Solution Manual to Kinematics and Dynamics of Mechanical Systems 3rd Edition by Russell

All 11 Chapters Covered




SOLUTIONS

, CONTENTS

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

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

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

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

Chapter 5 Dimensional Synthesis .................................................................................................81

Chapter 6 Static Force Analysis of Planar Mechanisms .............................................................159

Chapter 7 Dynamic Force Analysis of Planar Mechanisms ........................................................210

Chapter 8 Design & Kinematic Analysis of Gears .....................................................................288

Chapter 9 Design & Kinematic Analysis of Disk Cams .............................................................327

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

Chapter 11 Introduction to Robotic Manipulators .......................................................................409




@
@SSeeisismmicicisisoolalatitoionn

, CHAPTER 2

Problem 2.1 Statement:

Formulate an equation for the vector loop illustrated in Figure P.2.1. Consider that vector V j

always lies along the real axis.




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

Problem 2.1 Solution:

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

V1ei1 +V2 ei2 − Vj = 0 .

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

V1 cos1 +V2 cos2 − Vj = 0
.
V1 sin 1 +V2 sin 2 = 0

Problem 2.2 Statement:

Formulate an equation for the vector loop illustrated in Figure P.2.2. Consider that vector V j

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




@Seismi2cisolation
@Seismicisolation

, Figure aP.2.2 aVector aloop a(4 avectors awhere changes alength) ain a2-D acomplex aspace
a Vaj


Problem a2.2 aSolution:

Taking athe aclockwise asum aof athe avector aloop ain aFigure aP.2.2 aproduces athe aequation

V aei11 a +V ae2i2 a − aV3 a − aV
j a = a0 a.

When aexpanded aand aseparated ainto areal aand aimaginary aterms, athe avector aloop aequation
abecomes


V1 a cos1 a +V2 a cos2 a − aVj a= a0
.
V1 asin a1 a +V2 a sin a2 a − aV3 a = a0

Problem a2.3 aStatement:

Calculate athe afirst aderivative aof athe avector aloop aequation asolution afrom aProblem a2.2. a Consider

only aangles a 1 a, and avector from aProblem a2 ato abe atime-dependent.
a 2 a Vaj



Problem a2.3 aSolution:

Differentiating athe avector aloop aequation asolution afrom aProblem a2.2 aproduces athe aequation

i1V1ei1 + i2V2ei2 − V j = 0.

When aexpanded aand aseparated ainto areal aand aimaginary aterms, athe avector aloop aequation
abecomes



@Seismi3cisolation
@Seismicisolation