Kinematics and Dynamics of Mechanical Systems: Implementation in MATLAB® and Simscape Multibody™

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
Authors
1. Introduction to Kinematics
	1.1 Kinematics
	1.2 Kinematic Chains and Mechanisms
	1.3 Mobility, Planar, and Spatial Mechanisms
	1.4 Types of Mechanism Motion
	1.5 Kinematic Synthesis
	1.6 Units and Conversions
	1.7 Software Resources
	1.8 Summary
	References
	Additional Reading
2. Mathematical Concepts in Kinematics
	2.1 Introduction
	2.2 Complex Numbers and Operations
		2.2.1 Complex Number Forms
		2.2.2 Complex Number Addition
		2.2.3 Complex Number Multiplication and Differentiation
	2.3 Vector and Point Representation
	2.4 Linear Simultaneous Equations, Matrices, and Matrix Operations
		2.4.1 Linear Simultaneous Equation Systems and Matrices
		2.4.2 Matrix Transpose, Addition, Subtraction, and Multiplication
		2.4.3 The Identity Matrix and Matrix Inversion
	2.5 Intermediate and Total Spatial Motion
	2.6 General Transformation Matrix
	2.7 Summary
	References
	Additional Reading
	Problems
3. Fundamental Concepts in Kinematics
	3.1 Types of Planar and Spatial Mechanisms
		3.1.1 Planar Four-Bar Mechanism
		3.1.2 Slider-Crank Mechanism
		3.1.3 Geared Five-Bar Mechanism
		3.1.4 Planar Multiloop Six-Bar Mechanisms
		3.1.5 Spatial Four-Bar Mechanisms
	3.2 Links, Joints, and Mechanism Mobility
	3.3 Number Synthesis
	3.4 Grashof’s Criteria and Transmission Angle
	3.5 Circuit Defect
	3.6 Mechanism Inversion
	3.7 Passive Degree of Freedom and Paradoxes
	3.8 Summary
	References
	Problems
4. Kinematic Analysis of Planar Mechanisms
	4.1 Introduction
	4.2 Numerical Solution Method for Two Simultaneous Equations
	4.3 Link Velocity and Acceleration Components in Planar Space
	4.4 Four-Bar Mechanism Analysis
		4.4.1 Displacement Equations
		4.4.2 Velocity Equations
		4.4.3 Acceleration Equations
		4.4.4 Kinematics of Coupler Locations of Interest
		4.4.5 Instant Center, Centrodes, and Centrode Generation
	4.5 Slider-Crank Mechanism Analysis
		4.5.1 Displacement Equations
		4.5.2 Velocity Equations
		4.5.3 Acceleration Equations
		4.5.4 Centrode Generation
	4.6 Geared Five-Bar Mechanism Analysis
		4.6.1 Displacement Equations
		4.6.2 Velocity Equations
		4.6.3 Acceleration Equations
		4.6.4 Kinematics of Intermediate Link Locations of Interest
	4.7 Watt II Mechanism Analysis
	4.8 Stephenson III Mechanism Analysis
		4.8.1 Displacement Equations
		4.8.2 Velocity Equations
		4.8.3 Acceleration Equations
		4.8.4 Kinematics of Intermediate Link Locations of Interest
	4.9 Time and Driver Angular Velocity
	4.10 Mechanism Configurations
	4.11 Constructing Cognates
	4.12 Planar Mechanism Kinematic Analysis and Modeling in Simscape Multibody™
	4.13 Summary
	References
	Additional Reading
	Problems
5. Dimensional Synthesis
	5.1 Introduction
	5.2 Branch and Order Defects
	5.3 Planar Four-Bar Motion Generation: Three Precision Positions
	5.4 Order- and Branch-Defect Elimination
	5.5 Path Generation versus Motion Generation
	5.6 Stephenson III Motion Generation: Three Precision Positions
	5.7 Planar Four-Bar Function Generation: Three Precision Points
	5.8 Planar Four-Bar Function Generation: FSPs and MSPs
	5.9 Mechanism Dimensions: From Dimensional Synthesis to Kinematic Analysis
	5.10 Summary
	References
	Additional Reading
	Problems
6. Static Force Analysis of Planar Mechanisms
	6.1 Introduction
	6.2 Static Loading in Planar Space
	6.3 Four-Bar Mechanism Analysis
	6.4 Slider-Crank Mechanism Analysis
	6.5 Geared Five-Bar Mechanism Analysis
	6.6 Watt II Mechanism Analysis
	6.7 Stephenson III Mechanism Analysis
	6.8 Planar Mechanism Static Force Analysis and Modeling in Simscape Multibody™
	6.9 Summary
	References
	Additional Reading
	Problems
7. Dynamic Force Analysis of Planar Mechanisms
	7.1 Introduction
	7.2 Dynamic Loading in Planar Space
	7.3 Four-Bar Mechanism Analysis
	7.4 Slider-Crank Mechanism Analysis
	7.5 Geared Five-Bar Mechanism Analysis
	7.6 Watt II Mechanism Analysis
	7.7 Stephenson III Mechanism Analysis
	7.8 Mass Moment of Inertia and Computer-Aided Design Software
	7.9 Planar Mechanism Dynamic Force Analysis and Modeling in Simscape Multibody™
	7.10 Summary
	References
	Additional Reading
	Problems
8. Design and Kinematic Analysis of Gears
	8.1 Introduction
	8.2 Gear Types
	8.3 SPUR-Gear Nomenclature and Relationships of Mating Gears
		8.3.1 Spur-Gear Nomenclature
		8.3.2 Pressure Angle and Involute Tooth Profile
		8.3.3 Gear Center Distance and Contact Ratio
		8.3.4 Gear-Tooth Interference and Undercutting
		8.3.5 Backlash
	8.4 Helical-Gear Nomenclature
	8.5 Gear Kinematics
		8.5.1 Spur Gears and Gear Trains
		8.5.2 Planetary Gear Trains
		8.5.3 Rack and Pinion Gears
		8.5.4 Helical Gears
		8.5.5 Bevel Gears
		8.5.6 Worm Gears
	8.6 Summary
	References
	Additional Reading
	Problems
9. Design and Kinematic Analysis of Disk Cams
	9.1 Introduction
	9.2 Follower Types
	9.3 Follower Motion
		9.3.1 Rise, Fall, and Dwell
		9.3.2 Displacement, Velocity, Acceleration, and Jerk
		9.3.3 Constant Velocity Motion
		9.3.4 Constant Acceleration Motion
		9.3.5 Simple Harmonic Motion
		9.3.6 Cycloidal Motion
		9.3.7 Polynomial Motion
	9.4 Disk Cam Design and Pressure Angle
	9.5 Summary
	References
	Additional Reading
	Problems
10. Kinematic Analysis of Spatial Mechanisms
	10.1 Introduction
	10.2 RRSS Mechanism Analysis
		10.2.1 Displacement Equations
		10.2.2 Velocity Equations
		10.2.3 Acceleration Equations
	10.3 RSSR Mechanism Analysis
		10.3.1 Displacement Equations
		10.3.2 Velocity Equations
		10.3.3 Acceleration Equations
	10.4 Four-Revolute Spherical Mechanism Analysis
	10.5 Planar Four-Bar Kinematic Analysis Using RRSS and RSSR Kinematic Equations
	10.6 Spatial Mechanism Kinematic Analysis and Modeling in Simscape Multibody™
	10.7 Summary
	References
	Problems
11. Introduction to Robotic Manipulators
	11.1 Introduction
	11.2 Terminology and Nomenclature
	11.3 Robotic Manipulator Mobility and Types
	11.4 The General Transformation Matrix
	11.5 Forward Kinematics
		11.5.1 Definition and Application
		11.5.2 P-P-P
		11.5.3 R-P-P
		11.5.4 R-R-P
		11.5.5 R-R-R
		11.5.6 R-R-C
	11.6 Inverse Kinematics
		11.6.1 Definition and Application
		11.6.2 P-P-P
		11.6.3 R-P-P
		11.6.4 R-R-P
		11.6.5 R-R-R
		11.6.6 R-R-C
	11.7 Robotic Manipulator Kinematic Analysis and Modeling in Simscape Multibody™
	11.8 Summary
	References
	Additional Reading
	Problems
Appendix A: User Information and Instructions for MATLAB®
	A.1 Required MATLAB Toolkits
	A.2 Description of MATLAB Operators and Functions
	A.3 Preparing and Running Files in MATLAB and Operations in Simscape Multibody
	A.4 Description of Simscape Multibody Functions
	A.5 Rerunning MATLAB and Simscape Multibody Files with Existing *.csv Files
	A.6 Minimum Precision Requirement for Appendix File User Input
Appendix B: User Instructions for Chapter 4 MATLAB® Files
	B.1 Planar Four-Bar Mechanism
	B.2 Planar Four-Bar Fixed and Moving Centrode Generation
	B.3 Slider-Crank Mechanism
	B.4 Geared Five-Bar Mechanism (Two Gears)
	B.5 Geared Five-Bar Mechanism (Three Gears)
	B.6 Watt II Mechanism
	B.7 Stephenson III Mechanism
Appendix C: User Instructions for Chapter 6 MATLAB® Files
	C.1 Planar Four-Bar Mechanism
	C.2 Slider-Crank Mechanism
	C.3 Geared Five-Bar Mechanism (Two Gears)
	C.4 Geared Five-Bar Mechanism (Three Gears)
	C.5 Watt II Mechanism
	C.6 Stephenson III Mechanism
Appendix D: User Instructions for Chapter 7 MATLAB® Files
	D.1 Planar Four-Bar Mechanism
	D.2 Slider-Crank Mechanism
	D.3 Geared Five-Bar Mechanism (Two Gears)
	D.4 Geared Five-Bar Mechanism (Three Gears)
	D.5 Watt II Mechanism
	D.6 Stephenson III Mechanism
Appendix E: User Instructions for Chapter 9 MATLAB® Files
	E.1 S, V Profile Generation and Cam Design: Constant Velocity Motion
	E.2 S, V, A Profile Generation and Cam Design: Constant Acceleration Motion
	E.3 S, V, A, J Profile Generation and Cam Design: Simple Harmonic Motion
	E.4 S, V, A, J Profile Generation and Cam Design: Cycloidal Motion
	E.5 S, V, A, J Profile Generation and Cam Design: 3-4-5 Polynomial Motion
	E.6 S, V, A, J Profile Generation and Cam Design: 4-5-6-7 Polynomial Motion
Appendix F: User Instructions for Chapter 10 MATLAB® Files
	F.1 RRSS Mechanism
	F.2 RSSR Mechanism
Appendix G: User Instructions for Chapter 11 MATLAB® Files
	G.1 R-P-P Robotic Manipulator Forward Kinematics
	G.2 R-R-P Robotic Manipulator Forward Kinematics
	G.3 R-R-R Robotic Manipulator Forward Kinematics
	G.4 R-R-C Robotic Manipulator Forward Kinematics
	G.5 R-P-P Robotic Manipulator Inverse Kinematics
	G.6 R-R-P Robotic Manipulator Inverse Kinematics
	G.7 R-R-R Robotic Manipulator Inverse Kinematics
	G.8 R-R-C Robotic Manipulator Inverse Kinematics
Appendix H: User Instructions for Chapter 4 MATLAB® and Simscape Multibody™ Files
	H.1 Planar Four-Bar Mechanism
	H.2 Slider-Crank Mechanism
	H.3 Geared Five-Bar Mechanism (Two Gears)
	H.4 Geared Five-Bar Mechanism (Three Gears)
	H.5 Watt II Mechanism
	H.6 Stephenson III Mechanism
Appendix I: User Instructions for Chapter 6 MATLAB® and Simscape Multibody™ Files
	I.1 Planar Four-Bar Mechanism
	I.2 Slider-Crank Mechanism
	I.3 Geared Five-Bar Mechanism (Two Gears)
	I.4 Geared Five-Bar Mechanism (Three Gears)
	I.5 Watt II Mechanism
	I.6 Stephenson III Mechanism
Appendix J: User Instructions for Chapter 7 MATLAB® and Simscape Multibody™ Files
	J.1 Planar Four-Bar Mechanism
	J.2 Slider-Crank Mechanism
	J.3 Geared Five-Bar Mechanism (Two Gears)
	J.4 Geared Five-Bar Mechanism (Three Gears)
	J.5 Watt II Mechanism
	J.6 Stephenson III Mechanism
Appendix K: User Instructions for Chapter 10 MATLAB® and Simscape Multibody™ Files
	K.1 RRSS Mechanism
	K.2 RSSR Mechanism
Appendix L: User Instructions for Chapter 11 MATLAB® and Simscape Multibody™ Files
	L.1 R-P-P Robotic Manipulator Forward Kinematics
	L.2 R-R-P Robotic Manipulator Forward Kinematics
	L.3 R-R-R Robotic Manipulator Forward Kinematics
	L.4 R-R-C Robotic Manipulator Forward Kinematics
Index