Machine DynamicsMech 301

Dr. Dongming Gan

Assistant Professor in Robotics/ME

Course Logistics

• 3 credits, 45 Lectures + tutorials

• Grading– Hw: 20%

– Quizzes: 10%

– Final project: 10%

– Midterm: 20%

– Final: 40%

• References:– Main Textbook: J.J. Uicker, Jr., G.R. Pennock, and J.E. Shigley;Theory of Machines and Mechanism, Oxford, 4th int. edition

– Secondary (Just for the two final chapters on Robotics, etc.):L.Sciavicco, B. Siciliano, “Modeling and Control of RobotManipulators”, 2nd Edition, Springer-Verlag Advanced Textbooks inControl and Signal Processing Series, London, UK, 2000;

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Course Goals

• Goal:

– To present an overview of analysis, design and

synthesis of mechanism and machines by

considering kinematics and kinetics.

– The concepts of position, velocity, acceleration

and force analysis are presented in a thorough

manner.

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Week No Contents

Week 1(9-13 Feb) Mechanisms: Introduction, Pairs

Types of Mechanisms, Mobility, Classification

Week 2 (16-20 Feb) Kinematic Inversion, Grashof’s Law

Mechanical Advantage, Overlay Method

Position & Displacement: Moving point, Position

Assignment #1 - Due one week from the day it is assigned.

Week 3(23-27 Feb) Position Difference, Apparent Position, Absolute Position

Loop Closure Equation

Week 4(2-6 Mar) Position Analysis (Graphic), Position Analysis (Algebraic)

Velocity: Rotation, Velocity Difference

Assignment #2 - Due one week from the day it is assigned.

Week 5(9-13 Mar) Velocity Polygons, Apparent Velocity (Linear & Angular)

Quiz #1

Week 6(16-20 Mar) Direct & Rolling Contact, Velocity Analysis, Inst. Ctr of Velocity, Aronhold-Kennedy Thm

Locating Instant Ctrs of Velocity, The angular velocity ration Thm.

Assignment #3- Due one week from the day it is assigned.

Week 7(23-27 Mar) MIDTERM EXAM

Acceleration: Angular Acceleration

Acceleration Difference, Acceleration Polygons

30 Mar – 3 Apr Spring Break

Week 8(6-10 Apr) Apparent Acceleration, Apparent Angular Acceleration

Direct & Rolling Contact, Strategies for Acceleration Analysis

Complex Algebra (Position Analysis)

Assignment #4 - Due one week from the day it is assigned.

Week9(13-17 Apr) Complex Algebra (Velocity / Acceleration Analysis)

Static Force Analysis: Newton’s Laws, Applied & Constraint Forces, Free Body Diagrams

Teaching Plan

Chapter 2

Chapter 3

Chapter 1

Chapter 4

Chapter 13

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Week 10(20-24 Apr) Conditions for Equilibrium, 2 and 3 Force Members

4 Force Members, Friction Force Members, Dynamic Force Analysis: Center of Mass,

Mass Moments & Products of Inertia, D’Alembert’s Principle

Assignment #5 - Due one week from the day it is assigned.

Week 11(27 Apr-1 May) Cam Design: Classification of Cams & Followers, Displacement Diagrams

Graphical Layout of Cam profiles

Kinematic Coefficients of the Follower Motion

Week 12(4-8 May) Quiz #2

High Speed Cams

Standard Cam Motions

Assignment #6 - Due one week from the day it is assigned.

Week 13(11-15 May) Matching Derivatives

Reciprocating Flat Face Follower

Reciprocating Roller Follower

Week 14(18-22 May) Gears: Introduction to gearing,

involute tooth geometry, contact ratio,

Under cutting, Gear Trains

Week 15 (25-29 May)

*27 May- Al IsraaWalMi’raj*

*29 May- Last day of classes

Spatial Mechanisms: Euler Angles, Denavit-Hartenberg Parameters

Transformation Matrix Position Analysis

Matrix Velocity & Acceleration Analysis, Computer Programs for Mechanism Analysis, robot

Forward & Inverse Kinematics

Week 16(1-5 Jun) Final exams

Week 17(8-12 June)

*12 June- Grades dueFinal exams

Summer Break

Teaching Plan, contd.

Chapter 14

Chapter 6

Chapter 11

Chapter 7

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Theory of Machines & Mechanisms

• Issue: understanding

– the relationship between the geometry and

motions of a mechanism and

– the forces producing them

• Relevant issues:

– Kinematics: analysis of mechanism motions

– Design of Mechanisms

– Kinetics

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Mechanism examples

Serial Robots Parallel Robots

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Spherical 6-bar Slider-crank mechanism

Mechanics

• Contents: motion, time & forces

• Branches:Mechanics

Dynamics

Kinematics Kinetics

Statics

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Definitions

• Machine: combination of resistant bodies so

arranged that by their means the mechanical

forces of nature can be compelled to do work

accompanied by certain determinate motions.

• Mechanism: assemblage of resistant bodies,

connected by movable joints, to form a closed

kinematic chain with one link fixed and having

the purpose of transforming motion.

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Definitions

Joints

Links

Kinematics

ChainMechanism

Fix one

link as

frame

Machine

Add

input

energy

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Pairs/Joints

• Relative motion between elements “pairs”

– Recognize type of relative motion

– Assign variable parameters to measure motion

(pair variables)

• Kinematics Pairs

– Lower: surface contact between elements

– Higher: line or point contact

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Lower Pairsa) .

b) .

c) .

d) .

e) .

f) .

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Higher Pairs

• All those pairs that ….. they are NOT of the “lower type” e.g.

– Wheel rolling and/or sliding on a rail

– Ball rolling on a flat surface

– Cam contacting its follower, etc.

• “Wrapping Pair”: a subcategory where one of the links has one-way rigidity e.g.

– Belt & pulley

– Chain & sprocket

– Rope & drum etc.

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Mechanisms & Linkages

• Mechanisms: include both higher & lower

pairs

• Linkages: include only lower pairs

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