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




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@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 fP.2.2 fVector floop f(4 fvectors fwhere changes flength) fin f2-D fcomplex fspace
f Vfj


Problem f2.2 fSolution:

Taking fthe fclockwise fsum fof fthe fvector floop fin fFigure fP.2.2 fproduces fthe fequation

V fei11 f +V fe2 i2 f − fV3 f − fVj f = f0 f.

When fexpanded fand fseparated finto freal fand fimaginary fterms, fthe fvector floop fequation fbecomes

V1 f cos1 f +V2 f cos2 f − fVj f = f0
.
V1 fsin f1 f +V2 f sin f2 f − fV3 f = f0

Problem f2.3 fStatement:

Calculate fthe ffirst fderivative fof fthe fvector floop fequation fsolution ffrom fProblem f2.2. f Consider

only fangles f 1 f, and fvector from fProblem f2 fto fbe ftime-dependent.
f 2 f Vfj



Problem f2.3 fSolution:

Differentiating fthe fvector floop fequation fsolution ffrom fProblem f2.2 fproduces fthe fequation

i1V1ei1 + i2V2ei2 − V j = 0.

When fexpanded fand fseparated finto freal fand fimaginary fterms, fthe fvector floop fequation fbecomes

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