ME451 Kinematics and Dynamics

of Machine Systems

IntroductionSeptember 2, 2014

Dan NegrutUniversity of Wisconsin-Madison

Quote of the day: "The way to be happy is to like yourself and the way to like yourself is to do only things that make you proud.“ - Mark S. Lewis, professor, UT-Austin

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Overview, Today’s Lecture…

Discuss Syllabus Discuss schedule related issues Quick overview of what ME451 is about

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Instructor: Dan Negrut Polytechnic University of Bucharest, Romania

B.S. – Aerospace Engineering (1992)

University of Iowa Ph.D. – Mechanical Engineering (1998)

MSC.Software Product Development Engineer 1998-2005

University of Michigan Adjunct Assistant Professor, Dept. of Mathematics (2004)

Division of Mathematics and Computer Science, Argonne National Laboratory Visiting Scientist 2004-2005, 2006, 2010

University of Wisconsin-Madison, Joined in Nov. 2005 Research Focus: Computational Dynamics (Dynamics of Multi-body Systems) Established the Simulation-Based Engineering Lab (http://sbel.wisc.edu)

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ME451 – Fall 2014

Class time: 09:30AM – 10:45AM [ Tu & Th ] Room: 1153ME Contact:

Office 2035ME Phone 608 890-0914 E-Mail negrut@engr.wisc.edu

Other people involved with ME451 ADAMS-related questions: Justin Madsen (jcmadsen@wisc.edu) MATLAB-related questions: WoongJo Choi (wchoi26@wisc.edu) Assignment grader: Luning Fang (lfang9@wisc.edu)

Office Hours: Monday / Wednesday 2:30PM – 3:30PM Meeting outside office hours is fine, call or email to make sure I’m in

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Textbook

Edward J. HaugComputer Aided Kinematics and Dynamics of Mechanical Systems: Basic Methods(Allyn and Baker, 1989)

Book is out of print

Author provided PDF copy of the book, available for download at course website http://sbel.wisc.edu/Courses/ME451/2014/

On a couple of occasions, the material in the book will be supplemented with notes

We’ll cover Chapters 1 through 6 (a bit of 7 too)

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Course-Related Material

Handouts (slides and additional notes) will be printed out and provided before each lecture

Slides (pdf) as well as additional notes (pdf) for each lecture made available online at course website http://sbel.wisc.edu/Courses/ME451/2014/

I plan to also upload audio recording of each lecture in case you miss class or want to listen again to segments of a lecture

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Course-Related Material

Homework solutions will be posted at Learn@UW

Grades will be maintained online at Learn@UW

Syllabus available at http://sbel.wisc.edu/Courses/ME451/2014/ Updated as we go, will change to reflect current progress Shows topics we cover Homework assignments Exam dates and deadlines for projects

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Grading

Homework 40% Exams

Midterm 1 7.5% Midterm 2 7.5% Final 20%

Projects (Matlab) Project 1 7.5% Project 2 7.5% Final Project 10%

Total 100%

NOTE: Score related questions (homework/exams) must be raised withina week after the homework/exam is returned.

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Assignments

Pen and paper assignments Assigned every other lecture, almost always on Th Due one week later There will be about 9 HW assignments

Matlab/ADAMS assignments There will be about 9 Matlab and 6 ADAMS assignments

No late assignments accepted Two assignments with lowest scores will be dropped

Grading approach 50% - one random problem graded thoroughly 50% - for completing the other problems

Solutions will be posted on Learn@UW

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MATLAB and Simulink

MATLAB will be used extensively in ME451 It will be used to develop the basic simEngine2D MATLAB program which

will enable Kinematic and Dynamic Analysis of simple 2D mechanisms With the exception of the model data parser, it can be implemented using

standard MATLAB functionality

You are responsible for brushing up your MATLAB skills

Simulink might be used for ADAMS co-simulation

Matlab tutorial: September 16, Room TBA

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A Word on simEngine2D

A MATLAB program that you put together and by the end of the semester Should be capable of running basic 2D Kinematics and Dynamics analysis Each assignment adds a little bit to the core functionality of simEngine2D

You will: Setup a procedure to specify a model Implement various numerical solution sequences for different types of analysis Plot results of interest (positions, accelerations, reaction forces, etc.)

Link to past simEngine2D: [2010] http://sbel.wisc.edu/Courses/ME451/2010/SimEngine2D/index.htm [2011] http://sbel.wisc.edu/Courses/ME451/2011/SimEngine2D/index.htm Important: this year we change the format of the input files

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Projects

Two intermediate projects (using the simEngine2D) Kinematic analysis (assigned on October 21) Dynamic analysis (assigned on November 25) Each due one day before the each of the two midterm exams

Final Project, you’ll choose one of two options: ADAMS: you’ll choose the project topic, I decide if it’s good enough MATLAB:

Examples: use simEngine2D for analysis of a more complicated mechanism, or extend simEngine2D, etc.

Groups of two students for one project ok provided project has enough scope

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Exams

Two midterm exams, as indicated in syllabus Midterm 1: Tuesday, October 28 Midterm 2: Thursday, December 4 Review sessions: the evening before the exam, 6:30 pm (Room TBD)

Final Exam Tuesday, Dec. 16, at 2:45 PM Comprehensive Room: TBD (computer room) Requires you to use your simEngine2D to solve a simple problem

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Scores and Grades

Score Grade94-100 A87-93 AB80-86 B73-79 BC66-72 C55-65 D

Grading will not be done on a curve

Final score will be rounded to the nearest integer prior to having a letter assigned Example:

86.59 becomes AB 86.47 becomes B

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Quick Suggestions

Attend lecture if you find it useful If you attend, stay involved, pay attention, ask questions

Reading the textbook is good

Doing the homework is critical (and hard/time consuming)

Provide feedback Both during and at end of the semester I might be able to change small things that could make a difference in

the learning process

Scope of Kinematics and Dynamics

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Competencies gained, ME451

Ability to model a physical problem: Given a general mechanical system, understand how to generate in a systematic and

general fashion the equations that govern the time evolution of the mechanical system These equations are called the equations of motion (EOM)

Ability to solve a math problem (that is associated with dynamics) using computers Gain basic understanding of the techniques (called numerical methods) used to solve

the EOM We’ll rely on MATLAB to implement/illustrate some of the numerical methods used to

solve EOM

Ability to use commercial software to simulate and interpret the dynamics associated with complex mechanical system We’ll used the commercial package ADAMS, available at CAE

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Why/How Do Bodies Move?

Why? The configuration of a mechanism changes in time based on forces and/or motions applied to its components

Forces Internal (reaction forces) External, or applied forces (gravity, compliant forces, etc.)

Prescribed motion Somebody prescribes the motion of a component of the mechanical

system

How? They move in a way that obeys Newton’s second law However, there are additional conditions (constraints) that need to be

satisfied. These constraints come from the joints that connect the bodies (to be covered in detail later…)

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Putting it all together…

MECHANICAL SYSTEM =

BODIES + JOINTS + FORCES

THE SYSTEM CHANGES ITS CONFIGURATION IN TIME

WE WANT TO BE ABLE TO PREDICT & CHANGE/CONTROL

HOW SYSTEM EVOLVES

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Examples, Multibody Dynamics

Vehicle Suspension

Vehicle Simulation

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Examples, Multibody Dynamics

Powder, Additive Manufacturing (3D Printing)

Selective Laser Sintering (SLS) machine

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Courtesy of Professor Tim Osswald, Polymer Engineering Center, UW-Madison

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Powder Bed Roughness: Before and After Rollover

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“Studying the Effect of Powder Geometry on the Selective Laser Sintering Process,” H. Mazhar, J. Bollmann, E. Forti, A. Praeger, T. Osswald and D. Negrut, in SPE-ANTEC 2014

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Bulldozer Simulation

Vehicle: Total Mass: 7,300 kg 114 Parts 111 Kinematic

Constraints

Granular Material: 200,000 ellipsoids Cohesion = 500N Density 2000kg/m^3 ~0.7 million contacts

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Examples, Multibody Dynamics

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Examples of 2D Mechanisms

Windshield wiper mechanism[out of Haug’s book, available online]

Quick-return shaper mechanism[out of Haug’s book, available online]

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Nomenclature

Mechanical System, definition: A collection of rigid or deformable bodies that move in a fashion

consistent with mechanical joints that limit relative motions of pairs of bodies

Mechanical system, types of analysis Kinematic analysis Dynamic analysis Inverse Dynamic analysis Equilibrium analysis

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Kinematic Analysis

Concerns the motion of the system independent of the forces that produce the motion

Typically, the time history of one body in the system is prescribed

We are interested in how the rest of the bodies in the system move

Requires the solution linear and nonlinear systems of equations

Windshield wiper mechanism

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Dynamic Analysis

Concerns the motion of the system due to the action of applied forces/torques

Typically, a set of forces acting on the system is provided. Motions can also be specified on some bodies

We are interested in how each body in the mechanism moves

Requires the solution of a combined system of differential and algebraic equations (DAEs)

Cross Section of Engine

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Inverse Dynamic Analysis It is a hybrid between Kinematics and Dynamics

Basically, one wants to find the set of forces that lead to a certain desirable motion of the mechanism

Your bread and butter in Controls…

Windshield wiper mechanism Robotic Manipulator

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What is the Slant of This Course?

There are several ways to approach kinematics and dynamics of mechanical systems (that is, to find the time evolution of the mechanical system):

The ME240 way, on a case-by-case fashion Typically requires following a recipe, not always clear where it came from Typically works for small problems, not clear how to go beyond textbook cases

Use a graphical approach This was the methodology that used to be emphasized in ME451 (Prof. Uicker) Intuitive but doesn’t scale particularly well

Use a computational approach – this is the methodology emphasized in ME451 Leverages the power of the computer Relies on a unitary approach to analysis of any mechanical system

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Modeling & Simulation (1)

M&S applies to many (most?) disciplines: engineering, physics, chemistry, biology, economics, etc.

The goal is to figure out how “something” happens without having to actually (build it and) test it in real-life.

Modeling is the abstraction of reality while simulation is the execution of the model.

Computer M&S: Start with a physical phenomenon Use laws, principles, scientific theories to extract a mathematical model

(a set of equations that describe the salient features of the particular problem) Convert into a numerical model Implement into computer code Simulate, that is run the code Post-processing (data analysis, visualization, animation, …) Interpret results

“Essentially, all models are wrong, but some are useful.”George Box & Norman Draper

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Modeling & Simulation (2)

% Update position and velocity (using Newmark)q = q_prev + h*qd_prev + 0.5*h^2*((1-2*beta)*qdd_prev + 2*beta*qdd);qd = qd_prev + h*((1-gam)*qdd_prev + gam*qdd);

Geometrical Model

Mathematical Model

Numerical Model

Computer Implementation

Physical Reality

Post-processing

Simulation

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More on the Computational Perspective…

Everything that we do in ME451 is governed by Newton’s Second Law.

We pose the problem so that it is suited for solution using a computer:

1. Identify in a simple and general way the data that is needed to formulate the equations of motion.

2. Automatically solve the set of nonlinear equations of motion using appropriate numerical solution algorithms: e.g. Newton-Raphson, Newmark Numerical Integration Method, etc.

3. Provide post-processing support for analysis of results: e.g. plot time curves for quantities of interest, animate the mechanism, etc.

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Overview of the Class[Chapter numbers according to Haug’s book]

Chapter 1 – general considerations regarding the scope and goal of Kinematics and Dynamics (with a computational slant)

Chapter 2 – review of basic Linear Algebra and Calculus Linear Algebra: Focus on geometric vectors and matrix-vector operations Calculus: Focus on taking partial derivatives (a lot of this), handling time derivatives, chain rule (a lot of this too)

Chapter 3 – introduces the concept of kinematic constraint as the mathematical building block used to represent joints in mechanical systems This is the hardest part of the material covered Basically poses the Kinematics problem

Chapter 4 – quick discussion of the numerical algorithms used to solve Kinematics problem formulated in Chapter 3

Chapter 5 – applications (Kinematics) Only tangentially touching it; ADAMS assignments

Chapter 6 – formulation of the Dynamics problem: derivation of the equations of motion (EOM)

Chapter 7 – numerical methods for solving the Dynamics problem formulated in Chapter 6

Haug’s book is available online at the class website

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ADAMS Automatic Dynamic Analysis of Mechanical Systems

It says Dynamics in name, but it does a whole lot more Kinematics, Statics, Quasi-Statics, etc.

Philosophy behind software package Offer a pre-processor (ADAMS/View) for people to be able to generate

models Offer a solution engine (ADAMS/Solver) for people to be able to find the

time evolution of their models Offer a post-processor (ADAMS/PPT) for people to be able to animate

and plot results

It now has a variety of so-called vertical products, which all draw on the ADAMS/Solver, but address applications from a specific field: ADAMS/Car, ADAMS/Rail, ADAMS/Controls, ADAMS/Linear,

ADAMS/Hydraulics, ADAMS/Flex, ADAMS/Engine, etc.

ADAMS tutorial: October 9, Room TBA (given by Justin Madsen)