All 11 Chapters Covered
SOLUTIONS
,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
,
, 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
V e1i 1
V 2ei 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.
SOLUTIONS
,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
,
, 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
V e1i 1
V 2ei 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.
