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 P.2.2 Vector loop (4 vectors where V j changes length) in 2-D complex space

Problem 2.2 Solution:

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

V1 ei1 +V2 ei2 − V3 − 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 − V3 = 0

Problem 2.3 Statement:

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

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

Problem 2.3 Solution:

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

i1V1ei1 + i2V2ei2 − V j = 0.

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

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


@Seismi3cisolation
@Seismicisolation