Mechanisms for Generating Mathematical Curves

Mechanisms for Generating Mathematical Curves
اسم المؤلف
Iulian Popescu , Liliana Luca , Mirela Cherciu , Dan B. Marghitu
التاريخ
22 يناير 2021
المشاهدات
التقييم
(لا توجد تقييمات)
Loading...

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

تحميل

يجب عليك التسجيل في الموقع لكي تتمكن من التحميل
تسجيل | تسجيل الدخول

التعليقات

اترك تعليقاً