Kinematics and Dynamics of Mechanical Systems 3rd Edition Solutions Manual by Kevin Russell, Q. Shen & R. Sodhi|ISBN 978-1032328317

QUIVERS STUVIA




SOLUTIONS

, CHAPTER 2 Q




Preface …………………………………………...……………………………………….. 1
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Chapter 2 Mathematical Concepts in Kinematics ……………………………………….. 2
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Chapter 3 Fundamental Concepts in Kinematics ……………………………………….. 8
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Chapter 4 Kinematic Analysis of Planar Mechanisms ...................................................................19
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Chapter 5 Dimensional Synthesis ..................................................................................................81
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Chapter 6 Static Force Analysis of Planar Mechanisms ...............................................................159
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Chapter 7 Dynamic Force Analysis of Planar Mechanisms..........................................................210
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Chapter 8 Design & Kinematic Analysis of Gears .......................................................................288
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Chapter 9 Design & Kinematic Analysis of Disk Cams ...............................................................327
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Chapter 10 Kinematic Analysis of Spatial Mechanisms ................................................................364
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Chapter 11 Introduction to Robotic Manipulators .........................................................................409
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, CHAPTER 2 Q




Problem 2.1 Statement:
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Formulate an equation for the vector loop illustrated in Figure P.2.1. Consider that vector V j
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always lies along the real axis.
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Figure P.2.1 Vector loop (3 vectors where V j changes length) in 2-D complex space
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Problem 2.1 Solution:
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Taking the clockwise sum of the vector loop in Figure P.2.1 produces the equation
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V1 ei1 V2 ei2  Vj  0 .
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When expanded and separated into real and imaginary terms, the vector loop equation becomes
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V1 cos1 V2 cos2  Vj  0
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V1 sin 1 V2 sin 2  0
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Problem 2.2 Statement:
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Formulate an equation for the vector loop illustrated in Figure P.2.2. Consider that vector V j
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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
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Problem 2.2 Solution:
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Taking the clockwise sum of the vector loop in Figure P.2.2 produces the equation
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V1 ei1 V2 ei2  V3  Vj  0 .
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Q
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When expanded and separated into real and imaginary terms, the vector loop equation becomes
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V1 cos1 V2 cos2  Vj  0
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V1 sin 1 V2 sin 2  V3  0
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Problem 2.3 Statement:
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Calculate the first derivative of the vector loop equation solution from Problem 2.2. Consider
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only angles 1 , 2 and vector V j from Problem 2 to be time-dependent.
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Problem 2.3 Solution:
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Differentiating the vector loop equation solution from Problem 2.2 produces the equation
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i1V1ei1  i 2V e2 i2  V j 0.
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When expanded and separated into real and imaginary terms, the vector loop equation becomes
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1V1sin  1  V2 sin
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Q 2Q  2 V j 0 Q Q Q Q Q Q Q Q Q Q


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1V1cos 1  V2 2cos 
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2 0 Q Q Q Q Q