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Page 1: © 2012 Maplesoft, a division of Waterloo Maple Inc. , a ... › demo › streaming › ASEE... · © 2012 Maplesoft, a division of Waterloo Maple Inc. A CYBERNET group company Presenters

© 2012 Maplesoft, a division of Waterloo Maple Inc. , a CYBERNET group company

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© 2012 Maplesoft, a division of Waterloo Maple Inc. A CYBERNET group company

Presenters

Tim Vrablik

Associate Product Manager, MapleSim

Academic, Maplesoft

Scott Williamson

American Society for Engineering Education

Dr. Venkat Krovi

Professor, Mechanical and Aerospace

Engineering, SUNY Buffalo

Dr. James Andrew Smith

Biomedical Engineering Stream Coordinator,

Ryerson University

Presenters

Moderator

Dr. Thomas Doyle

Professor, Electrical and Computer

Engineering, McMaster University

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© 2012 Maplesoft, a division of Waterloo Maple Inc. A CYBERNET group company

Tim Vrablik

Associate Product Manager

MapleSim Academic

Maplesoft

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• Increasing class sizes, decreased funding

• Keeping curricular materials up-to-date with technology and industry requirements

• Trade-offs

– Theory vs. Practice

– Open vs. Closed Ended Problems

– Individual vs. Group Evaluation

– Traditional Lectures vs. Active Classrooms

Challenges to Engineering Education

Depth

Bre

adth

Current curriculum

Feasible region

Technology

Industry

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Prevailing Practice

Code snippets in text books

Industry-standard tools, massive learning curves and complexity

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Prevailing Practice

Code snippets in text books

Industry-standard tools, massive learning curves and complexity

Are we teaching concepts or software techniques?

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Pedagogical goal

Concepts ∙ Science ∙ Math ∙ Requirements ∙ Systems ∙ Theory

Models ∙ Virtual Simulation ∙ Visualization ∙ Parameters ∙ Design An effective bridge between

theoretical concepts and

realistic design applications

Experiments ∙ Validation ∙ Reality ∙ Intuition ∙ RT simulation

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Dr. Thomas Doyle

Professor, Electrical and Computer

Engineering

McMaster University

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Educational Techniques for the Next-Generation of Engineers:

Transforming the Freshman ‘Cornerstone’ Design Course Through Modeling and

Simulation

Dr. Thomas E. Doyle, P.Eng. Dept. of Electrical and Computer Engineering & Engineering 1 Program

McMaster University

Hamilton, Ontario, Canada

ASEE-Maplesoft Webinar Tuesday, May 29, 2012

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McMaster Engineering 1

• Engineering-1 Team

– Faculty members and program

– Teaching Professors

– Instructional Assistant Interns

• Freshman Engineering Class

– Common first year

– In 2011we had 1150 students in year 1

– 74% have no background in CAD solid modelling

– 99%+ have no experience is system modelling

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Motivation & Pedagogical Framing

• Engagement and Learning

– Capstone-style experience for freshmen (Cornerstone)

– Directed dissection - retrofit with specific design target

– Innate curiosity = better engagement

• Teaching vs. Demonstrating Design

– Traditional vs. Current

– Form vs. Function

– Closing design loop

• Spark Intellectual Curiosity

– Common experience elements

– Teach students to ask Engineering-type questions

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Fundamental Elements of New Course

• Introduce and follow complete design process in 12-week course

• Enhance core objectives with discussion and design of simple mechanisms

– Lectures on theory, simple mechanisms, and simulation

– Solid & System Modelling teaching in lab; Hand sketching and modeling calculations in tutorial

– Lab & tutorial assessment bi-weekly

• Team Project & Course Competition

– Directed dissection for mechanism retrofit with specific design target

• Use modeling and simulation to

– Allow iterative verification of design

– Validate final design

• Modeling:

– Form - solid modelling using Autodesk Inventor

– Function - system modelling using Maplesoft MapleSim

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Gearing Basics

• D – Pitch Circle Diameter

• z – Number of Teeth

• m – Module

• i – Gear Ratio

D

m z

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Directed Dissection Project

• Example - Floppy Drive – Each group has different input motor speed

– Ideal output linear speed of 0.0625 m/s for the read-head

• Example - CDROM Drive – Each group has different input motor speed

– Ideal output linear speed of 0.120 m/s for the read-head

You have recently been hired by company XYZ Mechanisms to work in a small

team of engineers. Your team’s first assignment is to modify the design of a

company product due to previously used components being unavailable. Your team

must first research how the product mechanically operates and then proceed with

your own retrofit design. However, before XYZ's CEO will approve the design

change, your team must model the system and validate your new design’s

functionality.

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The Design Process Problem

Statement

Problem Definition (or Framing) 1. Clarify objectives 2. Establish metrics for objectives 3. Identify constraints 4. Revise problem statement

Conceptual Design 5. Establish functions 6. Establish requirements (function specs) 7. Establish means for functions 8. Generate Design Alternatives 9. Refine and apply metrics to design alternatives 10. Choose a design

Preliminary Design 11. Model and analyze chosen design 12. Test and evaluate chosen design

Detailed Design 13. Refine and optimize chosen design 14. Assign and fix design details

Design Communication 15. Document final design

Documentation for Final Design (Report, Drawings, Models, etc.)

Reference: Dym and Little, “Engineering Design”, third edition.

Verification

Final Design

Validation

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Design Iteration

Hand Calculations Solid Modelling (Autodesk Inventor’s

Design Accelerator Tool)

Simulation and System Modeling (MapleSim)

D

m z D – Pitch Circle Diameter

z – Number of Teeth

m – Module

i – Gear Ratio

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The following three graphs (next page) validate the proposed gear train design. A brief

description of each is given below:

1. Figure 6 is a graph of the input angular velocity. This value (23963 RPM) is the exact angular

velocity of the motor provided by XYZ Mechanisms.

2. Figure 7 is a graph of the read-head displacement against time. Its amplitude is 26mm and it

varies linearly with time, as expected.

3. Figure 8 is a graph of the read-head linear velocity against time. Its amplitude is 0.1625m (to 4

decimal places), again as expected.

9

Fig 5: 3D MapleSim gear train model

Example Results: CDROM Retrofit Using Provided Gear Modules

Design Validation in MapleSim

The gears for the proposed gear train design were created in Autodesk Inventor, and the CAD

files exported out to MapleSim for validation. Figure 4 shows the 2D MapleSim schematic of the

validation model used to test the output linear speed and displacement:

Figure 5 (next page) shows the full 3D model, constructed from the CAD gear models,

corresponding to the above schematic:

8

Fig 4: 2D schematic of the validation model

10

Fig 6

Fig 7

Conceptual & Hand Calc. Solid Modelling

Simulation and System Modelling

2012 Team 2-031: N. Bandiera, A.

Mekic, and B. Kakwani

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Example Results: CDROM Retrofit Using Student Designed Gear Modules

2012 Team 2-053: K. J. Arbour and S. Berry

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Results

• Success in teaching the design process (vs. demonstration)

• Closed the design loop with immediate verification and validation

• Clear engagement from students across disciplines

• Successfully used student innate curiosity to enhance materials

• Improved cohesion of theory and practice between lecture, lab, and tutorial

• Encouraging to see first year students wanting to know more about system modeling and asking more Engineering-like questions

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Discussion and Further Work

• MapleSim has allowed instructor to shift the traditional Design & Graphics approach from focus on part form to system function.

• Higher Education Quality Council of Ontario (HEQCO – http://www.heqco.ca) has contracted a study of this technology enhancement for delivering the type of course.

• Adding 3-dimensional printers in September 2012 for the study of student experiential learning.

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Resources & Contact

• Available from my website:

– Lecture materials

– Example Cornerstone project specification

– Link to iTunesU lecture support videos

– Link to MapleSim spur and worm modules

• My coordinates:

– Thomas E. Doyle

[email protected]

– http://www.ece.mcmaster.ca/~doylet

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Dr. James Andrew Smith

Biomedical Engineering Stream

Coordinator Ryerson University

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The Benefits of Using a Dynamic Modeling Software Package in EE

Courses

James Andrew Smith, PhD, P.Eng.

Dept. of Electrical & Computer Engineering

Ryerson University

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Overview

• Context: 3rd Year EE Undergrad Course

• Inductive Learning Paradigm

• Why a New EE Tool?

• Examples

– Sine-driven Resistor

– OpAmp

– Motor + OpAmp

• Conclusions

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Teaching: ELE 604 Sensors & Measurement

• 3rd Year EE Course

• Introduction to

– Robotics

– Microsystems

• First taste of open-ended design

– Sensing goals

– Microcontrollers

– Support electronics

• Sensors

– Accelerometers

– Stain Gauge Load Cell

– Switches Sensors

Microcontrollers

Bridges

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ELE604 Learning Objectives

• Typical of Accredited Engg. Programs (CEAB/ABET)

• Design

– Use technical knowledge, design methodology, and appropriate design tools and related resources;

– Distinguish between different design steps and carries out steps; Analyze/evaluate progress of design.

• Use of Engineering Tools

– List current tools for analysis, simulation, visualization, synthesis, and design, and is competent in using them; Understand the accuracy/limitations of tools and verifies the results’ credibility .

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Educational Theme: Inductive Learning

• Learn rules by observing phenomena

– Given a phenomenon what was the model?

– Constructivist

–Generate knowledge through interaction

– Push students to explore

• As opposed to Deductive Learning

– Given model, what is the phenomenon?

– Cookbook labs

– Canned examples

– Standard method

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Why a New EE Tool?

• Existing Tools – PSPICE & Multisim

– Simulink® & MatLAB®

• What’s the problem? – Can’t see “under the hood”

– Hard to tie analytic models to numeric solutions.

• Enter MapleSim… – Common elements there

– Intuitive GUI

– Output underlying equations

*MATLAB® and Simulink® are a registered trademark of The MathWorks Inc.

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Ex. 1: Sine-driven Resistor

• How to layout system

• Modify input

• Run simulation

• View results

• Create equations

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Ex. 2: The Inverting OpAmp

• A fundamental circuit in EE and BME

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Op-Amp teaching methods

• Deductive Method (Traditional)

– Tell students the OpAmp “Golden Rules”

– Solve sample circuits by hand

• Lots of potential for error

– Check with SPICE and in labs

• Inductive Method (New)

– Draw schematics & simulate

– Extract equations

– Do equations match behaviour?

– Check in labs

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Step 1 – Draw the Circuit

• Include a Probe at the output

– Give measurand a recognizable name (“ProbeVolt”)

– You’ll use it later

Images: http://en.wikipedia.org/wiki/File:Digital_Multimeter_Aka.jpg, http://en.wikipedia.org/wiki/File:Resistors_color_code.jpg, http://en.wikipedia.org/wiki/File:Lm356.jpg , http://en.wikipedia.org/wiki/File:9V_matchstick-1.jpg

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Step 2 – Observe Behaviour

• Numerical Simulation in MapleSim

– Just like Simulink® in MatLAB®

• What is the analytical model? Read on…

-17.5 volts

*MATLAB® and Simulink® are a registered trademark of The MathWorks Inc.

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Step 3 – Generate Equations

• Add Equation Attachment

• Maple window opens

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Step 3 – Equations (cont’d)

• Select Main subsystem

– “Load Selected Subsystem”

• Manipulate Parameter Names

– Optionally rename 2nd col. of Parameters

– “Reassign Equations”

• View Equations

– May need to enter some Maple commands.

– Don’t Panic.

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Step 3 – Equations (cont’d)

• Find “use the GetEquations command directly”

– Erase all the red text and replace with 2 commands:

1. Link back to the MapleSim model:

A := MapleSim:-LinkModel():

2. Search for the equation which defines the “ProbeVolt” output:

A:-GetEquations('output' = definitions, 'params' = all, 'filter' = {ProbeVolt})

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Step 3 – Equations (cont’d)

R1R = Resistance of R1 R2R = Resistance of R2

Create link to the OpAmp Model in MapleSim What are the equations?

Make parametric

Search for the output (defined earlier) with filter

output

V = input voltage

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The Result Reinforces Learning!

• Software confirms what is in the book. • Familiarity: similar form is good.

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Ex. 3: Multi-Domain EE & MecE

• Multi-domain problems are possible, too

• DC motor (left) + OpAmp (right)

etc…

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Conclusions

• Multi-domain applications – MapleSim beats single-domain SPICE

– MapleSim GUI is as easy as Simulink®’s

• Inductive Learning – MapleSim has an advantage

– Better learning of model after observation due to equation generation

• Changing tools is never easy – Requires some effort

– I still export to Excel & Matlab to process data

*MATLAB® and Simulink® are a registered trademark of The MathWorks Inc.

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Acknowledgements

@Maplesoft: Ted, Tom, Gilbert, Tim, Graham and Derek

@Ryerson: BioRRG group, ELE604 students,

& Ryerson Design Chairs

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Venkat Krovi, PhD

Associate Professor,

Automation, Robotics and Mechatronics Laboratory

Mechanical and Aerospace Engineering,

SUNY Buffalo

[email protected]

http://mechatronics.eng.buffalo.edu

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Venkat Krovi

Research Interests Research Highlights

• Lifecycle treatment (design, analysis, implementation and verification) of smart, mechanical and mechatronic systems.

• Research Thrusts (a) Multi-robot Cooperative

Payload Transport

(b) Haptic Device Design

(c) Mediated Teleoperation;

(d) Haptic Rehabilitation

(e) Distributed real-time simulation/control of systems.

Professional Activities

• Founding Chair, ASME DSCD Robotics TC

• General Conference Chair, ASME International Design Engineering Technical Conferences, IDETC 2014.

• Member, Conference Activities Board and Industrial Activities Board, IEEE Robotics and Automation Society.

• Associate Editor, IEEE Transactions on Robotics (2012-2015)

• Past Technical Editor, IEEE/ASME Transactions on Mechatronics

• Past Associate Editor, ASME Journal of Dynamic Systems and Control

• M&R Conf. Chair, IDETC 2010

• Finance Chair, IROS 2014, ICRA 2012, ICRA 2012 & CASE 2010.

Honors

• NSF CAREER 2004

• 2000 Petro-Canada Young Innovator, McGill University

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Agenda

• Creation of Self-Paced MapleSim Tutorials to enhance a robotics course – 2010 ASME IDETC Conference, Aug. 16-18 2010 &

– ASEE Computers in Education (Special Issue on Robotics Education)

• Model-Based Control for Control Education. – 2010 Annual ASME DSCC Conference, Sept 12-15 2010 &

– ASEE Computers in Education (Special Issue on Robotics Education)

• Generation of Vehicle Dynamics Equations-of-Motion with Varying Fidelities. – 2007 ASME IMECE Conference.

• EOM Generation, Analysis, and Simulation for Complex Parallel Manipulators (Hexapod, HD2)

– 2010 ASME IDETC Conference, Aug. 16-18 2010 & 2011 ASME IDETC Conference, Aug. 28-31 2011

EDU

CA

TIO

N

RES

EAR

CH

Acknowledgments: Hrishi Shah, Sumit Tripathi, Anand Naik, Leng-Feng Lee, Xiaobo Zhou, Srikanth Kannan Madusudanan Sathia Narayanan, Seung kook Jun, Suren Kumar, Priyanshu Agrawal

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Role of Automated Symbolic

Generation of Equations of Motion in

Mechanisms and Robotics Education

Education

Publication H. Shah, S. Tripathi, L-F. Lee, and V. Krovi, "Role of Automated Symbolic Generation of Equations of Motion in Mechanism and Robotics Education,“ Proceeding of ASME 2010 International Design Engineering Technical Conferences, Montreal, Quebec, Canada, August 15-18, 2010. Shah, H. L., Tripathi, S., Lee, L.-F., and Krovi, V., “Role of Automated Symbolic Generation of Equations of Motion to Enhance Robotics Education", ASEE Computers in Education Journal, July-September 2010, Vol. I, No. 3, pp. 2-20 (WINNER OF 2010 HARDENS-SIMONS BEST JOURNAL PAPER AWARD).

1

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Education

• Self-paced MapleSim tutorials to aid in learning of kinematics and dynamics concepts in a robotics course.

• Not familiar with either theory /formulations or the tools .

• Linkage between Traditional Analytical and Automated Symbolic approaches

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Education

• Phased Introduction

– Simple Examples: Pendulum

– Intermediate examples: Double Pendulum/Fourbar

– Complex Examples: 3-RRR, 3PRR etc.

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Tutorials – Phase 1

Fx,Fy v/s t y v/s x

ω v/s θ θ v/s t Pendulum

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Tutorials – Phase 2

Fourbar

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Tutorials – Phase 3

Platform Center Active joints Passive joints

Platform Point Platform Point Platform Point

3RRR – MapleSim simulation

3PRR – MapleSim simulation

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Tutorials – Phase 3

3RRR – MapleSim EOM extraction

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Role of Automated Symbolic

Generation of Plant Models

in Control Education

Education

Publication S. Tripathi, H. Shah, L-F. Lee, V.N. Krovi, "Role of Automated Symbolic Generation of Plant Models in Control Education", Proceedings of 3rd Annual ASME Dynamic Systems and Control Conference, Cambridge, MA, September 13-15, 2010. Shah, H. L., Tripathi, S., Lee, L.-F., and Krovi, V., “Role of Automated Symbolic Generation of Equations of Motion to Enhance Robotics Education", ASEE Computers in Education Journal, July-September 2010, Vol. I, No. 3, pp. 2-20 (WINNER OF 2010 HARDENS-SIMONS BEST JOURNAL PAPER AWARD).

2

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Rotary Inverted (Furuta) Pendulum

• Spatial two link/two revolute system – Multivariable

– Nonlinear

– Under-actuated

– Naturally unstable

– Benefits from model-based control

• Available commercially – Quanser control experiment

Traditional Method Using Maplesim/Maple

2

1 {0}{1}

1 1( , )L m

2 2( , )L m

{2}

{3}

2

1

x axis

z axisy axis

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Rotary Inverted (Furuta) Pendulum

• “One-semester” independent study led to an MS Thesis

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Furuta Pendulum: Implementation

Overall MapleSim model

Simmechanics model with MapleSim controller

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Study of Vehicle Dynamics Modeling

Fidelity in Haptic Steer-by-Wire Driving

Simulators

Research

Publication Naik, A.P., Lee, L-F., and Krovi, V., “Study of Vehicle Dynamics Modeling Fidelity on Haptic Collaboration in Steer-by-Wire Systems,” Proceedings of the 2007 ASME International Mechanical Engineering Congress and Exposition, IMECE2007-41908, Seattle, WA, November 11 -15, 2007.

3

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Research: Haptic Driving Simulator

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Research: Haptic Steer-by-wire w/ varying modeling complexity

• Musculoskeletal Simulation Based Optimization of Rehabilitation Programs. – 2006 IEEE International Workshop on Virtual Rehabilitation.

• Musculoskeletal Simulation-based Parametric Study of Optimal Gait Frequency in Biped Locomotion. – 2008 IEEE/RAS-EMBS International Conference on Biomedical Robotics and

Biomechatronics

• Virtual Musculoskeletal Scenario-Testing Case-Studies. – 2008 IEEE/EMB Virtual Rehabilitation

• Rehabilitation Program Refinement Using Virtual Musculoskeletal Simulations – IEEE Transactions on Robotics, Special Issue on Rehabilitation Robotics.

® ®

*MATLAB ® and Simulink® are a registered trademark of The MathWorks Inc.

Build Model in MapleSim.

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Research: Haptic Steer-by-wire w/ varying modeling complexity

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Parallel Manipulators

Modeling and Analysis

Research

- Hexapod (MapleSim)

- High Definition Haptic Device (MapleSim)

.

4

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Research: Hexapod

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Research: Hexapod

® ®

*MATLAB ® and Simulink® are a registered trademark of The MathWorks Inc.

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Research: Hexapod

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Research: Hexapod

1 1 1 2 2 3 3 4 4 5 5 6 6[ , , , , , , , , , , , , , , , ]q s ax ay az a b a b a b a b a b a b 1 2 3 4 5 6 1 1 2 2 3 3 4 4 5 5 6 6[ , , , , , . , , , , , , , , , , , , , , ]q s s s s s s ax ay az a b a b a b a b a b a b

Various formulations possible

1 1 2 2 3 3 4 4 5 5 6 6[ , , , , , , , , , , , , , , , , , ]q xe ye ze ax ay az a b a b a b a b a b a b 1 2 3 4 5 6 1 1 2 2 3 3 4 4 5 5 6 6[ , , , , , , , , , , , , , , , , , , , , , , , ]q xe ye ze s s s s s s ax ay az a b a b a b a b a b a b

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Research: Hexapod

Simulation Without Gravity Simulation With Gravity

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Research: High Definition Haptic Drive

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Research Interests

• Lifecycle treatment (design, analysis, implementation and verification) of smart, mechanical and mechatronic systems.

• Research Thrusts (a) Multi-robot Cooperative

Payload Transport

(b) Haptic Device Design

(c) Mediated Teleoperation;

(d) Haptic Rehabilitation

(e) Distributed real-time simulation/control of systems.

Professional Activities

• Founding Chair, ASME DSCD Robotics TC

• General Conference Chair, ASME International Design Engineering Technical Conferences, IDETC 2014.

• Member, Conference Activities Board and Industrial Activities Board, IEEE Robotics and Automation Society.

• Associate Editor, IEEE Transactions on Robotics (2012-2015)

• Past Technical Editor, IEEE/ASME Transactions on Mechatronics

• Past Associate Editor, ASME Journal of Dynamic Systems and Control

• M&R Conf. Chair, IDETC 2010

• Finance Chair, IROS 2014, ICRA 2012, ICRA 2012 & CASE 2010.

Honors • NSF CAREER 2004

• 2000 Petro-Canada Young Innovator, McGill University

Thank You

http://mechatronics.eng.buffalo.edu

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Appendix

Extra slides

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Rotary Inverted (Furuta) Pendulum

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Furuta Pendulum (Cascaded Control Model)

20 22 24 26 28 30-0.2

-0.1

0

0.1

0.2

0.3

Time(sec)

Radia

ns

Motor Angle (1)

Pendulum Angle(2)

20 22 24 26 28 30-4

-2

0

2

4

6

8

Time(sec)

Vots

Control Voltage

0 2 4 6 8 10-0.1

-0.05

0

0.05

0.1

Time(sec)

Radia

ns

Motor Angle (1)

Pendulum Angle(2)

0 2 4 6 8 10-3

-2

-1

0

1

2

Time(sec)

Vots

Control Voltage

Input-Output Linearization code

Simulation Results

Overall Simulink® real-time model

Real-time run results

*MATLAB® and Simulink® are a registered trademark of The MathWorks Inc.

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Verification with CAD/SimMechanics Simulation

Virtual Reality Simulation SimMechanics Model Simulated with Input-Output Linearization Controller

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Testing with MATLAB® Real-Time Workshop

20 22 24 26 28 30-4

-2

0

2

4

6

8

Time(sec)

Vots

Control Voltage

20 22 24 26 28 30-0.2

-0.1

0

0.1

0.2

0.3

Time(sec)

Radia

ns

Motor Angle (1)

Pendulum Angle(2)

2 2

1 1

1 2 1 2

345.08, 35.44

0.20, 0.08

,

p d

p d

p p d d

K K

K K

K K K K

*MATLAB ® and SimMechanicsTM are a registered trademark of The MathWorks Inc.

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Research: Parallel Manipulator – Stewart Platform

®

*MATLAB® and Simulink® are a registered trademark of The MathWorks Inc.

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Research: Parallel Manipulator – Stewart Platform

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Furuta Pendulum: Automatically Generated Equations

Difference Between Hand Coded Lagrangian Modeling and MapleSim generated Mass Matrix

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Tim Vrablik

Associate Product Manager

MapleSim Academic

Maplesoft

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Maplesoft Education Solutions

Syst

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Eq

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Comprehensive application domains

Advanced analysis capabilities

Multidomain Modeling and Simulation Platform

Advanced Analysis Platform

Exp

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Sen

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Des

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P

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Maplesoft Education Solutions

MapleSim is a truly unique physical modeling platform:

• Built on a foundation of symbolic computation technology

• Makes available all of the complex mathematics involved in the development of engineering models

• Multidomain systems, multibody systems, plant modeling, control design

• Leverages the power of Maple to take advantage of extensive analytical tools

• Engineering models have an intimate connection to the underlying physics

• Systems-level equations easily available to students

Syst

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Multidomain Modeling and Simulation Platform

Advanced Analysis Platform

Exp

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Sen

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Des

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P

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Maplesoft Education Solutions

MapleSim leverages the advanced analysis capabilities of Maple:

• Maple has the world’s best symbolic and numeric solvers, making your models run extremely fast

• Knowledge capture - Interactive documentation

• High-level programming language with robust MapleSim API

Syst

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Multidomain Modeling and Simulation Platform

Advanced Analysis Platform

Exp

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Maplesoft Education Solutions

MapleSim and Maple work with your existing toolchain:

• Modelica 3.1 import/export

• MatLAB®/Simulink® import/export

• Excel connectivity

• LabVIEW and Veristand export

• dSpace export

• CAD: Solidworks, NX, Inventor

• Code generation: C, C#, Fortran, VB Sy

stem

-lev

el

Equ

atio

ns

Vib

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Op

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Multidomain Modeling and Simulation Platform

Advanced Analysis Platform

Exp

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Sen

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Des

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P

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Dyn

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*MATLAB® and Simulink® are a registered trademark of The MathWorks Inc.

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Conclusion

What if students could confidently answer the questions…

• What is design? What is engineering?

• How does modeling and analysis help engineers design better, safer products?

• How would you even start to design something as complex as a space ship?

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Questions?

w w w. m a p l e s i m . c o m

w w w. m a p l e s o f t . c o m / s u b s c r i b e