STUDY NOTES & REFERENCE GUIDE
All 11 Chapters Covered
SOLUTIONS
nolanjack ‐ Stuvia | Page 1 of 443
, STUDY NOTES & REFERENCE GUIDE
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
nolanjack ‐ Stuvia | Page 2 of 443
, STUDY NOTES & REFERENCE GUIDE
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
V1 ei 1
V2 ei 2
V j 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.
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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
V
1
ei 1
V2 ei 2
V3 V j
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
i1V 1ei1 + i V2 e2 i2 − V =j 0.
When expanded and separated into real and imaginary terms, the vector loop equation becomes
−1V1sin 1− V2 2sin 2− V =j 0
.
1V1 cos 1+ V
2 2cos 2= 0
nolanjack ‐ Stuvia | Page 4 of 443
All 11 Chapters Covered
SOLUTIONS
nolanjack ‐ Stuvia | Page 1 of 443
, STUDY NOTES & REFERENCE GUIDE
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
nolanjack ‐ Stuvia | Page 2 of 443
, STUDY NOTES & REFERENCE GUIDE
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
V1 ei 1
V2 ei 2
V j 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.
nolanjack ‐ Stuvia | Page 3 of 443
, STUDY NOTES & REFERENCE GUIDE
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
V
1
ei 1
V2 ei 2
V3 V j
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
i1V 1ei1 + i V2 e2 i2 − V =j 0.
When expanded and separated into real and imaginary terms, the vector loop equation becomes
−1V1sin 1− V2 2sin 2− V =j 0
.
1V1 cos 1+ V
2 2cos 2= 0
nolanjack ‐ Stuvia | Page 4 of 443
