CoMeT Tutorial 1.0-23

CoMeT-Lite Users Guide 1.0 – For academic use only © 2003 Martin Culpepper, Soohyung Kim and Patrick Petri

MIT Precision Systems Design and Manufacturing Laboratory http://psdam.mit.edu

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CoMeT

Compliant Mechanism Tool Users Guide 1.0

HexFlex six-axis compliant mechanism designed using CoMeT [2003 R&D 100 Award]

An academic version of CoMeT-Lite 1.0 is available at http://compliantmechanisms.org

Users guide includes tutorial exercises for CoMeT-Lite 1.0 and following CoMeT modules

● = CoMeT-Lite ■ = CoMeT-Advanced ► = Under development

Edit ● ■

Analyze ● ■

Sensitivity ■

Optimize ■

2D→3D Templates ►

Plasticity ►

Diagnosis ►

Thermal ►

Dynamics ►

Reconfigurability ►



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Table of Contents 1 LICENSE, REGISTRATION, SYSTEM REQUIREMENTS & CONTACTS- 5 -

1.1 License agreement................................................................................................. - 5 - 1.2 Registration ............................................................................................................ - 5 - 1.3 System requirements............................................................................................. - 5 - 1.4 Contact information ............................................................................................... - 5 -

2 INTRODUCTION TO COMET-LITE ........................................................... - 7 - 2.1 CoMeT-Lite as a design tool – Why is CoMeT-Lite needed?.............................. - 7 -

2.1.1 Human-in-the-loop compliant mechanism synthesis….. ............................... - 7 - 2.1.2 The new approach: CoMeT-Lite ........................................................................ - 7 - 2.1.3 Getting the most out of CoMeT-Lite with Tablet PCs...................................... - 8 -

2.2 CoMeT-Lite as a pedagogical tool ........................................................................ - 8 - 2.3 The nature and accuracy of CoMeT-Lite modeling ............................................. - 9 - 2.4 Organization and layout of this document .......................................................... - 9 -

3 EXAMPLE: BAR IN TENSION................................................................. - 10 - 3.1 Starting CoMeT-Lite ............................................................................................. - 11 - 3.2 Initial settings ....................................................................................................... - 11 -

3.2.1 Set units ............................................................................................................ - 11 - 3.2.2 Set material properties .................................................................................... - 12 -

3.3 Define topology, loads and constraints ............................................................. - 12 -

3.3.1 Create nodes..................................................................................................... - 12 - 3.3.2 Create beam elements ..................................................................................... - 13 - 3.3.3 Add constraints ................................................................................................ - 15 - 3.3.4 Define loads ...................................................................................................... - 16 -

3.4 Solve and query mechanism kinematics and mechanics ................................ - 16 -

3.4.1 Probe nodal displacements............................................................................. - 17 - 4 EXAMPLE: CANTILEVER BEAM WITH MULTIPLE LOADS................. - 19 -

4.1 Starting CoMeT-Lite ............................................................................................. - 20 - 4.2 Define topology, loads and constraints ............................................................. - 20 -

4.2.1 Define loads ...................................................................................................... - 20 - 4.3 Solve and query mechanism kinematics and mechanics ................................ - 23 -

4.3.1 Probe nodal displacements............................................................................. - 24 - 5 EXAMPLE: FOUR BAR COMPLIANT MECHANISM ............................. - 26 -

5.1 Starting CoMeT-Lite ............................................................................................. - 27 - 5.2 Initial settings ....................................................................................................... - 27 -

5.2.1 Set units ............................................................................................................ - 27 -



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5.2.2 Set material properties .................................................................................... - 29 - 5.3 Define topology, loads and constraints ............................................................. - 29 -

5.3.1 Create nodes..................................................................................................... - 29 - 5.3.2 Create beam elements ..................................................................................... - 32 - 5.3.3 Add constraints ................................................................................................ - 34 - 5.3.4 Create plates..................................................................................................... - 35 - 5.3.5 Define loads ...................................................................................................... - 35 - 5.3.6 Add centroids ................................................................................................... - 36 - 5.3.7 Remove construction geometry ..................................................................... - 36 -

5.4 Solve and query mechanism kinematics and mechanics ................................ - 38 -

5.4.1 Probe nodal displacements............................................................................. - 38 - 6 ADDITIONAL INFORMATION ................................................................. - 43 -

6.1 Node numbering................................................................................................... - 43 - 6.2 Help functions ...................................................................................................... - 43 - 6.3 Model constraint and topology ........................................................................... - 43 -

7 THE COMET-LITE GUI ............................................................................ - 44 - 7.1 Menu bar ............................................................................................................... - 44 - 7.2 Message box......................................................................................................... - 45 - 7.3 Mode menu ........................................................................................................... - 45 -

7.3.1 Edit mode .......................................................................................................... - 45 - 7.3.2 Analyze mode ................................................................................................... - 47 - 7.3.3 Sensitivity mode............................................................................................... - 49 - 7.3.4 Optimization mode ........................................................................................... - 49 - 7.3.5 Diagnosis mode................................................................................................ - 49 - 7.3.6 Plasticity............................................................................................................ - 49 - 7.3.7 Folded kinematics of 3D compliant mechanisms ......................................... - 50 - 7.3.8 Thermal expansion........................................................................................... - 50 - 7.3.9 Dynamic response ........................................................................................... - 50 - 7.3.10 Reconfigurability .............................................................................................. - 50 -

8 COMET-LITE INSTALLATION ................................................................ - 51 - 8.1 Installing CoMeT-Lite ........................................................................................... - 51 - 8.2 Launching CoMeT-Lite......................................................................................... - 52 - 8.3 Troubleshooting................................................................................................... - 52 -



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1 License, registration, system requirements & contacts CoMeT-Lite (a base installation of CoMeT) was developed by the MIT Precision Systems Design and Manufacturing Laboratory (PSDAM). This user guide is an introduction to the Beta release of CoMeT-Lite 1.0. CoMeT-Lite is furnished under a license (section 1.1) and may be used only in accordance with the terms of this license.

1.1 License agreement Read this license agreement before you use CoMeT-Lite. Downloading CoMeT-Lite software constitutes an agreement on your part to abide by this license agreement. CoMeT-Lite may be used for either academic or evaluation purposes after registration (see next section) and subject to the following terms. CoMeT-Lite may not be used for commercial purposes without explicit written consent from the director of PSDAM. You agree not to reverse engineer, re-create or use any part or whole of the CoMeT-Lite code by itself or in another program, document, or in any other means of information conveyance. CoMeT-Lite comes "as is" with no guarantees, liability or warranties express or implied. PSDAM and MIT will not be liable for damages resulting from the use of CoMeT-Lite or this user guide. The information and software discussed in this document are subject to change without notice. CoMeT-Lite is intended for concept evaluation purposes only. CoMeT-Lite should not be used for development or engineering purposes.

1.2 Registration Registration is required before you use this user guide or CoMeT-Lite. Registered users may access technical support and upgrades. To register provide:

□ Full Name □ Title □ Place of business □ E-mail address

This may be done by emailing the information to: [email protected] .

This information will not be shared beyond PSDAM.

1.3 System requirements Operating system: Windows 2000 or XP recommended Software: Matlab 6, R13 required RAM: Recommended 128 Mb minimum Computer: Tablet PC recommended; CoMeT-Lite will run on laptops and desktops

1.4 Contact information Prof. Martin Culpepper

MIT Precision System Design and Manufacturing Laboratory (PSDAM: http://psdam.mit.edu/)

Phone: 617 452 2395 Fax: 509 693 0833 [email protected]

http://compliantmechanisms.org



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2 Introduction to CoMeT-Lite 2.1 CoMeT-Lite as a design tool 2.1.1 Human-in-the-loop compliant mechanism synthesis…..

Students and practicing engineers generally design compliant mechanisms using this synthesis process:

Create geometryin CAD/FEA

t~10s of minutes

Sketch concepton papert~minutes

Define loads& constraints

t~minutes

Mesh model &analyze

t~10s of minutes

Evaluateresults

t~minutes

Finaldesign

Iteratet~10s of minutes to hours

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The manual (human-in-the-loop) and automated components within the iterative loop may take tens of minutes for simple mechanisms and hours or days for complex mechanisms. For inexperienced users, this process is exhausting and holds little pedagogical value or intellectual reward. Likewise, experienced designers would prefer to spend time creating new designs rather than running CAD/FEA. The real issue to be addressed is not the lack of a good synthesis tool which can better pair the strengths of the designer and the computer. CoMeT was created to address this issue.

2.1.2 The new approach: CoMeT-Lite

CoMeT-Lite is equipped with a GUI which allows designers to define a mechanism’s geometry, boundary conditions and loading conditions via hand sketches. This approach provides a more effective way for the designer (creative engine) and computer (analytic engine) to “converse” about the mechanism and analyze the mechanism. This is accomplished via a GUI that automatically converts the designer’s sketch into matrix equations which are “understood” and analyzed by MATLAB. The GUI converts MATLAB’s analysis back to a sketch (flexed mechanism shape) and numbers (stresses, strains and displacements) which are easily understood by the designer. As a result, the synthesis (or exploratory learning process) process can be completed in minutes rather than hours or days.

Sketch loads &Constraints

t~minutes

Sketch conceptIn CoMeT-Lite

t~minutes

MATLABanalysis

t< 5 seconds

Finaldesign

1 2 3

EvaluateResultst~minutes 4

Iteratet~minutes



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2.1.3 Getting the most out of CoMeT-Lite with Tablet PCs

On a Tablet PC a designer may sketch on screen with a “pen”, thus better emulating pen-paper design.

Analysis & iterationDeformation

Optimize

Stress & and strain

Geometry

Sensitivity

Key boardHand sketch

Boundary conditions

Key boardHand sketch

or

or

A: CoMeT-Lite run on a Tablet PC B: CoMeT-Lite analysis procedure

Figure 1: CoMeT-Lite GUI on a Tablet PC and the CoMeT-Lite analysis procedure

2.2 CoMeT-Lite as a pedagogical tool and research tool Use in the classroom:

CoMeT-Lite was funded in-part through the Microsoft-MIT iCampus project. A main focus of this project was to develop software tools that can be used at MIT to improve learning in science and engineering. CoMeT-Lite was designed for use as:

(1) An exploratory learning tool – The sketching and analysis components enable students to rapidly explore many designs and learn about screw axes (3D), virtual centers of rotation, stress, strain and stiffness. Through exploration, students gain a working sense of compliant mechanism fundamentals.

(2) A project design tool – CoMeT-Lite can be used to enhance learning in students’ compliant mechanism projects. Students may spend more time on the project’s learning goals rather than devoting project time to learning a CAD program and/or an FEA program. This can be done without loosing sight of the important fundamentals of the analysis. CoMeT-Lite is used at MIT (2.000: How & Why Machines Work–psdam.mit.edu/2.000/start.html) by students to design compliant robotic nano-manipulators.

Team 1 Team 2 Team 3 A: 2.000 class project: x-y nano-manipulator B: Students prepare for nano-manipulator contest

Figure 2: Student design project – Nano-manipulator with x-y compliant mechanism



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Use in compliant mechanism research:

CoMeT-Lite has been used at MIT to synthesize 1st order designs of compliant mechanisms for robotics applications and award winning Nanomanipulation equipment. Future development for educational purposes is ongoing under continued Microsoft funding through the MIT iCampus project. Development for research-based applications (modules: 2D→3D templates, plasticity, dynamics, reconfigurability) is ongoing under National Science Foundation grant 0348242, CAREER-Research and Education Plans for Modeling and Design of Fixtures and Six-Axis Manipulators for Nanomanufacturing, awarded by the NSF Nanomanufacturing program.

2.3 The nature and accuracy of CoMeT-Lite modeling CoMeT-Lite is based on linear, isotropic elasticity theory. This method is generally accurate to within 5 % of experimental results for small-moderate mechanism displacements. This level of accuracy is sufficient to identify promising designs for bench-level studies. CoMeT-Lite does not model geometric non-linearities, stress concentrations, stress stiffening or P-∆ effects. CoMeT advanced addresses such issues.

2.4 Organization and layout of this document This user guide is structured in a different manner than traditional user guides. Following this chapter, we jump into tutorial examples that provide hands-on training with the software. These tutorials are followed by a section on helpful hints and best practices, then sections covering CoMeT-Lite commands. The last section in the user guide describes the installation process for CoMeT-Lite.

Sections 3, 4 and 5 contain tutorial exercises which require that MATLAB and CoMeT-Lite be installed on your computer. Sections 3 and 4 demonstrate how to analyze flexible machine elements (bars and cantilevers). Section 5 demonstrates how to perform an analysis on a precision compliant mechanism.

It is also recommended that you browse section 7 before starting the tutorials. Section 7 covers the basics of the CoMeT GUI, commands and program capabilities.

See section 8 for installation instructions.



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3 Example: Bar in tension This is an exercise in modeling a classical, compliant structure (not mechanism). In this example, we show you:

(1) The commands used to complete modeling steps in any analysis

(2) The commands used to complete the example modeling steps [shaded in gray]. Be sure to follow the shaded directions

For your reference the following files are located within the Matlabroot\comet\ directory.

(1) A file containing the completed model (bar-[finished].mat)

(2) A video showing the completion of this example in full (bar.wmv)

Please see section 8.1 for the location and explanation of the Matlabroot directory.

Example: Rod in tension Problem definition

One end of a steel rod is rigidly affixed to a wall while the other end of the bar is subject to force,

Fx. Material Geometry Loading

z x

y

z x

yx

Steel

E = 205 GPa

- Length L = 1.00 m

- Height h = 0.05 m

- Width w = 0.05 m

Fx = 5000 N



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3.1 Starting CoMeT-Lite To start CoMeT-Lite, start Matlab, then type “cometlite” at the Matlab prompt. For more details, see section 8.

3.2 Initial settings Before creating a model, users should set the units and materials.

3.2.1 Set units

One can choose a unit system from the following systems:

□ Inches and pounds □ mm-MPa-g □ SI □ CGS □ British

Be sure to follow the shaded commands on the left for all tutorial exercises

Example commands General commands

Start a new CoMeT file In Edit mode, click on File menu and select New.

Start a new CoMeT file

In Edit mode, click on File menu and select New.

Set unit system to SI

Units

1) Click on the Other button.

2) Click on the Units button.

3) Select SI from the drop down menu.

4) Click on the Change + convert button.

Setting the units system

1) While in Edit mode, click on the Other button.


3) Select the unit system you’d like to use in the drop down menu.

4) Click Change labels to change labels used in the analysis. Click Change+convert to change labels and to convert the values in the present CoMeT model to the new unit system.



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3.2.2 Set material properties

Users may assign pre-set material properties, such as Young’s Modulus, shear Modulus, Poisson’s ratio, yield stress and density by choosing appropriate material types from a material list. Custom values may be keyed in.


Setting material properties to those of steel

Materials

1) Click on the Material button.

2) Select Steel from the drop down menu.

Setting material properties

Using standard materials



3) Select a material from the drop down menu:

- Aluminum

- Steel

- Copper

- Cu-Be

- Silicon

Properties are shown in the text windows.

Using custom material properties



3) Type the appropriate values into the text boxes.

3.3 Define topology, loads and constraints In this step, users build a model for analysis. Clicking the Edit button launches the editor. By default, the Edit mode starts automatically when CoMeT-Lite is launched.

3.3.1 Create nodes

We will not be creating nodes in this example. This will be covered in section 5.3.1.



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3.3.2 Create beam elements


Sketch beams

Theta x

Create

Beams

Rectangular

w and h

1) Click on the Beams button.

2) Click on the Create button.

3) Open the drop down menu and select Rectangular (0)

4) Set theta x =0, w = 0.05, h = 0.05.

As we are working in SI units, the values are assigned in meters.

You will now sketch the start and end points of the bar, the points do not have to be exact, you will move them to the exact location later.

5) Click near (0, 0) in the sketch window to start the beam which will model the rod.

6) Click near (1, 0) in the sketch window to finish the beam.

Sketch beams



3) Open the drop down menu and select the beam type:

- Rectangular cross-section - Circular cross-section - Tapered cross-section and length - Curved

4) Set values for beam parameters:

The x axis is defined along a vector from a beam’s first to last node. The theta x option sets the rotation of a beam about its’ x axis.

5) Click within the sketch window to define the beginning of the beam.

6) Click within the sketch window to define the end of the beam.



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Adjust position of rod endpoints

Enter

Probe

Nodes

1) Click on the Nodes button.

2) Click on the Probe button.

3) Click on first node (near 0,0) in the sketch window.

4) Enter X=0, Y=0 and Z = 0.

5) Press the Update Last button.

6) Click on the second node (near 1, 0) in the sketch window.

7) Enter X=1, Y=0 and Z = 0.

8) Press the Update Last button.

Adjust position of beam endpoints


2) Click Probe button.

3a) Click on the node at the end of the beam and enter the new X, Y, and Z coordinates.

or

3b) Click on the Move button to move beam end nodes by mouse click.



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3.3.3 Add constraints

CoMeT-Lite will only allow nodes that have the following constraint characteristics:

Type Graphic representation

(1) Free to move in all 6 DOF (default) Blue circle

(2) Coupled between beam elements Blue circle at intersection of beams

(3) Grounded to constrain all 6 DOF Black square


Adding constraints

Select

EZ +/-ground

Nodes


2) Click on the EZ +/- Ground button.

3) Select the Toggle radio button (usually selected by default).

4) Ground the node located at [ 0, 0 ].

The node changes from a blue circle to a black square.

Adding constraints

Option 1: EZ +/- Ground button



3) Check the Toggle radio button to tell CoMeT-Lite that you want to toggle the grounded-free state of nodes by clicking on them.

4) Click on nodes to ground or free them.

Use the Probe button



3) Click on the node to be grounded.

4) Check the Grounded check box on the left side of the CoMeT-Lite GUI.



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ExaggeratedNode displacement

3.3.4 Define loads

The magnitude and direction of Force and Moment loads acting upon nodes may be set.


Applying loads

Create

Loads

Force

FxFyFz

Node

1) Click on the Loads button.


3) Select Force from the drop down menu. 4) Enter Fx = 5000, Fy = 0, Fz = 0.

As we are working in SI units, Forces are assigned in Newtons.

5) To apply the load, click on the node located at [1,0].

Applying loads



3) Select Force or Moment from the

drop down menu. 4) Type a magnitude of the desired load in the text box.

5) Click on the node to which the load should be applied.

The head of the vector representing the load is represented in the sketch window as resting on the node it is acting upon.

We now have a fully translatable (so MATLAB can analyze) mechanism sketch:

● Geometry ● Constraints ● Loads

3.4 Solve and query mechanism kinematics and mechanics

Click on the Analyze button to run the analysis. This button is located in the bottom right of the CoMeT-Lite GUI, above the message box.

In addition to the deformation plot, there are several ways to obtain results from the analysis.



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3.4.1 Probe nodal displacements Example commands General commands

Resizing the view and mechanism ampfactor

MainConfigure

Slider

Plot

1) Click on the View button.

2) Click on the Auto scale button to fit the deformed mechanism to the screen.

3) Click on the Main button.

4) Click on the Configure button.

5) Click on the Slider to set the ampfactor to ~ 7500 to 8800.

6) Click on the Plot button to update the view.

Resizing the view and mechanism ampfactor


2) Click on the Auto scale button to fit the deformed mechanism to the screen.


4) Click on the Configure button.

5) Click on the Slider to set the ampfactor to a desired value.

6) Click on the Plot button to update the view.

Checking node displacements

Node

MainProbe node

1) Click on the Probe node button.

2) Click on the grounded (leftmost) node, all displacements and

rotations should be 0.




3) Click on a node to see how it was displaced.



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3) Click on the displaced (rightmost) node.

The displacement of the end node in the x direction is 9.75×10-6

m. This displacement is too small to be of much use in a

compliant mechanism, ~ 10 microns, due to the high tensile

stiffness of the rod. It might however, serve as a good

constraint. Note the other displacements and rotations are zero

as expected.

Stress and reaction forces

Select beam

MainProbe other

1) Click on the Probe other button.

2) Click on the middle of the rod (not on a node) to query the

reaction forces on the rod and stress in the rod.



2) Click on the middle of the rod (not a node) to activate a display which shows the reaction forces on the rod and stress in the rod.

If a stress value is not displayed, click on the Configure button in Analyze mode and check the Compute stresses check box, then repeat steps 1 and 2.

Optional: Save your work 1) Click on File menu, select Save as and provide a file name.

Saving your work

1) Click on File menu, select Save as and provide a file name.

- End of example -



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4 Example: Cantilever beam with multiple loads In this example, we show you:

(1) The commands used to complete modeling steps in any analysis

(2) The commands used to complete the example modeling steps [shaded in gray]. Be sure to follow the shaded directions

For your reference the following files are located within the Matlabroot\comet\ directory.

(1) A file containing the geometry needed to start the exercise (cantilever-[template].mat)

(2) A file containing the completed model (cantilever-[finished].mat)

(3) A video showing the completion of this example in full (cantilever.wmv)

Please see section 8.1 for the location and explanation of the Matlabroot directory.

Example: Cantilever beam in combined loading Problem definition

A combination of loads is placed on a cantilevered beam. One end of the beam is rigidly affixed

to a wall while the other end of the bar is subject to a combination of loads: Material Geometry Loading

z x

y

z x

y

Steel

E = 205 GPa

L = 1.00 m

h = 0.05 m

w = 0.05 m

Fx = 4000 N

Fy = -2000 N

Mz = 1000 N-m



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4.2 Define topology, loads and constraints Example commands General commands

Geometry, units and material The units, materials and constraints are the same as those

defined in the first example. Rather than recreate this file, you

may open a template file which contains the geometry of the

cantilever with the correct units and material properties.

1) Open the File menu.

2) Select the Load option.

3) Browse to the location where you installed CoMeT-Lite.

4) Open the Example_files directory.

5) Select the file cantilever-[template].mat. 6) Click on the Open button.

The file should open in CoMeT-Lite as shown below.

Open an existing file

1) Open the File menu.

2) Select the Load option.

3) Browse to the location of the file.

4) Select the file.

6) Click on the Open button.

4.2.1 Define loads

In the CoMeT-Lite sketch window, Forces are displayed in RED, and Moments are displaced in GREEN. Example commands General commands

Modify view point to prepare for multiple load settings All loads to be applied to the beam do not lie in the x-y view



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plane and therefore can not be seen in the default x-y view. We

will modify the view prior to applying the loads so that we may

see all of the loads when they are applied.

View

Rotate

Free node

Grounded node


2) Click on the Rotate button.

Click in the sketch window and drag/rotate the view until the view

resembles that shown above.

Applying loads Create Fx

Loads

Create

Node

FxFyFz




As we are working in SI units, Forces are assigned in Newtons.

Applying loads




drop down menu.

4) Enter the Cartesian (x, y, z) components of the load to be applied.


The head of the vector representing the load is represented in the sketch window as resting on the node it is acting upon.



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5) To apply the load, click on the node located at (1,0,0).

Create Fy

Loads

Create

Node

FxFyFz

1) Deselect the Create button.


3) Select Force from the drop down menu. 4) Enter Fx = 0, Fy = -2000, Fz = 0.

5) To apply the load, click on the node located at [ 1,0 ].

Note: We could have simultaneously specified Fx and Fy as

components of one load in the same step. We chose to specify

them separately so that the Forces could be viewed in the sketch

window independently and modified independently.

Create Mz



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Node

Loads

Create

MxMyMz

1) Deselect the Create button.


3) Select Moment from the drop down.

4) Enter Mx = 0, My = 0, Mz = 1000.

5) To apply the load, click on the rightmost node located at [1,0].

As we are working in SI units, moments are assigned in Newton-

meters.

We now have a fully translatable (so MATLAB can analyze) mechanism sketch:

● Geometry ● Constraints ● Loads

4.3 Solve and query mechanism kinematics and mechanics Click on the Analyze button to run the analysis. This button is located in the bottom right of the CoMeT-Lite GUI, above the message box.



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In addition to the deformation plot, there are other ways to obtain results from the analysis.



MainProbe node

Node

1) Click on the Main button if it is not already depressed.


3) Click on the leftmost node to verify all displacements and

rotations are 0.

4) Click on the rightmost node to observe the displacements

and rotations. Note that the z rotation at the node is zero, the

rotations due to Fy (-2000 N) and Mz (1000 N-m) have

canceled each other out.




3) Click on a node to see how the mode was displaced.


Select beam

Main

Probe other



2) Click on the middle of the cantilever (not a node) to activate a display which shows the reaction forces on the cantilever and stress in the cantilever.




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2) Click on the middle of the cantilever (not on a node) to

query the reaction forces on the cantilever and the maximum

stress within the cantilever.


Saving your work


- End of example –



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5 Example: Four bar compliant mechanism In this example, we show you:

(1) The commands used to complete modeling steps in any analysis (2) The commands used to complete the example modeling steps [shaded in gray]. Be sure to follow the shaded directions

For your reference the following files are located within the Matlabroot\comet\ directory. (1) A file containing the completed model (fourbar-[finished].mat) (2) A video showing the completion of this example in full (fourbar.wmv)

Please see section 8.1 for the location and explanation of the Matlabroot directory. Example: Four bar compliant mechanism

Problem definition A mechanism is needed to support and guide an optical element through a rotation about its center with low parasitic errors 1. A four-bar compliant mechanism, controlled by an actuation Force F, is suggested as a solution. Maintaining a maximum stress of less than 10% of the yield stress is desired to reduce the kinematic errors due to micro-scale dislocation propagation within the steel.

In this example, you will develop the CoMeT-Lite model of a four bar compliant mechanism (see above) and perform a rapid design check to flesh out the approximate sizes and feature locations/orientations needed to meet the design requirements given in the table below.

Optical element

Base

MechanismClamp

Element center

Force

Screw axis

Link 1

Link 2

Link 3

Link 4

zx

y

Rigid plate

Elementcenter

Material Geometry [All dimension in inches] Force Design requirements

1Parasitic errors: Motions in directions other than intended motions. Our parasitic errors are in x, y, z, θx and θy



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Steel E = 30 Mpsi

σy = 100 ksi

Envelope

Instantcenter

xy

F = ±1 lbf Range: ∆θz ± 50 µradians

Parasitic errors: ∆x, ∆y < 20 µinches


5.2 Initial settings Before creating a model, users should set the units and materials.

5.2.1 Set units

One can choose a unit system from the following systems:

□ Inches and pounds □ mm-MPa-g □ SI □ CGS □ British


Start a new CoMeT file In Edit mode, click on File menu and select New.

Start a new CoMeT file

In Edit mode, click on File menu and select New.

Setting the unit system to inches and pounds

Units

UnitsOther



3) Select inches and pounds from the drop down menu.

4) Click on the Change + convert button if inches and

Setting the unit system

1) In Edit mode, click on the Other button.


3) Select the unit system you’d like to use in the drop down menu.

4) Click Change labels to change labels used in the analysis. Click Change+convert to change labels and to convert the values in the present CoMeT model to the new unit system.



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pounds was not already selected.



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5.2.2 Set material properties

Users can set material properties, such as Young’s Modulus, shear Modulus, Poisson’s ratio, yield stress and density by choosing appropriate material types from the material lists, or by entering custom values.


Setting material properties to those of steel

Steel

100000

OtherMaterial

Using custom material properties


2) Select Steel from the drop down menu.

The yield stress (sigmay) displayed for the default steel properties must be changed to match our application.

3) Type 100000 in the sigmay box & hit the Enter key on your

keyboard.

Setting material properties

Setting custom material properties



3) Type the appropriate values into the respective text boxes.

Setting standard materials

1) Click Other in the object buttons.


3) Select a material from the drop down menu:

- Aluminum

- Steel

- Copper

- Cu-Be

- Silicon

4) Properties are shown in the text windows.

5.3 Define topology, loads and constraints In this step, users build a model for analysis. Clicking the Edit button launches the editor. By default, CoMeT-Lite enters the Edit mode when it is launched. You have been setting material and unit system properties in the Edit mode.

5.3.1 Create nodes

One can create, move and delete nodes. Nodes may be used to define:

(1) The start and endpoint of beams

(2) The vertices of rigid plates

(3) As construction geometry

Here we will create nodes which have two functions:



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(1) Outline the boundary of the mechanism

(2) Provide nodes with which we can make a rigid plate that emulates the rigid clamps and optics


Setting the sketch plane parallel with the x-y plane

ViewStandard

Planar/Iso


2) Click on the Standard button.

3) Click on the Planar/Iso button.

Setting the sketch plane parallel with the x-y plane


2) Click on the Standard button.

3) Click on the Planar/Iso button.

Setting the view zoom scale

5

x:2y:2z:0

View

Zoom


2) Click on the Zoom button.

3) Enter 5 in the Axes range text box to define the limits on the x and y axes.

Setting the view zoom scale


2) Click on the Zoom button.

3) Enter a number in the Axes range text box to define the limits on the viewed axes.

4) Enter the position of a point for the sketch view to focus upon.



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4) Enter x = 2, y = 2, z = 0.

5) Press the Update View button

Note: this process sets the x-y sketch plane at z = 0 and

defines the view center at x = y = 2.

Create nodes to outline the mechanism envelope and instant center position

Create

Nodes

~ (0,0)

~ (3.15, 2.25)

~ (3.15, 0)

~ (0, 2.25)

~ (1.57,1.61)

1) Click on the Node button.

2) Click Create button.

3) Click near four points to define approximate vertices of the mechanism’s envelope: (0,0) (0, 2.25) (3.15, 2.25) (3.15, 0). Vertices (0, 2.25) and (3.15, 2.25) are only used as guides (e.g. construction geometry) to help outline the size of the device. We will later remove the vertices before the mechanism is analyzed.

4) Click near (1.57,1.61) to place a node near the desired instant center of rotation.

There is no need to be hyper-accurate in locating these nodes as we are seeking a 1st order analysis. You can view node locations and move them if they are off the intended position by say more than ~ 0.1 inch.

1) Click on the Move button.

2) Click on the node to be moved, and then click on the new location.

Create nodes

1) Click on the Node button.

2) Click Create button.

3) Indicate the positions of nodes by clicking desired points in the main plot view.



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5.3.2 Create beam elements


Sketch beams

Create

Beams

1st 3rd

Instant center

2nd



3) Select Rectangular (0) from the drop down menu.

4) Set theta x =0, w = 0.1, h = 0.5

As we are working in inches-pounds, the w and h values are assigned in inches.

5) Read the entirety of step 5 before proceeding:

Draw the first link/beam by clicking on the node near (0,0) and then click to end the 1st beam as shown in the figure above. This beam should terminate at about y = 0.97 inches (see figure below for 0.97 dimension) and a line along this beam should intersect the desired instant center (see figure above for example).

6) Read the entirety of step 6 before proceeding

Draw the third link/beam by clicking on the node near (3.15,0) and then click to end the beam near the endpoint of the 3rd beam as shown in the figure above. This beam should terminate at about y = 0.97 inches (see figure below for 0.97 dimension) and a line along this beam should intersect the desired instant center (see figure above for example).

Sketch beams



3) Select the beam type from the drop down menu:

- Rectangular cross-section - Circular cross-section - Tapered cross-section and length - Curved

4) Set values for beam parameters.

The x axis is defined along a vector from a beam’s first to last node. The theta x option sets the rotation of a beam about its’ x axis.

5) Click within the sketch window to define the beginning of the beam.

6) Click within the sketch window to define the end of the beam.



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Envelope

Instantcenter

xy

7) Draw the second link/beam by clicking on the end nodes of the 1st and 3rd links.

Adjust beam endpoints positions (if necessary)

You only need do this if more accurate positioning of beam endpoints is needed. If they are not accurately placed to your liking:


2) Click on the Move button to move beam end nodes by clicking on a node and then clicking on the nodes’ new location.

Adjust beam endpoint positions


2) Click Probe button to click on a beam end node and enter the new X, Y, and Z coordinates.

or

3) Click on the Move button to move beam end nodes by mouse click.



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5.3.3 Add constraints

CoMeT-Lite only allows nodes that have the following constraint characteristics:

(1) Free to move in all 6 DOF (default) Blue circle

(2) Coupled between beam elements Blue circle at intersection of beams

(3) Grounded to constrain all 6 DOF Black square


Adding constraints

EZ+/-Ground

Nodes

1) Make sure the Nodes button is selected.


3) The Toggle radio button should be selected by default. If not, select it. This will enable you to toggle nodes between grounded and free states.

4) Ground the bottom nodes on the 1st and 3rd links/beams by clicking on them. A grounded node is represented by a black, square symbol.

Adding constraints

Free nodes are shown as blue circles while grounded nodes appear as black squares. There are two ways to constrain nodes.

Option 1: EZ +/- Ground button


2) Click on the EZ +/- Ground button

3) Check the Toggle radio button to tell CoMeT-Lite that you want to switch the grounded-free state of nodes by clicking on them.

4) Click on the nodes to be grounded. You can “toggle” a node between grounded and free states by repeated selection of the node.

Option 2: Use the Probe button



3) Click on the node to be grounded.

4) Check the Grounded check box on the left side of the CoMeT-Lite GUI.

5) Click on the Update button.



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5.3.4 Create plates


Adding plates

Create

Plate

Nodes selected

1) Click on the Plates button.


3) Select the three nodes that will form the vertices of the rigid plate.

Note: Depending on how you sketched your mechanism, the nodes you select may not be nodes 5, 6 or 7. It is sufficient to select the nodes indicated in the preceding figure.

Adding plates

1) Click on the Plates button.


3) Select the three nodes that will form the vertices of the rigid plate. You may remove nodes from the plate by selecting the appropriate button.

5.3.5 Define loads


Applying loads

Create

Loads

Forceparameters

1st

2nd

Applying loads




drop down menu. 4) Type the magnitude of the desired load in the text box.


The head of the vector representing the load is always represented in the sketch window as resting on the node it is acting upon.



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As we are working in inches-pounds units, forces are assigned

in pounds.

5) To apply the load, click on the node between the 1st and 2nd

links/beams.

5.3.6 Add centroids

Centroids are added to the vertex of a plate/rigid body to tell CoMeT to analyze the screw kinematics of the plate/rigid body.


Adding centroids

Create

Centroids

1) Click on the Centroids button.


3) Click on the apex of the rigid plate, e.g. the instant center.

A pink triangle is added to indicate the location of the centroid.

Adding centroids

1) Click on the Centroids button.


3) Click on one or more nodes for

which you want to monitor the screw

kinematics.

A pink triangle is added to indicate the location a new centroid.

5.3.7 Remove construction geometry

Before we can have a translatable (so MATLAB can analyze) mechanism sketch, we must remove the “free floating nodes” that were used to define the top of the mechanism’s envelope. These nodes must be deleted before we analyze the model.


Removing the extra nodes Deleting nodes



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Delete

Nodes


2) Click on the Delete button.

3) Click on the top two nodes to delete them.


2) Click on the Delete button.

3) Click on the nodes you wish to delete.



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5.4 Solve and query mechanism kinematics and mechanics Click on the Analyze button to run the analysis. This button is located in the bottom right of the CoMeT-Lite GUI, above the message box.


Optional: Scaling the amplification factor You may wish to scale the ampfactor by moving the slider, then clicking on the Plot button to update the display.

SliderMain

Plot


Probenode

Main

39.8 µradians


2) Click on node at the apex of the plate (see figure above).

Node displacements






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Our “first guess” was pretty close, the parasitic errors in x and y

are less than 2 micro-inches. Unfortunately, the range is 10

micro radians too low. To fix this, we will re-enter Edit mode and

change the cross sections of the beams to reduce the rotation

stiffness of the mechanism.

Modify beam parameters 1) Click on the Edit button to re-enter Edit mode.

Modify

Beams

w

UpdateLast 2) Click on the Beams button.

3) Click on the Modify button.

4) Click on the 1st link/beam.

5) Change the width, w, of the beam from 0.1 to 0.09 inches.

6) Click on the Update Last button at the bottom of the screen.

7) Click on the 3rd link/beam.

8) Change the width, w, of the beam from 0.1 to 0.09 inches.

9) Click on the Update Last button at the bottom of the screen.

Modify beam parameters 1) Click on the Edit button to re-enter

Edit mode.


3) Click on the Modify button.

4) Click on the beam you wish to

modify.

5) Change the beam parameters.

6) Click on the Update Last button at

the bottom of the screen.

Re-evaluate node displacements 1) Click on the Analyze button to re-enter the analysis mode. You may wish to scale the ampfactor by moving the slider and then clicking the Plot button to update the display.

Node displacements






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Probenode

Main

54.6 µradians


3) Click on node at the apex of the plate (see figure above).

From this information, we may make three important

observations:

A. The parasitic errors in x and y are less than 2 micro-inches.

B. The half range is now larger than the 50 µradian requirement.

C. The performance of the mechanism is very sensitive to beam

thickness (we only changed it by 0.010 inches) and achieved

nearly a 25% change in performance. Tolerances on this

dimension will be key.

Checking stresses

Probeother

Main

Stress


2) Click on the middle of the links/beams (not on a node) to

query the reaction forces on the links/beams and maximum


1) Click on the Probe other button

2) Click on the middle of the link/beam (not a node) to activate a display which shows the reaction forces on the link/beam and stress in the link/beam.




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stress within the links/beams.

3) The stress in each beam is less than 10% of the yield stress

of 100 000 psi.

Checking screw theory kinematics

Probe otherMain

Position & orientation

1) Make sure the Probe other button is still selected.

2) Click on the screw axis symbol, represented by an .

The x-y position of the screw axis (instant center) is close

enough to the desired position to prove that this mechanism

concept is a reasonable approach to pursue. We could continue

to improve the accuracy of the analysis through iteration.

Checking screw theory kinematics


2) Click on the screw axis,

represented by an .

The position and orientation of the screw axis are displayed.


Saving your work


- End of example -

This tutorial exercise has shown how CoMeT-Lite can be use to validate mechanism concepts. At this point we end the tutorial, however the reader should realize that the design engineer would likely continue the analysis by improving the node position accuracy, analyzing the stiffness and analyzing the load capacity of the flexure. A reasonable next step would be to re-enter Edit mode and reposition the nodes to be closer to their intended positions, then perform another analysis.



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6 Additional Information 6.1 Node numbering CoMeT-Lite renumbers nodes during analysis, making the grounded nodes the higher number nodes. As a result, Node 1 may no longer be Node 1 after switching into Analyze mode. This renumbering process will be removed from the program in the next release of the software.

6.2 Help functions CoMeT-Lite provides helpful hints and instructions embedded in the GUI. These include:

- Messages posted to the message box in the lower right corner

- Mouse hover messages that appear if the mouse cursor remains over a button, field, or field

label for one second

6.3 Model constraint and topology A few things are not immediately apparent and should be noted below:

- A fully formed or “translatable” model that can be analyzed must contain AT LEAST

a. One beam

b. One grounded node

c. One load

- There are some “topological” requirements:

a. Structure must not be under constrained. Every node must be connected, directly or

indirectly, to ground.

b. Grounded nodes should not be loaded or assigned a centroid.

6.4 Matlab – CoMeT-LITE compatibility CoMeT-Lite has been designed in and tested with Matlab Release 13, version 5.1 (service pack 1). Based upon our experience, it is likely that CoMeT-Lite will work with version 6.5.0.

6.5 Font sizes in CoMeT-Lite In the full version of CoMeT, users may set font sizes and colors. This capability has been restricted in CoMeT-Lite to simplify the installation procedure. If you should find the fonts too small or large, contact Prof. Culpepper to obtain a customized copy of CoMeT-Lite with the proper font sizing for your screen resolution.



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7 The CoMeT-Lite GUI The GUI is broken into the following sections: □ Main menu bar □ Mode options □ Option tools □ Thumb nail view □ Sketch window □ Mode buttons □ Message window

Main menu bar

Mode options

Option tools

Thumb-nail view

Sketch window

Mode buttons

Message window

Figure 3: CoMeT-Lite Graphical User Interface (GUI)

7.1 Menu bar General CoMeT-Lite commands may be issued via menus in the menu bar.

File menu Command Description New Make a new CoMeT file

Load Open a file

Save As Save a file as another file name

Save Save a file

Set Path Set the directory where files are saved by default

Print Print the current window

Exit CoMeT Exit CoMeT-Lite and close the window

View menu Command Description Standard Choose a standard view:

- Planar/ISO: Sketch window = Planar Thumbnail view = Isometric

- Swap views: Swap the sketch & thumbnail views

- View from below: Reverse view point

Re-center Re-center view by clicking on the sketch window

Rotate Rotate view by clicking & dragging in the sketch window

Zoom Zoom in by clicking two corners of a region of interest



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Auto Scale Adjust the view to match the current mechanism size Done Return to main CoMeT-Lite GUI

Preference Menu Command Description Change Material

Change material properties

Change Units

Change unit system

Color scheme

Set CoMeT-Lite GUI color scheme

Selecting Disabled in CoMeT-Lite Save Current Preferences

Save user preferences to CoMeTPrefs.mat.

Reset Preferences to Default

Reset preferences to the original installed default values

Help Menu Command Description CoMeT help CoMeT-Lite help, not available in beta release

About CoMeT

Display information about CoMeT-Lite

7.2 Message box

The message box contains the last fifty helpful hints, directions and alerts.

7.3 Mode menu

The mode menu is used to switch between the Edit mode and the Analyze mode. Comet Advanced has additional modes which are listed in sections 7.3.3-7.3.5. New modes currently under development are listed in sections 7.3.6-7.3.10.

7.3.1 Edit mode

Edit mode is used to create the geometry of a mechanism, specify loads, specify boundary conditions, assign units and assign material properties.



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Options used to create, modify and delete model components are shown in the following figure.

Figure 4: Commands available in Edit mode

The Mode options and corresponding parameters are summarized in the following table. Note: The Create or Modify buttons must be selected in each mode to access the parameters.

Edit mode options and parameters Option Parameters Description

Beam

CoMeT-Lite models four types of beam elements: - Rectangular cross-section - Circular cross-section - Tapered cross-section and length - Curved Different properties are required according to beam type. The theta x option window sets the beam rotation about its x axis (axis defined along a vector from a beam starting point to an ending point). Beams can be created between nodes or by clicking on a start and end point.

Nodes

Nodes are points in space. In CoMeT-Lite, one can define the position of a node by clicking a mouse or by keying in the position. CoMeT-Lite only allows nodes that are: - Free to move in all 6 DOF (Blue dots) - Coupled between beams (Blue dots between beams) - Grounded to constrain all 6 DOF (Black squares)



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Load

Two load types may be applied in CoMeT-Lite: - Forces [Fx, Fy, Fz ] - Moment [Μx, Μy, Μz] In the Edit mode, one can define the magnitude and direction of loads. Loads may only be applied at nodes.

Centroid

A centroid may be assigned to a node to indicate that the user wants CoMeT-Lite to determine the screw kinematics (e.g. instant center) of this point when it analyzes the mechanism. See section 5.3.6 for demonstration and more explanation.

Plate

Users can create plates by picking three or more nodes in the main plot view. Plates are infinitely rigid bodies contained within a compliant mechanism. See section 5.3.4 for demonstration and more explanation.

7.3.2 Analyze mode

The Analyze mode is used to trigger the MATLAB analysis of the mechanism and to study qualitative and quantitative results.

The Analyze mode has two options: Main and View.

The Main option has three tools:

(1) Configure

(2) Probe node

(3) Probe other



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Main option tools Parameters Description

Configure

With the Configure tool, one can set the scale of motion/displacement scaling. This scaling, called ampfactor, is useful for mechanisms where the displacement/motion under load is too small to see at a 1:1 scale. For instance, the ampfactor is set at 8800 in the illustration at left. The beam width is used to define the thickness of the beam grphic displayed in the window. This does not change the geometry of the beam, it only changes the graphics display of the beam.

Probe node

Probe nodes by clicking on them. When a node has been selected, you may view how the node has displaced.

Probe other: Beam probe

The following information can be obtained by probing a beam with the Probe other tool: (1) Reaction forces (2) Reaction moments (3) Stress



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Probe other: Centroid probe ( )

The following information can be obtained by probing a centroid with the Probe other tool: (1) Centroid displacements (2) Relate actuator forces to centroid motions

FA = Vector of actuator forces applied to a mechanism XC = Vector of centroid displacements/rotations

AFC FSX = and ACFinv FXS =

(3) Relate actuator displacement inputs to centroid motions XA = Vector of actuator displacements applied to a mechanismXC = Vector of centroid displacements/rotations

AXC XSX = and ACXinv XXS = Note after clicking on a matrix call button (e.g. the SF button in the illustration at left), the matrix appears at the MATLAB command prompt within the MATLAB GUI, not within the CoMeT-Lite GUI. We are working on a more straight forward means to provide this data within the CoMeT-Lite GUI.

Probe other: Screw axis ( )

The following information can be obtained by probing an instant screw axis or instant center with the Probe other tool:

(1) Location of the instant screw axis/instant center

(2) Orientation of the instant screw axis/instant center In 2D, the instant screw axis is seen as an instant center.

7.3.3 Sensitivity mode

This module is available in advanced CoMeT only. While using this module, one may determine sensitivity of mechanism performance to variations in mechanism geometry and loading. This module is designed primarily for use in tolerance analysis.

7.3.4 Optimization mode

This module is available in advanced CoMeT only. The module is used to optimize various mechanism attributes (mass, deflection, stress, etc…) via multiple input/criteria optimization.

7.3.5 Diagnosis mode

This module is available in advanced CoMeT only. This module is designed to analyze the components of a mechanism and provide design feedback which diagnosis which parts of the mechanism are most and least useful in achieving a desired kinematic goal.

7.3.6 Plasticity

This module is presently under development. The module is being designed to analyze the kinematic and mechanics behavior of mechanisms for which parts of the mechanism must be plastically deformed. For instance, this module may be used to design the compliant mechanisms and flexures that are plastically deformed to obtain alignment. Practical examples may be found in plastic deformation of hinged flexures used in fiber optic alignment and laser cavity alignment.



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7.3.7 Folded kinematics of 3D compliant mechanisms

This module is under development. A major focus of PSDAM research is to develop synthesis tools, manufacturing processes and best practices/rules of thumb that enable the formation of monolithic 3D compliant mechanisms from 2D sheets of material. This module will determine the kinematics of the 3D mechanism and the shape of the 2D template which can be formed or folded (ala origami) to make a 3D mechanism.

7.3.8 Thermal expansion

This module is under development. This module is designed for use in precision mechanism design where the thermal expansion of a compliant mechanism may cause unwanted errors in its kinematic behavior.

7.3.9 Dynamic response

This module is under development. The module is designed to predict the natural frequencies and mode shapes for the 1st, 2nd and 3rd modes. The module is target for use with spatial (6 axis) compliant mechanisms.

7.3.10 Reconfigurability

This module is under development. The module is designed to identify components of the mechanism that may be actively actuated/controlled and thereby actively modify the behavior of the mechanism.



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8 CoMeT-Lite installation CoMeT-Lite Beta does not have an automated installation. Fortunately manual setup is simple and requires less than 10 minutes. The reader should complete the directions exactly as they are laid out. We recommend that you close all programs and log on as Administrator. Installation consists of four steps:

1. Download CoMeT-Lite files

2. Unzip CoMeT-Lite files

3. Create a directory which will house the CoMeT-Lite files

4. Copy CoMeT-Lite files into the directory created in step 3

8.1 Installing CoMeT-Lite MATLAB must be installed before you install CoMeT-Lite. MATLAB should be closed down

during the installation.

Step 1: Download CoMeT-Lite files

Open a web browser and go to http://compliantmechanisms.org. The most recent download and upgrades may be found by clicking on the Design Tools link. Download the file CoMeT-Lite_X.Y.zip to your computer (X and Y represent version numbers), making sure to keep note of the location to which you are saving the file.

Step 2: Unzip CoMeT-Lite files

You will need an unzipping program such as Winzip (winzip.com) to unzip the CoMeT-Lite files from the zip file you downloaded. Unzip the files, keeping note of the location to which you extracted the files. You will need to copy these files in the next step.

Step 3: Create a directory to contain CoMeT-Lite files

Create a directory called “comet” within the MATLAB program or Matlabroot directory. For example, if MATLAB is installed in c:\software\matlab\, then the Matlabroot directory is c:\software\matlab.

Step 4: Copy CoMeT-Lite files

Copy all CoMeT-Lite files and folders you unzipped in step 2 to the comet directory created in step 3.



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8.2 Launching CoMeT-Lite 1. Start MATLAB

2. Change the working directory to the directory where the CoMeT-lite files were copied

3. Type “cometlite” at the MATLAB command prompt

A new window showing the CoMeT-Lite GUI will appear. You may then start using CoMeT.

8.3 Troubleshooting We recommend the following after installation:

1) Reboot the computer

2) Log on as Administrator and launch CoMeT-Lite, verify the CoMeT-Lite software runs properly

3) Log off the Administrator account

4) Log on with your user account and verify the CoMeT-Lite works properly

If CoMeT-Lite works when you are logged on as Administrator and does not work properly when you are logged on with another user account, you may need to set the security permissions on the Matlabroot directory and the comet directory to allow your user account to read/write to these folders. See windows help for instructions on how to do this.

Should you have other types of problems with this installation, please erase the installation, reboot the computer and retry the installation. If you are unable to complete the installation, email Prof. Culpepper ([email protected]) with a detailed description of the problem/error messages.



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– Final page of document –



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Compliant Mechanism Tool

Documents

CoMeT Tutorial 1.0-23