Classical and Modern Approaches in the Theory of Mechanisms is a study of mechanisms in the broadest sense, covering the theoretical background of mechanisms, their structures and components, the planar and spatial analysis of mechanisms, motion transmission, and technical approaches to kinematics, mechanical systems, and machine dynamics. In addition to classical approaches, the book presents two new methods: the analytic-assisted method using Turbo Pascal calculation programs, and the graphic-assisted method, outlining the steps required for the development of graphic constructions using AutoCAD; the applications of these methods are illustrated with examples. Aimed at students of mechanical engineering, and engineers designing and developing mechanisms in their own fields, this book provides a useful overview of classical theories, and modern approaches to the practical and creative application of mechanisms, in seeking solutions to increasingly complex problems.

Nicolae Pandrea, University of Pitesti, Romania Prof. Pandrea teaches at the Faculty of Mechanics and Technology, University of Pitesti, Romania. He has served as President of the Scientific and Technical Committee in Romania, and is a member of the Romanian Academy of Technical Sciences. Professor Pandrea is the author of 250 papers and six books.

Dinel Popa, University of Pitesti, Romania Prof. Dinel Popa has taught at the University of Pitesti for over 25 years. His areas of expertise are: Mechanics, Mechanisms, Vibrations, Acoustics, and Numerical Methods.

Nicolae-Doru Stãnescu, University of Pitesti, Romania Prof. Stãnescu teaches at the Faculty of Mechanics and Technology, University of Pitesti, Romania. He is a member of the International Institute of Acoustic and Vibration, in USA, and Société des Ingénieurs de l'Automobile, France. He has written 200 papers and 10 books, and his areas of expertise include non-linear vibrations, dynamical systems, stability, chaos, and numerical analysis.

Classical and Modern Approaches in the Theory of Mechanisms is a study of mechanisms in the broadest sense, covering the theoretical background of mechanisms, their structures and components, the planar and spatial analysis of mechanisms, motion transmission, and technical approaches to kinematics, mechanical systems, and machine dynamics. In addition to classical approaches, the book presents two new methods: the analytic-assisted method using Turbo Pascal calculation programs, and the graphic-assisted method, outlining the steps required for the development of graphic constructions using AutoCAD; the applications of these methods are illustrated with examples. Aimed at students of mechanical engineering, and engineers designing and developing mechanisms in their own fields, this book provides a useful overview of classical theories, and modern approaches to the practical and creative application of mechanisms, in seeking solutions to increasingly complex problems.

Preface xi

About the Companion Website xiii

1 The Structure of Mechanisms 1

1.1 Kinematic Elements 1

1.2 Kinematic Pairs 1

1.3 Kinematic Chains 2

1.4 Mobility of Mechanisms 3

1.4.1 Definitions 3

1.4.2 Mobility Degree of Mechanisms without Common Constraints 5

1.4.3 Mobility Degree of Mechanisms with Common Constraints 5

1.4.4 Mobility of a MechanismWritten with the Aid of the Number of Loops 7

1.4.5 Families of Mechanisms 7

1.4.6 Actuation of Mechanisms 9

1.4.7 Passive Elements 9

1.4.8 Passive Kinematic Pairs 10

1.4.9 Redundant Degree of Mobility 10

1.4.10 Multiple Kinematic Pairs 11

1.5 Fundamental Kinematic Chains 11

1.6 Multi-pairs (Poly-pairs) 14

1.7 Modular Groups 15

1.8 Formation and Decomposition of PlanarMechanisms 16

1.9 Multi-poles and Multi-polar Schemata 18

1.10 Classification of Mechanisms 18

2 Kinematic Analysis of Planar Mechanisms with Bars 21

2.1 General Aspects 21

2.2 Kinematic Relations 21

2.2.1 Plane-parallel Motion 21

2.2.2 Relative Motion 23

2.3 Methods for Kinematic Analysis 24

2.3.1 The Grapho-analytical Method 24

2.3.2 The Method of Projections 24

2.3.3 The Newton-Raphson Method 25

2.3.4 Determination of Velocities and Accelerations using the Finite Differences Method 26

2.4 Kinematic Analysis of the RRR Dyad 27

2.4.1 The Grapho-analytical Method 27

2.4.2 The Analytical Method 31

2.4.3 The Assisted Analytical Method 35

2.4.4 The Assisted Graphical Method 35

2.5 Kinematic Analysis of the RRT Dyad 46

2.5.1 The Grapho-analytical Method 46

2.5.2 The Analytical Method 49

2.5.3 The Assisted Analytical Method 52

2.5.4 The Assisted Graphical Method 53

2.6 Kinematic Analysis of the RTR Dyad 60

2.6.1 The Grapho-analytical Method 60

2.6.2 The Analytical Method 63

2.6.3 The Assisted Analytical Method 66

2.6.4 The Assisted Graphical Method 66

2.7 Kinematic Analysis of the TRT Dyad 73

2.7.1 The Grapho-analytical Method 73

2.7.2 The Analytical Method 77

2.7.3 The Assisted Analytical Method 79

2.7.4 The Assisted Graphical Method 80

2.8 Kinematic Analysis of the RTT Dyad 85

2.8.1 The Grapho-analytical Method 85

2.8.2 The Analytical Method 87

2.8.3 The Assisted Analytical Method 90

2.8.4 The Assisted Graphical Method 90

2.9 Kinematic Analysis of the 6R Triad 95

2.9.1 Formulation of the Problem 95

2.9.2 Determination of the Positions 96

2.9.3 Determination of the Velocities and Accelerations 97

2.9.4 The Assisted Analytical Method 98

2.9.5 The Assisted Graphical Method 99

2.10 Kinematic Analysis of Some Planar Mechanisms 103

2.10.1 Kinematic Analysis of the Four-Bar Mechanism 103

2.10.2 Kinematic Analysis of the Crank-shaft Mechanism 109

2.10.3 Kinematic Analysis of the Crank and Slotted Lever Mechanism 113

3 Kinetostatics of Planar Mechanisms 117

3.1 General Aspects: Forces in Mechanisms 117

3.2 Forces of Inertia 118

3.2.1 The Torsor of the Inertial Forces 118

3.2.2 Concentration of Masses 118

3.3 Equilibration of the Rotors 119

3.3.1 Conditions of Equilibration 119

3.3.2 The Theorem of Equilibration 119

3.3.3 Machines for Dynamic Equilibration 121

3.4 Static Equilibration of Four-bar Mechanisms 124

3.4.1 Equilibration with Counterweights 124

3.4.2 Equilibration with Springs 126

3.5 Reactions in Frictionless Kinematic Pairs 126

3.5.1 General Aspects 126

3.5.2 Determination of the Reactions for the RRR Dyad 127

3.5.3 Determination of the Reactions for the RRT Dyad 133

3.5.4 Determination of the Reactions for the RTR Dyad 139

3.5.5 Determination of the Reactions for the TRT Dyad 145

3.5.6 Determination of the Reactions for the RTT Dyad 150

3.5.7 Determination of the Reactions at the Driving Element 155

3.5.8 Determination of the Equilibration Force (Moment) using the Virtual Velocity Principle 156

3.6 Reactions in Kinematic Pairs with Friction 157

3.6.1 Friction Forces and Moments 157

3.6.2 Determination of the Reactions with Friction 160

3.7 Kinetostatic Analysis of some Planar Mechanisms 161

3.7.1 Kinetostatic Analysis of Four-bar Mechanism 161

3.7.2 Kinetostatic Analysis of Crank-shaft Mechanism 164

3.7.3 Kinetostatic Analysis of Crank and Slotted Lever Mechanism 166

4 Dynamics of Machines 169

4.1 Dynamic Model: Reduction of Forces and Masses 169

4.1.1 Dynamic Model 169