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 sP.2.2 sVector sloop s(4 svectors swhere changes slength) sin s2-D scomplex sspace
s Vsj


Problem s2.2 sSolution:

Taking sthe sclockwise ssum sof sthe svector sloop sin sFigure sP.2.2 sproduces sthe sequation

V sei11 s +V se2 i2 s − sV3 s − sV
j s = s0 s.

When sexpanded sand sseparated sinto sreal sand simaginary sterms, sthe svector sloop sequation sbecomes

V1 s cos1 s +V2 s cos2 s − sVj s = s0
.
V1 ssin s1 s +V2 s sin s2 s − sV3 s = s0

Problem s2.3 sStatement:

Calculate sthe sfirst sderivative sof sthe svector sloop sequation ssolution sfrom sProblem s2.2. s Consider

only sangles s 1 s, and svector from sProblem s2 sto sbe stime-dependent.
s 2 s Vsj



Problem s2.3 sSolution:

Differentiating sthe svector sloop sequation ssolution sfrom sProblem s2.2 sproduces sthe sequation

i1V1ei1 + i2V2ei2 − V j = 0.

When sexpanded sand sseparated sinto sreal sand simaginary sterms, sthe svector sloop sequation sbecomes

−1V1 sin 1 −  2V2 sin  2 − V j = 0
.
1V1 cos 1 +  2V2 cos 2 = 0
@Seismi 3cisolation
@Seismicisolation