.3)

The cable chosen must have a breaking strength of 10 times the working load,

therefore a cable of 1600 lb breaking strength or more should suffice. An abridged table

of available cables is shown below in table 3.

Table 3. Sample Listing of Cables for Use in Transmissions

Cables 2124, 2125 and 2126 are all suitable for use with the shoulder capstan but the

best choice is cable 2126 for its 7x19 construction allowing for greater cable flexibility.

An explanation of cable construction can be found in appendix A. This cable also has the

properties of a 1760 lb breaking strength and a diameter of 1/8 in. At this point the cable

breaking strength must be adjusted according to table 2 in section 2.3.1. The minimum

recommended capstan diameter for a cable of 7x19 construction is 25 times the cable

diameter or in this case 3.125 in., the size of the complimenting smaller capstan. The

effective breaking strength must now be reduced to 92% of that stated in table 2.

0.92*1760 1619lb lb= (2.4)

It is now confirmed that the adjusted breaking strength is still 10 times the working

load. The line stress must now be determined for comparison to the line stresses in the

24

other two stages of reduction. Having similar line stresses in a transmission allows for a

more uniform behavior in cable stretch.

Again, the cable loading ‘CL’ is 160 lb and the cross sectional area ‘A’ of a 1/8 in.

diameter cable is 0.0123 in2. The stress ‘S’ is given below in eqn. 2.5.

2

16013040

0.0123

lbS psi

in= = (2.5)

The stresses for the other two stages were 10430 psi and 12430 psi. While the three

stresses are not equal, they are within 80% of each other. Further investigation of this

phenomenon is warranted in future research with particular focus on cable cycle life and

the affect of the different stresses on overall device performance

After having verified the cable and capstan diameter selection, the stiffness for this

stage can be found using eqn. 2.1. The transmission length ‘L’ is 9.66 in., which is

determined by allowing for clearances between capstans and CVT shafts. The driven

capstan radius ‘R’ is 3.125 in. The reduction position ‘x’ is set equal to the transmission

length ‘L’ to maximize stiffness and the young’s modulus ‘E’ for the cables is 6.3 Mpsi.

The rotational stiffness ‘k’ is given below in eqn. 2.6.

2 2 252 *(3.125 ) *0.0123 *6.31

* 1.563*102 9.66

in in Mpsik lb in

in= = − (2.6)

The transmissions for the elbow and wrist rotation are calculated in a similar matter.

Complete calculations can be seen in appendix B.

The overall torsional stiffness keff for the shoulder transmission was found to be

1.049*105 lb-in. The linearized deflection at the end-effector of the cobot arm can be

calculated assuming a rigid arm. The angular deflection ‘D’ can be found by dividing the

total maximum shoulder torque ‘T’ by the effective torsional stiffness ‘keff’. This can be

seen below in eqn. 2.7.

3

5

5004.765*10

1.049*10

lb inD rad

lb in

−−= =

− (2.7)

25

The sine of D is then multiplied by the arm length of 24 in. to yield the linearized arm

deflection (0.114 in.) due to transmission stiffness in eqn. 2.8.

sin( )*24 0.114D in in= (2.8)

An acceptable deflection in the cobot arm was determined by approximating the

deflection in the flesh of a human fist against a tabletop. The writer observed that the

flesh at the bottom of his own fist deforms when pressure is applied allowing for up to

0.25 inches of deflection. While no formal testing was conducted in this area it does

warrant further research to determine a quantification of a ‘good’ virtual constraint metric

for robot-human interaction.

2.3.3 Loading Design Results

The results of the calculations and iterations in finding the transmission specifications

are given below in tables 1, 2 and 3 for each transmission stage.

Table 4. Specification of Shoulder Reduction Stages

Stage A1-A2 A2-A3 A3-A4

Capstan Size Ratio

(inches)

6.25 : 3.125

10.0 : 2.0

10.0 : 1.0

Rotational Stiffness

(lb-in/rad)

1.563 * 105

1.344 * 106

4.186 * 105

Line Stress

(psi)

13040

10430

12430

Table 5. Specifications of Elbow Reduction Stages

Stage B1-B2 B2-B3

Capstan Size Ratio

(inches)

6.25 : 2.0 11.25 : 1.0


(lb-in/rad)

1.2 * 105 7.804 * 10

5

Line Stress

(psi)

12020 12730

26

Table 6. Specification of Forearm Reduction Stages

Stage C1-C2 C2-C3 C3-C4

Capstan Size Ratio

(inches)

5.0 : 2.0

2.0 : 1.0

3.0 : 3.0


(lb-in/rad)

6.034 * 103

1.319 * 103

8.768 * 103

Line Stress

(psi)

8704

8704

190.11

The nomenclature used in tables 4, 5 and 6 coincides with fig. 21 of the entire

wearable cobot design below.

Fig. 22. Wearable Arm Cobot

27

2.4 Cable Wrapping Design

Cable wrapping design requires that a cable spool consistently onto its capstan to

ensure consistent performance. Cable wrapping design includes cable spacing to prevent

scrubbing, supporting the cable on 1/3 of its circumference and consistency in axial cable

travel. These three criteria can be fulfilled through the use of a helical groove for the

cable to spool into.

Scrubbing in cable wrapping is the rubbing of cables as they spool and unspool on a

capstan. This leads to cable wear and loss of cable strength due to cable fatigue

decreased cross-sectional area. Scrubbing can be prevented by cutting a helical groove

for the cable to spool into with a helix height slightly more (~0.005 in) than that of the

cable diameter. The capstans in the wearable cobot design have helical groove cuts that

will support the cable on 1/2 of its circumference.

Axial cable travel is inherent to cable transmissions but seldom addressed in design.

It must be noted that spooling a cable onto a capstan requires that it takes up space in the

axial direction of the capstan. Below, in fig. 22, a capstan spooling a cable onto itself is

depicted. The beginning position is denoted by ‘X0’ and the distance the cable travels

axially is denoted by ‘d’.

Fig. 23. Cable travel in a spooling capstan

28

Consistency in axial cable travel between capstan pairs is crucial in maintaining

consistent cable line tension. Uneven cable travel between 2 capstans forces stretch in

the cable. This stretch, in turn, creates a tension in the cable that will adversely affect

device performance, as the cable tension will become a function of loading and capstan

position. The added cable stress may also shorten cable life by driving the working load

beyond design specifications. In a 1/8 in. cable (sava #2126) stretch on the order of

0.001 in. yields approximately 10 lbs of cable tension. Large amounts of cable stretch are

created by incorrectly mounting capstans or through faulty capstan design.

Take, for example, a capstan pair of 1 inch (capstan 2) and 5 inch (capstan 1)

diameters. They both share a helix of 0.1 inch per revolution. The starting position of

the cable is denoted by the boxed ‘1’ and the final cable position, after one revolution of

capstan 1, by the boxed ‘2’ in figure 23. One revolution of capstan 1 will cause capstan 2

to turn 5 times. Since the helixes of the capstans are not matched according to the axial

travel and capstan diameter the axial cable travel at capstan 2 is 5 times that of capstan 1.

This would cause approximately 0.013 inch of cable stretch over a transmission length of

6 inches. Cable stretch of 0.013 inch will cause very noticeable, if not problematic,

changes in cable tension in all but the smallest of cables

Fig. 24. Uneven Cable Travel in Capstan Pairs

Matching axial cable travel prevents stretching and keeps cable tension consistent

throughout the range of operation; this is achieved by taking the helix of the smaller

capstan and multiplying it by the ratio between the 2 capstans. For example, if a size

29

ratio between capstans is 10 to 1 then every 1 turn on the large capstan will produce 10

turns on the smaller capstan. Since the cable is wrapping and unwrapping from a helix,

the axial travel distance over 1 turn on the large capstan should equal the same axial

travel distance as 10 turns on the smaller capstan. This will yield a matched axial cable

travel preventing cable stretch.

The equation for matching axial cable travel through the respective capstan helixes is

given below. The ratio of the large capstan radius (D1) to the small capstan radius (D2)

multiplied by the small capstan helix height per turn (H2) should equal the larger capstan

helix height per turn (H1).

12 1

2

DH H

D= (2.9)

Please note that the limiting factor in this design is the helix on the smaller capstan as

it has more wrappings than the larger capstan. Therefore it is advantageous to design

capstan thickness starting from the smaller capstan.

2.5 Cable Tensioning Design

Cable transmission design depends on pre-tensioning the transmission cables to

increase stiffness and eliminate backlash [13]. A pre-tensioning method that is simple,

compact and non-destructive to the capstan shafts is desirable. A common method for

smaller operational torques is to sandwich the capstans between a retaining ring and nut

creating friction between the sandwiched capstans to maintain cable tension. The pre-

tensioning of the sandwich capstan design may require 2 people to achieve. The

wearable cobot is designed to accommodate torques of up to 500 lb-in at the shoulder

joint and while the static calculations confirm that the sandwiched capstan design would

support this torque, it is difficult to investigate creep between the 2 capstans.

In the sandwiched capstan method, shown in fig. 23, a ball termination is swaged

onto both ends of the cable. These fittings are placed into the capstan and can be

tensioned using opposing torques created by conventional wrenches via the capstan

30

extensions. At this point nuts are used to create frictional forces between the capstans

that will hold the cable tension. This method has been used in cable tensioning for the

WAM manipulator [14].

Fig. 25. Sandwiched Capstan Tensioning Scheme

In the wearable cobot the cable tensioning design consists of 2 cables, one for each

the positive and negative torques. Each cable is hard connected to the capstans with

fittings. Below is a diagram of the tensioning scheme in fig. 24. In the wrist

transmission the sandwiched capstan tensioning method is used because of the relatively

small capstan sizes and forces.

31

Fig. 26. Capstan Tensioning Scheme

The cable is outfitted with a threaded or ball termination fitting on either end. The

ball termination fits into the small capstan and the threaded termination fitting threads

into a block that fits into the large capstan. A bolt is threaded into the other side of the

threaded block and is used to tighten the cabling. In the next chapter we will verify this

tensioning scheme as well as cable wrapping methods and also verify shoulder joint

stiffness.

32

CHAPTER 3

Results and Conclusions

3.1 Cable Mounting and Tensioning

The guidelines for mounting and tensioning the shoulder transmission are discussed

in this section. These guidelines are applicable to all transmissions designed in this

paper. An isometric view of the shoulder transmission is shown in fig. 27.

Fig. 27. Wearable Cobot Shoulder Transmission

33

The cable used in this transmission must be carefully mounted to avoid damage to

itself. As mentioned in the previous section the cable is held into the capstans by either a

swaged ball fitting or a threaded lug fitting as shown in fig. 28.

Fig. 28. Cable Mounting Points

The ball fitting is held by a hole drilled into the side of the smaller capstan. The

threaded lug fitting is threaded into a block, which is placed into the larger capstan and

tensioned by a bolt.

34

Fig. 29. Cables Spooling into Capstan Grooves

The cable must rest easily within the machined groove on each capstan as shown in

fig. 29. Rhythmic creaking of the cable is an indicator of a cable resting into a groove

that is too small or other mechanical problem. Oiling the cable and groove with a

multipurpose lubricant will help prevent some premature cable wear and also oxidation of

the steel cable.

To create the correct amount of tension, locking pliers and a torque wrench must be

used. Suppose a cable should be tensioned to 10 lbs and it is on a capstan of 10 inches.

The complementing smaller capstan shaft must be held steady with the locking pliers and

the torque wrench must impose a torque of 100 lb-in on the 10-inch capstan shaft.

Plucking the cable and recording the tone produced will indicate the 10 lbs of tension.

35

The transmission stage must then be tensioned via tensioning bolts until the cable

produces that same tone. The tensioning method is explained below.

When tensioning the cable each stage must be tensioned individually and completely

independent of the other stages. This means that if certain stages share common shafts,

such as stage 1 and stage 2, stage 1 must be mounted and tensioned first before stage 2

capstans can even be placed on its respective shafts. This process will allow for the

greatest facility in cable tensioning, as manipulation of key components may be

necessary to achieve the correct cable tension.

To achieve the desired tension a specific process must be followed. Tensioning, i.e.

the turning of the bolt to tension the cable, must only occur at the extreme of capstan

travel. This will allow for greater ease of cable movement as the contact area between

the cable and the groove is minimized. This is achieved by turning the capstan to the

extreme of its travel and then turning the appropriate tensioning bolt. The process is then

repeated for the complimenting bolt by turning the capstan set to its other extreme of

travel.

The tensioning of the cable at the extreme of travel will create a high, local tension

from the large capstan to the initial spooling site of the smaller capstan. When the

capstans are turned back and forth the tension will distribute evenly across the entire

cable. The tensioning process must be repeated several times (4-5 times) to ensure the

appropriate and uniform tension throughout the cable.

3.2 Results

The starting torque for the shoulder transmission was found to be approximately 16.5

lb-in. The linearized deflection of the arm under maximum loading is 0.566 inches.

Empirical testing shows 0.49 inches of this deflection can be attributed to the bending of

the arm. Therefore the linearized deflection due to cable compliance at 24 inches from

the shoulder joint is 0.076 inches.

Shaft A3 suffers from a noticeable amount of deflection when under full loading.

Shaft A3 and shaft A4 bow towards each other due to the loading. This bowing creates a

variable cable tension due to inconsistent transmission length. The cable groove width on

36

the large capstan on shaft A3 was machined narrower by 0.1 inches. This also creates a

variable cable tension due to inconsistent axial cable travel between shafts A3 and A4.

The bearing in shaft A4 contains a foreign object, most likely a small aluminum chip that

produces a rhythmic noise while in use and is likely adversely affecting performance.

Appropriate solutions for all the above mentioned problems are discussed in the section

3.4 Future Work.

3.3 Conclusions

A 3-DOF wearable arm cobot was designed for use as a master controller in

telerobotic operations. A detailed design of the wearable arm cobot is complete at this

time. Its wearable design allows for an increased telepresence in terms of a 1-to-1

correlation in human arm movement. The wearable cobot’s cable driven transmissions

allow joint torques to be suitably reduced for use with CVTs. This design is also the first

to incorporate a wearable mechanism with spherical CVTs.

The shoulder transmission has been built, assembled and tested. Difficulties in

assembly mainly dealt with convenience of disassembly to ease the wrapping of cable.

An alternate mounting method between the capstans and shafts would help to better

accommodate. Further research is warranted to determine an appropriate start torque for

this system. Since the start torque is 16.5 lb-in, the application of 0.688 lbs (at 24 inches

from the shoulder) to start movement will noticeably affect the sensitivity of the cobot. It

should be noted that at the time this paper was written the robot had been assembled for 2

weeks and a break in period of a few thousand cycles should be considered for the

bearings and cables. The deflection due to cable compliance at 24 inches from the

shoulder joint is 0.076 inches. This translates to a mechanical rotational stiffness of

1.58*105 lb-in/rad, approximately 1/3 more stiff than theorized. This can be improved

upon by amending the shaft bowing issues discussed in the previous section.

37

3.4 Future Work

Future work includes completing fabrication and testing of the remaining wearable

cobot. A minor redesign will be implemented to increase the rigidity of the system by

adding a bearing to further support shafts A3 and A4. The bearing on shaft A4 will be

replaced. The large capstan on shaft A3 will be remade to the precise specifications.

Also, lightening of components and the addition of bearings at shafts A3 and A4 may

reduce the start torque. Safety stops will also be designed and placed to protect the user

and to prevent the device from exceeding its limits.

The current design will employ the use of a 6-axis force transducer but alternative

intent sensing measures at the CVT level must be investigated. The development of

adjustable cobot arm length must also be investigated to accommodate a wide variety of

users.

A new mounting method using ShaftlocTM

sleeves should be considered to allow

greater flexibility in capstan mounting. The new all-metal-contact CVT will be

implemented with the new powered cobot control algorithm.

38

APPENDIX A

Sava Cable Catalog

Select Pages from Sava Cable Catalog Pertaining to Design and Cable Selection

51

APPENDIX B

MathCAD Calcations

Stiffness Calculations for Individual Transmissions

58

APPENDIX C

Engineering Drawings

105

REFERENCES

[1] Peshkin, M. A., Colgate, J. E., Wannasuphoprasit, W., Moore, C. A., Gillespie, B.

and Akella, P., Cobot Architecture, IEEE Trans. Robot. Automat., vol. 17, pp. 377–

390, Aug. 2001 (13)

[2] http://lims.mech.northwestern.edu/projects/utla/

[3] Wannasuphoprasit, W., Akella, P., Peshkin, M.A., Colgate, J.E. “Cobots: a novel

material handling technology,” ASME Vol. 98-WA/MH-2, 1998.

[4] Moore, Carl A. “Design, Construction, and Control of a 3-Revolute Arm Cobot,”

Ph.D. dissertation, Dept. Mech. Eng., Northwest Univ., IL, 1999

[5] Schloerb, David W. A Quantitative Measure of Telepresence. Presence:

Teleoperators and Virtual Environments. Vol. 4, no. 1, pp. 64-80. Winter 1995.

[6] Rosenberg, Louis B. Virtual Fixtures: Perceptual Tools for Telerobotic

Manipulation. IEEE Conference Proceedings, 1993, pp. 76-82.

[7] Colgate, J. E. and Brown, J. M., 1994, “Factors Affecting the Z-Width of a Haptic

Display,” Proc. IEEE International Conf. On Robotics and Automation, pp. 3205-

3210.

[8] Colgate, J. E. and Schenkel, G. C., 1997. “Passivity of a Class of Sampled-Data

Systems: Application to Haptic Interface,” Journal of Robotic Systems, 14(1), pp.

37-47.

[9] Faulring, E. L., Colgate, J. E. and Peshkin, M. A. A High Performance 6-DOF

Haptic Cobot. Proc. IEEE ICRA, pp. 1980-1985, 2004.

[10] Heckendorn, F. and Kress, R., “Outline for Large-Scale System Operations and

D&D Report,” U.S. Dept. of Energy, WSRC-TR-2000-00364.

[11] Peters, R. A., Campbell, C., Bluethmann, W. J. and Huber, E. Robonaut Task

Learning through Teleoperation. Proc. IEEE ICRA, pp. 2806-2811, 2003

[12] http://robonaut.jsc.nasa.gov/status/Jul_Robonaut_Status_03.htm

106

[13] Salisbury, K., Townsend, W., Eberman, B. and DiPietro, D. Preliminary design

of a whole-arm manipulation system (WAMS). Robotics and Automation, 1988.

Proceedings 1988 IEEE International Conference, April 1988 Page(s):254 - 260 vol.1

[14] Townsend, William T., “The Effect of Transmission Design on the Force-

Controlled Manipulator Performance,” Ph.D. dissertation, Artificial Intelligence

Laboratory, M.I.T., MA, 1988.

107

BIOGRAPHICAL SKETCH

Jason Yap Chua

Jason Yap Chua was born January 24, 1980 in Jacksonville, Florida. After completing

the International Baccalaureate program at the Stanton College Preparatory School he

attended Florida State University with a Bright Futures Academic Scholarship to obtain

his Bachelor’s Degree in Mechanical Engineering. During his undergraduate studies

Jason worked as a machinist in the FAMU-FSU College Department of Mechanical

Engineering Machine Shop. After his graduation in 2003, he pursued graduate studies at

Florida State University. His research interests are primarily in robotics, wearable

robotics, controls and mechanisms.

design of a wearable cobot - flvc

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