Analytical Elements of Mechanisms

by Dan B. Marghitu , Malcolm J. Crocker

• ISBN13: 9780521623834
• ISBN10: 0521623839
• Format: Hardcover
• Copyright: 2001-06-18
• Publisher: Cambridge University Press

Summary

Mechanisms are fundamental components of machines. They are used to transmit forces and moments and to manipulate objects in industrial machinery, robots, automobiles, aircraft, mechatronics devices and biomechanical systems. A knowledge of the kinematic and dynamic properties of mechanisms is essential for their design and control. This book describes methods and algorithms for the analysis of kinematic systems. Beginning with basic concepts, the book then discusses a variety of problem-solving approaches and computational techniques. Its distinctive feature is its focus on the contour equation as a powerful, computationally efficient tool that will help the reader to design complex spatial mechanisms. This handy text will be useful for senior or graduate students, researchers and practising engineers working in robotics, vehicle dynamics, mechatronics and machine design.

Table of Contents

Preface	ix
Introduction	1	(20)
Degrees of Freedom	1	(1)
Motion	1	(1)
Links and Joints	2	(9)
Number of Degrees of Freedom	11	(7)
Planar Mechanisms	18	(3)
Position Analysis	21	(23)
Absolute Cartesian Method	21	(6)
Vector Loop Method	27	(7)
R-RRR-RRT Mechanism	34	(3)
R-TRR-RRT Mechanism	37	(3)
R-RRR-RTT Mechanism	40	(4)
Velocity and Acceleration Analysis	44	(14)
Driver Link	44	(1)
RRR Dyad	45	(2)
RRT Dyad	47	(1)
RTR Dyad	48	(2)
TRT Dyad	50	(8)
Contour Equations	58	(25)
Introduction	58	(1)
Formulation of the Problem	59	(1)
Contour Velocity Equations	60	(2)
Contour Acceleration Equations	62	(2)
Diagram Representing a Mechanism	64	(1)
Independent Contour Equation Method for Mechanisms	64	(1)
Notation	65	(1)
R-RRR-RRT Mechanism	66	(7)
R-TRR-RRT Mechanism	73	(5)
R-RRR-RTT Mechanism	78	(5)
Dynamic Force Analysis	83	(37)
Force, Moment, Couple	83	(2)
Newton's Second Law of Motion	85	(2)
D'Alembert's Principle	87	(1)
Free-Body Diagrams	88	(1)
Computation of Joint Forces by Using Individual Links	89	(2)
Computation of Joint Forces by Using the Contour Method	91	(20)
Computation of Joint Force for Dyads	111	(9)
Mechanisms with Gears	120	(33)
Introduction	120	(1)
Geometry and Nomenclature	120	(5)
Interference and Contact Ratio	125	(2)
Linkage Transformation	127	(1)
Ordinary Gear Trains	128	(1)
Epicyclic Gear Trains	129	(12)
Differential	141	(4)
Gear Force Analysis	145	(8)
Open Kinematic Chains	153	(15)
Kinematics of Open Kinematic Chains	153	(6)
Generalized Inertia Forces	159	(3)
Generalized Active Forces	162	(3)
Numerical Simulation	165	(1)
Kinetic Energy	166	(2)
Kinematic Chains with Continuous Flexible Links	168	(13)
Transverse Vibrations of a Flexible Link	168	(1)
Equations of Motion for a Flexible Link	169	(12)
Problems	181	(42)
Appendix 1 R-RRR-RRT Mechanism - Mathematica Program for Position Analysis	223	(4)
Appendix 2 R-TRR-RRT Mechanism - Mathematica Program for Position Analysis	227	(3)
Appendix 3 R-RTR-RRT Mechanism - Mathematica Program for Position Analysis	230	(3)
Appendix 4 R-RTR-RRT Mechanism - Mathematica Program for Velocity and Acceleration Analysis for &phis; = 45°	233	(4)
Appendix 5 R-RRR-RRT Mechanism - Mathematica Program for Velocity and Acceleration Analysis for &phis; = 45°	237	(7)
Appendix 6 R-RRR-RRT Mechanism - Mathematica Program for Velocity and Acceleration Analysis for &phis; = 45° by Using the Contour Method	244	(5)
Appendix 7 R-TRR-RRT Mechanism - Mathematica Program for Velocity and Acceleration Analysis for &phis; = 45° by Using the Contour Method	249	(4)
Appendix 8 R-TRR-RRT Mechanism - Mathematica Program for Joint Reactions	253	(9)
Appendix 9 Laws of Motion	262	(3)
Appendix 10 Three DOF Open Kinematic Chain - Mathematica Program for Dynamics	265	(8)
Bibliography	273	(2)
Index	275