autodesk's vex® robotics curriculum unit 15: linkages · 2 autodesk's vex robotics unit...

1

Autodesk's VEX® Robotics Curriculum

Unit 15: Linkages

2 ■ Autodesk's VEX Robotics Unit 15: Linkages

Overview

In Unit 15, you learn about linkages: why they are used and how they are designed. You build yourown linkage to use with a drivetrain and a gripper from previous units, improving on overall robotdesign. Design process and findings are also communicated.

The concepts behind linkages have countless real-world applications. In STEM Connections, we posequestions regarding a pair of vise grips that make use of an adjustable four-bar linkage system. Aftercompleting the Think and Build Phases, you see how those concepts come into play in the real world.

Unit Objectives

After completing Unit 15: Linkages, you will be able to:

■ Describe the primary use for linkages and determine uses for linkages in a robot design.■ Use Dynamic Simulation in Autodesk Inventor Professional to analyze four-bar linkage

mechanisms.■ Apply the knowledge gained in the Unit 15: Linkages - Think Phase to design and build a linkage.■ Understand the advantages of linkage designs.

Prerequisites and Related Resources

Related resources for Unit 15: Linkages are:

■ Unit 1: Introduction to VEX and Robotics.■ Unit 2: Introduction to Autodesk Inventor.■ Unit 4: Microcontroller and Transmitter Overview.■ Unit 5: Speed, Power, Torque, and DC Motors.■ Unit 6: Gears, Chains, and Sprockets.■ Unit 12: Object Manipulation■ Unit 13: Rotating Joints

Key Terms and Definitions

The following key terms are used in Unit 15: Linkages:

Term

Definition

Four-BarLinkage

Or simply a 4-bar or four-bar, is the simplest movable linkage. It consists of fourrigid bodies (called bars or links), each attached to two others by single jointsor pivots to form a closed loop. Four-bars are simple mechanisms common inmechanical engineering machine design and fall under the study of kinematics.

Joint A link between two rigid components, such as parts or subassemblies. A jointapplies force from the first component on the second component.

Overview ■ 3

Term

Definition

Linkage Designed to convert some input motion into a different output motion, it typicallyconsists of a series of rigid links. Each link has one or more joints that rotate freely,connecting the links. Typically, one link is fixed and cannot move, and one link isdriven in some input motion.

Mechanism An assembly with one or more degrees of freedom in specific components. Amechanism is also called a dynamic assembly.

Simulation A process by which the mathematical relationships between various parts ofmechanisms are used to emulate or predict physical relationships and their effects.

Trace A graphical representation of the path followed by a point on a mechanism.

Required Supplies and Software

The following supplies and software are used in Unit 15: Linkages:

Supplies

Software

VEX Classroom Lab Kit Autodesk® Inventor® Professional 2010

One of the drivetrains built in Unit 9: DrivetrainDesign 1 > Build Phase or Unit 10: DrivetrainDesign 2 > Build Phase

Gripper built in the Unit 12: ObjectManipulation > Build Phase

Notebook and pen

Work surface

Small storage container for loose parts

One soda can


Academic Standards

The following national academic standards are supported in Unit 15: Linkages.

Phase

Standard

Think Science (NSES)■ Unifying Concepts and Processes: Change, Constancy, and Measurement; Form and

Function■ Physical Science: Motions and Forces■ Science and Technology: Abilities of Technological Design Technology (ITEA)■ 5.8: The Attributes of Design Mathematics (NCTM)■ Algebra Standard: Understand patterns, relations, and functions.■ Measurement Standard: Understand measurable attributes of objects and the

units, systems, and processes of measurement.■ Communication: Communicate mathematical thinking coherently and clearly to

peers, teachers, and others.■ Connections: Recognize and apply mathematics in contexts outside of

mathematics.

Create Science (NSES)■ Unifying Concepts and Processes: Form and Function■ Physical Science: Motions and Forces■ Science and Technology: Abilities of Technological Design Technology (ITEA)■ 5.8: The Attributes of Design■ 5.9: Engineering Design■ 6.12: Use and Maintain Technological Products and Systems Mathematics (NCTM)■ Numbers and Operations: Understand numbers, ways of representing numbers,

relationships among numbers, and number systems.■ Algebra Standard: Understand patterns, relations, and functions.■ Geometry Standard: Use visualization, spatial reasoning, and geometric modeling

to solve problems.■ Measurement Standard: Understand measurable attributes of objects and the

units, systems, and processes of measurement.

Overview ■ 5

Phase

Standard

Build Science (NSES)■ Unifying Concepts and Processes: Change, Constancy, and Measurement; Form and

Function■ Physical Science: Motions and Forces■ Science and Technology: Abilities of Technological Design Technology (ITEA)■ 5.8: The Attributes of Design■ 5.9: Engineering Design■ 6.11: Apply the Design Process Mathematics (NCTM)■ Algebra Standard: Understand patterns, relations, and functions.■ Geometry Standard: Use visualization, spatial reasoning, and geometric modeling

to solve problems.■ Numbers and Operations: Compute fluently and make reasonable estimates■ Measurement: Understand measurable attributes of objects and the units,

systems, and processes of measurement.■ Measurement: Apply appropriate techniques, tools, and formulas to determine

measurements.■ Connections: Recognize and apply mathematics in contexts outside of

mathematics.■ Problem Solving: Solve problems that arise in mathematics and in other contexts.■ Problem Solving: Apply and adapt a variety of appropriate strategies to solve

problems.


Phase

Standard

Amaze Science (NSES)■ Unifying Concepts and Processes: Change, Constancy, and Measurement; Form and

Function■ Physical Science: Motions and Forces■ Science and Technology: Abilities of Technological Design Technology (ITEA)■ 5.8: The Attributes of Design■ 5.9: Engineering Design■ 6.11: Apply the Design Process Mathematics (NCTM)■ Algebra Standard: Understand patterns, relations, and functions.■ Geometry Standard: Use visualization, spatial reasoning, and geometric modeling

to solve problems.■ Numbers and Operations: Compute fluently and make reasonable estimates.■ Communication: Communicate mathematical thinking coherently and clearly to

peers, teachers, and others.■ Connections: Recognize and apply mathematics in contexts outside of

mathematics.■ Measurement: Understand measurable attributes of objects and the units,

systems, and processes of measurement.■ Measurement: Apply appropriate techniques, tools, and formulas to determine

measurements.■ Problem Solving: Solve problems that arise in mathematics and in other contexts.■ Problem Solving: Apply and adapt a variety of appropriate strategies to solve

problems.

Think Phase ■ 7

Think Phase

Overview

This phase describes characteristics of and common applications for linkages.

Phase Objectives

After completing this phase, you will be able to:

■ Describe the primary use for linkages. ■ Determine uses for linkages in a robot design.


Related phase resources are:

■ Unit 5: Speed, Power, Torque, and DC Motors.■ Unit 6: Gears, Chains, and Sprockets.■ Unit 12: Rotating Joints.■ Unit 13: Object Manipulation.


The following supplies are used in this phase:

Supplies

Notebook and pen

Work surface


Research and Activity

Linkages are designed to convert input motion into a different output motion. A linkage typicallyconsists of a series of rigid links. Each link has one or more joints which rotate freely, connecting thelinks together. Typically, one link is fixed and cannot move and one link is driven in some input motion.Linkages are a fundamental part of machine design because of their ability to create such a widevariety of output motions and their ability to alter the path, velocity, and acceleration of the input.Very precise and somewhat complicated motions can be designed using a simple linkage design.Linkage motions are extremely repeatable. Linkages are all around us in the world. A simple linkage found on a pair of vice grips is shown here.

The second picture shows the linkage at the other end of its motion. This is a linkage with four links;each link has two joints and they are connected in a closed system. This is one of the most commontypes of linkage system.

Think Phase ■ 9

An example of a more complex linkage is shown here:

Four-Bar Linkages

The simplest and one of the most common linkage types is the four-bar linkage. This is a closed-looplinkage system that can provide a wide variety of motion types. The most basic type of four-bar linkageis one in which the links are equal length and parallel to each other. You focus on this linkage type forthe rest of this unit.


An example of a four-bar linkage in which opposing links are parallel and of equal length is shownhere:

In the above example of a four-bar linkage, the link on the left side is the fixed link. This fixed link istypically attached to the robot structure. One of the diagonal links is the driven link. The output linkis the link at the far right. Some sort of object manipulator is mounted on the output link. When thelinkage travels through its motion, the output link remains parallel to the fixed link as shown.

Think Phase ■ 11

This type of motion is useful for any application in which you want the object manipulator to stay inthe same orientation as the robot arm moves. Some examples of this linkage are shown:

The above example uses two four-bar linkages; each side of the claw is a four-bar linkage. These areuseful because the tip of the claw remains in the same orientation while the claw opens and closes.

The above robot utilizes a four-bar linkage to deploy its tools. The tools remain parallel to the floor at all timesduring their deployment.


This robot uses four-bar linkages for its front suspension.

Varying Motion

By modifying the lengths of the links in the four-bar linkage, it is possible to create very differentmotions. This is extremely useful for robot design. Imagine needing a robot that can pick up a cup ofwater, lift it up without spilling, and then pour it out once it reaches over the height of a bucket. Thismotion is possible by using a modified four-bar linkage.

Try playing with linkage lengths and experiment to find the optimal motion for your application.

Create Phase ■ 13

Create Phase

Overview

In this phase, you review four-bar linkages. Using Dynamic Simulation, you analyze two differentmechanisms.

The completed exercise

Phase Objectives


■ Use Dynamic Simulation to analyze four-bar linkage mechanisms.

Prerequisites

Before starting this phase, you must have:

■ A working knowledge of the Windows operating system.■ Completed Unit 1: Introduction to VEX and Robotics > Getting Started with Autodesk Inventor.■ Completed Unit 2: Introduction to Autodesk Inventor > QuickStart for Autodesk Inventor.


Technical Overview

The following Autodesk® Inventor® tools are used in this phase: Icon

Name

Description

ConstructionMode

Is the environment for modifying your model.

OutputGrapher

Displays graphs and numerical values of all the input and output variablesduring and after a simulation. The Output Grapher contains a toolbar, abrowser, a time steps pane, and a graph window. Also, shortcut menushave content based on the location of the cursor when you right-click.

Trace Creates a graphical representation of the path followed by a point on amechanism.

Publish toStudio

Activates the Studio envirnoment so the current simulation results can berecorded in either a realistic or an illustrative style of animation.

RenderAnimation

Uses assembly constraints and parameters as animation input. You cananimate the same mechanistic movement you are designing in yourproduct.


The following software is used in this phase:

Software

Autodesk Inventor Professional 2010

Create Phase ■ 15

Exercise: Analyze Mechanisms In this exercise, you review four-bar linkages. UsingDynamic Simulation, you analyze two differentmechanisms.

The completed exercise

Open the File 1. Make IFI_Unit15.ipj the active project file. 2.

Open Drag_Link.iam. It is important to notethat the length of 1 + 4 is not greater than 2 + 3.

3. Drag bar 2 to review the motion of the four-bar

linkage. Undo to return the mechanism to itsoriginal position.

Start Dynamic Simulation You use Dynamic Simulation to analyze productsunder real-world conditions without having to buildphysical prototypes. In this section of the exercise,you determine the motion of the four-bar linkage. 1.

On the Environments tab, Begin panel, clickDynamic Simulation.

2. If required, click No to close the dialog box. 3.

Review the browser. The assembly constraintsare automatically converted into joints.

4. On the Simulation Player, click Run or Replay

the Simulation. No parameters are applied tothe mechanism, so there is no motion.

5.

On the Simulation Player, click ConstructionMode.


6.

In the browser, under Standard Joints, right-click Revolution:6. Click Properties.

7.

On the dof 1 (R) tab, click Edit Imposed Motion.

8.

Select the Enable Imposed Motion check box.

9.

Click the arrow beside Input Grapher. ClickConstant Value.

10. Enter 300 rpm. 11.

Click OK. Review the joint axes and direction ofrotation.


the Simulation. The mechanism moves for onesecond. In this example, bars 2, 3, and 4 havecontinuous motion.

13. In the browser, click Revolution:2. Review the

location of the joint. 14.

On the Results panel, click Output Grapher.

15.

Under Standard Joints, expand Revolution:2 >Accelerations. Select the A [1] check box.

Create Phase ■ 17

16.

Review the Output Grapher. The acceleration ofthe joint is displayed.

17.

In the Output Grapher window, double-click onthe graph. A vertical line is displayed and themechanism moves to the matching position.

18. On the keyboard, press the forward or back

arrow keys to cycle the mechanism. Note theposition of the mechanism and the position ofthe line on the graph.

Create Traces Dynamic Simulation can create a trace of thetrajectory path and velocity and/or accelerationvectors in the graphics window by activating theOutput Grapher and setting up the traces you wantdisplayed. In this exercise, you trace the path of twojoints on the mechanism. 1.

On the Output Grapher toolbar, click Add Trace.

2.

In the graphics window, select the corner of thejoint between bars 2 and 3.

A sphere is displayed at the location.

3. Click Apply. The trace is displayed.


4.

Repeat this workflow for the joint between bars3 and 4.

5. Click Cancel. Since you have already run a

simulation, the traces are displayed. 6.

On the Simulation Player, click Rewind to theBeginning of the Simulation.

The trace is no longer displayed. 7.

On the Simulation Player, click Run or ReplaySimulation. You can now see the motion path ofthe two joints.

8. Close the Output Grapher. 9.

On the Simulation Player, click ConstructionMode.

Analyze a Second Mechanism In this section of the exercise, you analyze a secondmechanism to determine the motion. 1.

Open Crank_Rocker.iam. It is important to notethat the length of 2 + 3 is not greater than 3 + 4.

2.

On the Environments tab, Begin panel, clickDynamic Simulation.

3. If required, click No to close the dialog box. 4.

Review the browser. The assembly constraintsare automatically converted into joints.

Create Phase ■ 19

5.

In the browser, under Standard Joints, right-click Revolution:2. Click Properties.

6.

On the dof 1 (R) tab, click Edit Imposed Motion.

7.

Select the Enable Imposed Motion check box.

8. Click the arrow beside Input Grapher. Constant

Value should be selected. 9. Enter 60 rpm. You will be creating an animation

of this mechanism, so you are setting a lowvalue.

10.

Click OK. Review the joint axes and direction ofrotation.

11.

On the Simulation Panel, enter 3 for Final Time.


the Simulation. The mechanism movesfor three seconds. In this example, bar 2has continuous motion. Bars 3 and 4 haveoscillating motion.

13. In the browser, click Revolution:5. Review the

location of the joint. 14.

On the Results panel, click Output Grapher.

15. Under Standard Joints, expand Revolution:5 >

Accelerations. Select the A [1] check box. 16.

Review the Output Grapher. The acceleration ofthe joint is displayed.

17. In the Output Grapher window, double-click

the graph. A vertical line is displayed and themechanism moves to matching position.


18. On the keyboard, press the forward or back

arrow keys to cycle the mechanism. Note theposition of the mechanism and the position ofthe line on the graph.

Use Traces 1.

On the Output Grapher toolbar, click Add Trace.

2. In the graphics window, select the corner of

the joint between bars 2 and 3. A sphere isdisplayed at the location.

3.

Click Apply. The trace is displayed.

4.

Repeat this workflow for the joint betweenbars 3 and 4.

5. Click Cancel. 6.

On the Simulation Player, click Rewind to theBeginning of the Simulation.

The trace is no longer displayed.

7.

On the Simulation Player, click Run or Replaythe Simulation. You can now see the motionpath of the two joints.

8. Close the Output Grapher. 9. Do not return to the construction environment.

You must be in the simulation environment tocreate the animation.

Create an Animation Dynamic Simulation creates parameters for InventorStudio that make the creation of an animation muchsimpler. In this section of the exercise, you create astudio animation. 1.

On the Animate panel, click Publish to Studio.

2.

On the Animation Timeline, click AnimationOptions.

3.

Under Length, for Seconds, enter 5.

4. Click OK.

Create Phase ■ 21

5.

On the Animation Timeline, drag the slider to 4seconds.

6. In the browser, expand Animation Favorites. 7.

Right-click Simulation_Timeline. Click AnimateParameters.

8. In the Animate Parameters dialog box, under

Action, for End, enter 300. 9. Under Time, click Specify. 10. For Start, enter 1. For End, enter 4. 11. Click OK. 12.

On the Render panel, click Render Animation.

13. On the Output tab, under Time Range, click

Entire Animation. 14. Select the Launch Player check box. 15.

Click Open an Existing Folder.

16. For File Name, enter Crank_Rocker. 17. Click Save. 18. Click Render. 19. Click OK. The animation is created. This may

take a few minutes.

20. Close the player when the animation is

finished. 21. Close all windows. 22. Close the file. Do not save changes.


Build Phase

Overview

In this phase, you design and build a linkage to lift a soda can without spilling its contents.

Phase Objectives


■ Apply the knowledge gained in the Unit 15: Linkages > Think Phase to design and build a linkage. ■ Use your knowledge of geometry to calculate the shape of the linkage and to plot out the

resulting range of motion.


Before starting this phase, you must have completed:

■ Unit 15: Linkages > Think Phase.


■ Unit 1: Introduction to VEX and Robotics.■ Unit 4: Microcontroller and Transmitter Overview.■ Unit 5: Speed, Power, Torque, and DC Motors.■ Unit 6: Gears, Chains, and Sprockets.■ Unit 12: Object Manipulation.■ Unit 13: Rotating Joints.



Supplies

VEX Classroom Lab Foundation Kit

One of the drivetrains built in Unit 9: Drivetrain Design 1 > Build Phase or Unit 10: Drivetrain Design2 > Build Phase

The gripper built in the Unit 12: Object Manipulation > Build Phase

Notebook and pen

Work surface

Build Phase ■ 23

Supplies

Small storage container for loose parts

One soda can

Optional: Autodesk Inventor Professional 2010

Activity

Design and Build a Linkage

In this activity, you design and build a linkage to lift a soda can without spilling its contents. You useyour previously designed gripper to grasp the soda can. You then mount the linkage to a drivetrainof your choice. This robot will then be used in the Amaze Phase to place the soda can on a stack oftextbooks. Your goal is to successfully place the can on the highest possible stack of textbooks withoutspilling it.

1.

In your notebook, brainstorm different linkages that could be used to lift the soda can. Anexample of a four-bar linkage is shown in the following image.

When designing your linkage, you will need to consider many factors; some of which include:


■ What range of motion is needed from the linkage?■ How far can the soda can tilt before its contents are spilled?■ What type of gear reduction should be used to make sure it can lift the weight of the gripper

and the can?■ How fast should the linkage rotate?■ How will the gripper attach to it?■ How much reach does the arm need?■ How/where will the linkage attach to the drivetrain?

Work as professionals in the engineering and design fields by leveraging the powerof Autodesk Inventor to explore potential solutions through the creation and testing of digitalprototypes. Note: Come to class prepared to build and test your best ideas! Team members can download afree version of Autodesk Inventor Professional to use at home by joining the Autodesk StudentEngineering and Design Community today at www.autodesk.com/edcommunity.

2. Based on your criteria, choose a design and start building! 3. Attach your gripper to your completed linkage. 4. Once your linkage is complete, hook it up to a Microcontroller and test out the functionality.

Make improvements as you see fit. Pay careful attention to the range of motion generated. 5. Mount the entire linkage to the chosen drivetrain. 6. Plug motors and servos into the appropriate ports in the Microcontroller. Test your linkage with a

transmitter to make sure everything is functioning correctly. 7. Move on to the Amaze Phase and get ready for your upcoming challenge!

Amaze Phase ■ 25

Amaze Phase

Overview

In this phase, you use your robot from Unit 15: Linkages > Build Phase to place a soda can on thehighest possible stack of textbooks without spilling the contents of the can.

Phase Objectives


■ Explain the advantages of linkage designs. ■ Modify your design on the fly for improved results.


Before starting this phase, you must have:

■ Completed Unit 15: Linkages > Think Phase. ■ Completed Unit 15: Linkages > Build Phase. ■ An assembled single-jointed arm from the Unit 13: Rotating Joints > Build Phase attached to the

gripper created in the Unit 12: Object Manipulation > Build Phase that is attached to a drivetrain ofyour choice.


■ Unit 1: Introduction to VEX and Robotics.■ Unit 4: Microcontroller and Transmitter Overview.■ Unit 5: Speed, Power, Torque, and DC Motors.■ Unit 6: Gears, Chains, and Sprockets.■ Unit 7: Advanced Gears.■ Unit 8: Friction and Traction.■ Unit 12: Object Manipulation.■ Unit 13: Rotating Joints.



Supplies

VEX Classroom Lab Kit

The robot built in the Unit 15: Linkages > Build Phase


Supplies

Notebook and pen

Work surface

3’ x 3’ of open space

Five to fifteen textbooks

Evaluation

Soda Can Stack Challenge

In this phase, you use your robot from Unit 15: Linkages > Build Phase to place a soda can on a stackof textbooks without spilling the contents of the can. The goal is to place the soda can on the highestpossible stack of textbooks.

1. Fill a soda can with water.2. Place your robot from the previous phase on the ground behind the can.3. Place one textbook in front of the can.4. Using your robot’s gripper, grab the soda can.5. Using the robot’s linkage, slowly lift the soda can.6. Gently attempt to place the soda can on the textbook without spilling any of the water from the

can.7. Each time you successfully place the soda can on the stack of books without spilling it, add

another textbook to the stack and try again.8. Continue adding textbooks until you’ve gone as high as you possibly can!

Engineering Notebook

In your engineering notebook, calculate the theoretical maximum height that your linkage can reach.

■ Were you able to successfully place a soda can at that height without spilling it? If not, what

design factors prevented this from happening?. ■ If you were to redesign your robot to repeat this challenge, what feature(s) would you allow for

more reliable placement? ■ What feature(s) would you add to allow for placement on higher stacks?

Presentation

Present your design and potential improvements to the class. Pick the most unique feature of yourdesign and explain it to the class. How did you come up with this idea?

STEM Connections ■ 27

STEM Connections

Background

Vise grips are useful tools because the jaws can be adjusted to close in parallel around different sizesurfaces. Additionally, adjustments can be made to vary the amount of force exerted on the closingjaws as they grip an object.

Science

Traditionally, the material used in the manufacture of vise grips is steel.

1. Why do you think steel is a good choice of material?2. Can you describe any disadvantages of using steel as the primary material for vise grips?3. Can you think of some new materials that can be incorporated into the design of vise grips to make

them more effective, more durable, and easier to use?

Technology

The surface of the vise grip jaws are serrated.

1. What are the advantages of this surface design?2. Are there changes that can be made to the design of the jaw to accommodate gripping fragile

objects?3. Can you think of examples from nature where a serrated jaw design is used to improve efficiency?


Engineering

As shown in the image, vise grips are based on a four-bar linkage system. The vise grips depicted havea maximum gripping range of approximately two inches.

1. What engineering changes can you make to increase the distance that the jaws can open and

close?2. What engineering changes can you make to increase the amount of force that can be applied at

the jaws?3. Can you think of engineering changes that would make it easier and more comfortable for a

person using the vise grips to maximize the force applied at the jaws?

Math

A 12-inch wide x 12-inch long x 4-inch deep flat-bottomed wire basket is attached as the movinglink on a four-bar linkage system like the one shown in the Build Phase. Each of the two long parallellinks is 24 inches long as measured from the center of their pivot points. In a manufacturing plant,assembled vise grips are placed in a basket and moved from a starting position on the right througha 180-degree arc and then unloaded from the basket when they get to the left side. As the parts aremoved from right to left, they pass through a spray stream of powder-coating material (similar tospray paint) for final finishing before they are packaged and shipped.

1. Calculate the horizontal distance that the basket travels over the 180-degree arc.2. If the motor operating this linkage assembly is running at five rpms with a full load, how much

time does it take to move through a 180-degree arc to transport the basket from the right side tothe left side?

3. If one basket load holds 12 vise grips, how many vise grips can be powder coated in one hour?

autodesk's vex® robotics curriculum unit 15: linkages · 2 autodesk's vex robotics unit...

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