Mechanisms for Generating Mathematical Curves

Mechanisms for Generating Mathematical Curves
Springer Tracts in Mechanical Engineering
Iulian Popescu
Liliana Luca
Mirela Cherciu
Dan B. Marghitu
Contents
Part I Basic Theory of Mechanisms
1 Structural Analysis of Planar Mechanisms 3
1.1 Kinematic Joints . 3
1.2 Kinematic Links and the Degree of Freedom 8
1.3 Substitution of Fourth Class Joints . 10
1.4 Assur’s Principle and Kinematic Groups . 11
1.5 Kinematic and Structural Diagrams . 17
References . 20
2 Kinematic Analysis of Planar Mechanisms 21
2.1 Closed-Loop Method . 21
2.1.1 Kinematics of the Driving Links and Assur Groups 24
2.1.2 Kinematics of the Slider-Crank Mechanism 34
2.2 Kinematics of Third Order Triad . 39
References . 44
Part II Synthesis and Analysis of Mechanisms for Generating
Mathematical Curves
3 Mechanisms for Generating Straight Lines and Arcs 47
3.1 An Approximate Rectilinear Guiding Mechanism . 47
3.1.1 The Synthesis of a New Mechanism . 47
3.1.2 The Structure and Kinematics of the New
Mechanism . 49
3.1.3 Results Obtained . 51
3.2 Mechanism for Approximation of Arcs 54
3.2.1 Trajectories . 54
3.2.2 Velocities and Accelerations . 57
References . 61
ix4 Mechanisms for Generating Conical Curves . 63
4.1 Mechanism Ellipsograph . 63
4.1.1 Introduction . 63
4.1.2 The Mechanism Synthesis 64
4.1.3 The Mechanism Analysis . 65
4.1.4 Results Obtained . 65
4.2 Mechanisms for Generating Parabolas . 72
4.2.1 Case of Parabola Based on Pedal Curve 72
4.2.2 A New Mechanism for Generating Parabola . 80
4.2.3 Case for Generation of Parabola as Envelope
of a Line . 89
4.3 Mechanisms for Generating Hyperbolas 95
4.3.1 Case of Hyperbola Based on Pedal Curve . 95
4.3.2 A New Mechanism for Generating Hyperbola 104
4.4 Conic-Generating Mechanism Based on a Locus Problem . 114
4.4.1 Geometrical Considerations . 114
4.4.2 The Mechanism Synthesis 114
4.4.3 The Mechanism Analysis . 114
4.4.4 Results Obtained . 116
References . 119
5 Mechanisms for Generating Some Plane Mathematical Curves 121
5.1 Mechanisms for Generating Cissoids 122
5.1.1 The Cissoid of a Circle 122
5.1.2 The Straight Line Cissoid . 125
5.2 Mechanism for Generating Berard’s Curve 130
5.2.1 The Mechanism Synthesis 130
5.2.2 The Mechanism Analysis . 131
5.2.3 Results Obtained . 132
5.3 Mechanism for Generating the Egg-Shaped Curve 142
5.3.1 Introduction . 142
5.3.2 The Mechanism Synthesis 143
5.3.3 The Mechanism Analysis . 144
5.3.4 Results Obtained . 145
5.3.5 The Influence of Inputs on the Curve’s Shape 147
5.4 Mechanism for Generating the Double Egg Curve 152
5.4.1 The Mechanism Synthesis 152
5.4.2 The Mechanism Analysis . 152
5.4.3 Results Obtained . 153
5.4.4 The Influence of Inputs on the Curve’s Shape 157
5.5 Mechanism for Generating Bernoulli Quartic 159
5.5.1 The Mechanism Synthesis 159
5.5.2 The Mechanism Analysis . 160
5.5.3 Results Obtained . 161
x Contents5.6 Mechanism for Generating MacLaurin’s Trisectrix 166
5.6.1 Introduction . 166
5.6.2 The Mechanism Synthesis 167
5.6.3 The Mechanism Analysis . 167
5.6.4 Results Obtained . 168
5.6.5 The Influence of Inputs on the Curve’s Shape 172
5.7 Mechanism for Generating the Ophiuride . 175
5.7.1 Introduction . 175
5.7.2 The Mechanism Synthesis 175
5.7.3 The Mechanism Analysis . 177
5.7.4 Results Obtained . 178
5.7.5 Considerations Regarding the Mechanism
Functionality 180
5.7.6 The Influence of Input Data on the Curve’s Shape . 180
5.8 Mechanism for Generating Pascal’s Snail . 186
5.8.1 The Mechanism Synthesis 186
5.8.2 The Mechanism Analysis . 188
5.8.3 Results Obtained . 188
References . 192
6 Mechanism for Generating Spatial Curves 193
6.1 Screw Mechanism . 193
6.1.1 Input Data 193
6.1.2 Generation of Cylindrical Helix 195
6.1.3 Generation of Conical Helix . 195
6.1.4 Generation of Complex Spatial Curves . 196
6.2 Six-Bar Linkage Mechanism 202
6.2.1 Input Data 202
6.2.2 Generation of Cylindrical Helix with Variable Pitch . 203
6.2.3 Generation of Conical Helix with Variable Pitch 204
6.2.4 Generation of Complex Spatial Curves with Variable
Pitch 205
References .
كلمة سر فك الضغط : books-world.net
The Unzip Password : books-world.net