Kinematics and Dynamics of Mechanical Systems: Implementation in MATLAB® and Simscape Multibody™ (3rd Edition) by Kevin Russell, Qiong “John” Shen & Raj S. Sodhi — A detailed and contemporary guide to mechanism kinematics, synthesis, statics and dynamics

All 11 Chapters Covered
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SOLUTIONS

, CONTENTS

Preface bg …………………………………………...……………………………………….. 1
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bg Chapter 2 Mathematical Concepts in Kinematics ………………………………………..
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bg Chapter 3 Fundamental Concepts in Kinematics
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b g 8 Chapter 4
bg bg b g Kinematic Analysis of Planar Mechanisms ................................................ 19
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Chapter 5 bg b g Dimensional Synthesis ....................................................................................... 81
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Chapter 6 bg b g Static Force Analysis of Planar Mechanisms................................................... 159
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Chapter 7 bg b g Dynamic Force Analysis of Planar Mechanisms ............................................. 210
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Chapter 8 bg b g Design & Kinematic Analysis of Gears .......................................................... 288
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Chapter 9 bg b g Design & Kinematic Analysis of Disk Cams .................................................. 327
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Chapter 10 Kinematic Analysis of Spatial Mechanisms ...................................................... 364
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Chapter 11 Introduction to Robotic Manipulators................................................................ 409
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, CHAPTER 2 bg




Problem 2.1 Statement:
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Formulate an equation for the vector loop illustrated in Figure P.2.1.
bg bg bg bg bg bg bg bg bg bg b g Consider that vector V j
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always lies along the real axis.
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Figure P.2.1 Vector loop (3 vectors where changes length) in 2-D complex space
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b g Vj bg




Problem 2.1 Solution:
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Taking the clockwise sum of the vector loop in Figure P.2.1 produces the equation
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V ei11 V e2 i2
bg
b g
bg
b g
 Vj
bg b g 0.
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When expanded and separated into real and imaginary terms, the vector loop equation becomes
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V1 cos1 V2 cos2  Vj
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0 bg

.
V1 sin 1 V2 sin 2  0
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Problem 2.2 Statement:
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Formulate an equation for the vector loop illustrated in Figure P.2.2.
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always lies along the real axis and vector is always perpendicular to the real axis.
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V3
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, Figure P.2.2 Vector loop (4 vectors where changes length) in 2-D complex space
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b g Vj bg




Problem 2.2 Solution: bg bg




Taking the clockwise sum of the vector loop in Figure P.2.2 produces the equation
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V ei11 V e2i2
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b g
bg
b g
 V3 bg b g V
j
bg b g  0. bg bg




When expanded and separated into real and imaginary terms, the vector loop equation becomes
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V1 cos1 V2 cos2  Vj
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bg 0
b g
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.
V1 sin 1 V2 sin 2  V3
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0 bg




Problem 2.3 Statement:bg bg




Calculate the first derivative of the vector loop equation solution from Problem 2.2.
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only angles 1 , and vector
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bg from Problem 2 to be time-dependent.
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2
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Problem 2.3 Solution: bg bg




Differentiating the vector loop equation solution from Problem 2.2 produces the equation
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i1V ei1  i2 V ei2 j  V bg bg
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 0.
When expanded and separated into real and imaginary terms, the vector loop equation becomes
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1V sin
1
1 2 V2 sin
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2
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 j  bg b g bg bg b g bg b g


V 0 .
1V cos1 2  V cos
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2 b g bg bg b g


1 0@Seismi
b g 2 3cisolation
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