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

All11ChaptersCovered
v v v




SOLUTIONS

, CONTENTS

Preface v …………………………………………...……………………………………….. v 1

v Chapter 2 Mathematical Concepts in Kinematics ………………………………………..
v v v v v v v 2

v Chapter 3 Fundamental Concepts in Kinematics
v v v v v v ……………………………………….. v 8

v Chapter 4 Kinematic Analysis of Planar Mechanisms ...................................................................19
v v v v v v




Chapter 5 Dimensional Synthesis ..................................................................................................81
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Chapter 6 Static Force Analysis of Planar Mechanisms................................................................159
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Chapter 7 Dynamic Force Analysis of Planar Mechanisms ..........................................................210
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Chapter 8 Design & Kinematic Analysis of Gears ........................................................................288
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Chapter 9 Design & Kinematic Analysis of Disk Cams ................................................................327
v v v v v v v v




Chapter 10 Kinematic Analysis of Spatial Mechanisms .................................................................364
v v v v v v




Chapter 11 Introduction to Robotic Manipulators ..........................................................................409
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, CHAPTER2 v




Problem 2.1 Statement:
v v




Formulate an equation for the vector loop illustrated in Figure P.2.1. Consider that vector Vj
v v v v v v v v v v v v v v v




always lies along the real axis.
v v v v v




Figure P.2.1 Vector loop (3 vectors where Vj
v v v v v v v v changes length) in 2-D complex space v v v v v




Problem 2.1 Solution:
v v




Taking the clockwise sum of the vector loop in Figure P.2.1 produces the equation
v v v v v v v v v v v v v




V1ei1 +V2 ei2 −Vj = 0.
v
v
v
v
v v v v




When expanded and separated into real and imaginary terms, the vector loop equation becomes
v v v v v v v v v v v v v




V1 cos1 +V2 cos2 −Vj = 0 v v



.
v v v v v




V1 sin1 +V2 sin2 = 0
v
v
v v
v
v
v




Problem 2.2 Statement:
v v




Formulate an equation for the vector loop illustrated in Figure P.2.2. Consider that vector Vj
v v v v v v v v v v v v v v v




always lies along the real axis and vector V3
v v v v v v v v is always perpendicular to the real axis.
v v v v v v




@Seismi2cisolation
@Seismicisolation

, Figure P.2.2 Vector loop (4 vectors where Vj
v v v v v v v v changes length) in 2-D complex space v v v v v




Problem 2.2 Solution:
v v




Taking the clockwise sum of the vector loop in Figure P.2.2 produces the equation
v v v v v v v v v v v v v




V1ei1 +V2 ei2 −V3 −Vj = 0.
v
v
v
v
v v v v v v




When expanded and separated into real and imaginary terms, the vector loop equation becomes
v v v v v v v v v v v v v




V1 cos1 +V2 cos2 −Vj = 0 v v



.
v v v v v




V1 sin1 +V2 sin2 −V3 = 0
v
v
v v
v
v
v
v
v




Problem 2.3 Statement:
v v




Calculate the first derivative of the vector loop equation solution from Problem 2.2. Consider
v v v v v v v v v v v v v




only angles 1 , 2 and vector Vj from Problem 2 to be time-dependent.
v v
v
v v v v v v v v v




Problem 2.3 Solution:
v v




Differentiating the vector loop equation solution from Problem 2.2 produces the equation
v v v v v v v v v v v




i1Vei1 +i V2 ei2 −V j = 0.
v v
v
v v v
v
v v v



1 2


When expanded and separated into real and imaginary terms, the vector loop equation becomes
v v v v v v v v v v v v v




−1V 1sin 1− V2 sin
v
2  2−V j= 0
v v v v v v v v v v v



.
v




1V cos 1 + V
v
2 cos 2 = 0
v v v v v v




1 2



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@Seismicisolation