Geometric design of linkages:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Springer
2000
|
| Series: | Interdisciplinary applied mathematics
11 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXI, 320 S. graph. Darst. |
| ISBN: | 0387989838 |
Staff View
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| 245 | 1 | 0 | |a Geometric design of linkages |c J. Michael McCarthy |
| 264 | 1 | |a New York u.a. |b Springer |c 2000 | |
| 300 | |a XXI, 320 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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Record in the Search Index
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| adam_text | Contents
Preface vii
1 Introduction 1
1.1 Linkages 2
1.2 Mobility 3
1.2.1 Planar Linkages 4
1.2.2 Spherical Linkages 6
1.2.3 Spatial Linkages 6
1.2.4 Platform Linkages 7
1.3 Workspace 8
1.4 Linkage Design 9
1.4.1 Approximate Straight Line Mechanisms 9
1.5 Summary 11
1.6 References 11
1.7 Exercises 12
2 Analysis of Planar Linkages 13
2.1 Coordinate Planar Displacements 13
2.1.1 The PR Open Chain 14
2.1.2 The RR Open Chain 16
2.1.3 The RPR and 3R Chains 17
2.2 Position Analysis of the RRRP Linkage 18
2.2.1 The Output Slide 18
2.2.2 The Range of Crank Rotation 19
xii Contents
2.2.3 The Coupler Angle 21
2.2.4 The Extreme Slider Positions 21
2.2.5 The RRPR Linkage 22
2.3 Position Analysis of the 4R Linkage 23
2.3.1 Output Angle 24
2.3.2 Coupler Angle 25
2.3.3 Transmission Angle 26
2.3.4 Coupler Curves 27
2.4 Range of Movement 29
2.4.1 Limits on the Input Crank Angle 29
2.4.2 Limits on the Output Crank Angle 31
2.4.3 The Classification of Planar 4R Linkages 32
2.4.4 Grashof Linkages 34
2.4.5 Folding Linkages 35
2.5 Velocity Analysis 35
2.5.1 Velocity of a Point in a Moving Link 35
2.5.2 Instant Center 37
2.6 Velocity Analysis of an RR Chain 37
2.6.1 The Jacobian 37
2.6.2 The Centrode 38
2.7 Velocity Analysis of a Slider Crank 39
2.7.1 Mechanical Advantage 40
2.8 Velocity Analysis of a 4R Chain 41
2.8.1 Output Velocity Ratio 41
2.8.2 Coupler Velocity Ratio 43
2.8.3 Kennedy s Theorem 43
2.8.4 Mechanical Advantage in a 4R Linkage 45
2.9 Summary 46
2.10 References 46
2.11 Exercises 46
3 Graphical Synthesis in the Plane 48
3.1 Displacement of a Planar Body 48
3.1.1 The Pole of a Displacement 50
3.1.2 Determining the Position of a Point 50
3.1.3 An Alternative Construction for the Pole 51
3.1.4 The Pole Triangle 51
3.2 The Geometry of an RR Chain 53
3.2.1 The Dyad Triangle 53
3.2.2 The Center Point Theorem 54
3.3 Finite Position Synthesis of RR Chains 55
3.3.1 Two Precision Positions 56
3.3.2 Three Precision Positions 57
3.3.3 Four Precision Positions 59
3.3.4 Five Precision Positions 61
Contents xiii
3.4 The Geometry of the PR and RP Chains 62
3.4.1 Finite Position Synthesis of PR Chains 62
3.4.2 Finite Position Synthesis of RP Chains 64
3.5 The Design of Four Bar Linkages 66
3.6 Summary 67
3.7 References 67
3.8 Exercises 67
4 Planar Kinematics 69
4.1 Isometry 69
4.1.1 Planar Translations 70
4.1.2 Planar Rotations 70
4.1.3 Planar Displacements 72
4.1.4 The Composition of Two Displacements 73
4.1.5 Relative Displacements 74
4.1.6 Relative Inverse Displacements 75
4.2 The Geometry of Displacement Poles 76
4.2.1 The Pole of a Displacement 76
4.2.2 Perpendicular Bisectors and the Pole 77
4.2.3 Pole of a Relative Displacement 78
4.2.4 The Pole of a Relative Inverse Displacement ... 79
4.3 The Pole Triangle 80
4.3.1 The Pole of a Composite Displacement 80
4.3.2 The Triangle of Relative Displacement Poles ... 82
4.3.3 The Image Pole Triangle 82
4.3.4 The Circumscribing Circle 83
4.4 Summary 84
4.5 References 84
4.6 Exercises 85
5 Algebraic Synthesis of Planar Chains 86
5.1 A Single Revolute Joint 86
5.2 The Geometry of RR Chains 87
5.2.1 Perpendicular Bisectors 87
5.2.2 The Dyad Triangle 88
5.2.3 The Center Point Theorem 89
5.3 Finite Position Synthesis of RR Chains 90
5.3.1 The Algebraic Design Equations 90
5.3.2 Parameterized Form of the Design Equations . . 92
5.3.3 Two Precision Positions 92
5.3.4 Three Precision Positions 93
5.3.5 Four Precision Positions 95
5.3.6 Five Precision Positions 101
5.4 The Design of PR Chains 104
5.4.1 The Design Equations 104
xiv Contents
5.4.2 Two Positions 106
5.4.3 Three Positions 106
5.4.4 Four Positions 107
5.5 The Design of RP Chains 108
5.5.1 The Design Equations 108
5.6 Planar Four Bar Linkages 109
5.6.1 Solution Rectification 109
5.6.2 Function Generation 112
5.7 Summary 113
5.8 References 114
5.9 Exercises 114
6 Analysis of Spherical Linkages 116
6.1 Coordinate Rotations 116
6.1.1 The Composition of Coordinate Rotations .... 117
6.1.2 The RR Open Chain 118
6.1.3 The 3R Open Chain 119
6.2 Position Analysis of a 4R Linkage 120
6.2.1 The Coordinates of O, A, B, and C 120
6.2.2 The Output Angle 121
6.2.3 The Coupler Angle 123
6.2.4 Coupler Curves 124
6.2.5 The Transmission Angle 125
6.3 Range of Movement 126
6.3.1 Limits on the Input Crank Angle 126
6.3.2 Limits on the Output Crank Angle 128
6.3.3 Classification of Spherical 4R Linkages 130
6.3.4 Grashof Linkages 132
6.3.5 Folding Linkages 133
6.4 Angular Velocity 133
6.5 Velocity Analysis of an RR Chain 134
6.6 Velocity Analysis of the 4R Linkage 134
6.6.1 The Output Velocity Ratio 135
6.6.2 The Coupler Velocity Ratio 136
6.6.3 Instantaneous Rotation Axis 136
6.6.4 Mechanical Advantage 137
6.7 Summary 138
6.8 References 138
6.9 Exercises 139
7 Spherical Kinematics 140
7.1 Isometry 140
7.1.1 Spatial Translations 141
7.1.2 Spatial Rotations 141
7.1.3 Spatial Displacements 143
Contents xv
7.1.4 Composition of Rotations 143
7.1.5 Relative Rotations 144
7.1.6 Relative Inverse Rotations 145
7.2 The Geometry of Rotation Axes 146
7.2.1 The Rotation Axis 146
7.2.2 Perpendicular Bisectors and the Rotation Axis . . 147
7.2.3 The Rotation Angle 148
7.2.4 The Rotation Defined by j and S 150
7.2.5 Eigenvalues of a Rotation Matrix 151
7.2.6 Rotation Axis of a Relative Rotation 152
7.2.7 Rotation Axis of a Relative Inverse Rotation . . . 153
7.2.8 Rotational Displacements 153
7.3 The Spherical Pole Triangle 154
7.3.1 The Axis of Composite Rotation 154
7.3.2 The Triangle of Relative Rotation Axes 158
7.3.3 The Spherical Image Pole Triangle 158
7.4 Summary 159
7.5 References 160
7.6 Exercises 160
8 Algebraic Synthesis of Spherical Chains 162
8.1 A Single Revolute Joint 162
8.2 Spherical Displacements 163
8.3 The Geometry of Spherical RR Chains 165
8.3.1 Perpendicular Bisectors 166
8.3.2 The Spherical Dyad Triangle 166
8.3.3 The Center Axis Theorem 168
8.4 Finite Position Synthesis of RR Chains 170
8.4.1 The Algebraic Design Equations 170
8.4.2 Parameterized Form of the Design Equations . . 172
8.4.3 Two Specified Orientations 172
8.4.4 Three Specified Orientations 173
8.4.5 Four Specified Orientations 175
8.4.6 Five Specified Orientations 179
8.5 Spherical 4R Linkages 182
8.5.1 Solution Rectification 183
8.5.2 Function Generation 186
8.6 Summary 187
8.7 References 187
8.8 Exercises 188
9 Analysis of Spatial Chains 189
9.1 The Kinematics Equations 189
9.1.1 Joint Axes 190
9.1.2 The Common Normal 190
xvi Contents
9.1.3 Coordinate Screw Displacements 191
9.1.4 The Denavit Hartenberg Convention 192
9.2 The Analysis of Spatial Open Chains 193
9.2.1 The 3R Wrist (S Joint) 193
9.2.2 The RS Chain 195
9.2.3 The TS Chain 196
9.2.4 The TPS and TRS Chains 197
9.2.5 The CC Chain 198
9.3 Velocity Analysis of Spatial Open Chains 200
9.3.1 Partial Twists of an Open Chain 201
9.3.2 The Jacobian of a Spatial Open Chain 202
9.4 The RSSR Linkage 203
9.4.1 The Output Angle 203
9.5 The RSSP Linkage 206
9.6 The 4C Linkage 207
9.6.1 The Kinematics Equations 208
9.6.2 The Spherical Image 209
9.6.3 The Vector Loop Equation 210
9.7 The 5TS Spatial Linkage 211
9.8 Summary 213
9.9 References 214
9.10 Exercises 214
10 Spatial Kinematics 215
10.1 Spatial Displacements 215
10.1.1 Homogeneous Transforms 216
10.1.2 Composition of Displacements 216
10.1.3 Relative Displacements 217
10.1.4 Screw Displacements 218
10.1.5 The Screw Matrix 219
10.2 Lines and Screws 219
10.2.1 Pliicker Coordinates of a Line 220
10.2.2 Screws 220
10.2.3 Dual Vector Algebra 221
10.2.4 Orthogonal Components of a Line 223
10.2.5 The Spatial Displacement of Screws 226
10.3 The Geometry of Screw Axes 227
10.3.1 The Screw Axis of a Displacement 227
10.3.2 Perpendicular Bisectors and the Screw Axis . . . 228
10.3.3 Rodrigues s Equation for Screws 231
10.4 The Spatial Screw Triangle 233
10.4.1 The Screw Axis of a Composite Displacement . . 233
10.4.2 The Spatial Triangle 234
10.4.3 The Composite Screw Axis Theorem 235
10.4.4 Dual Quaternions and the Spatial Triangle .... 236
Contents xvii
10.4.5 The Triangle of Relative Screw Axes 237
10.5 Summary 237
10.6 References 238
10.7 Exercises 238
11 Algebraic Synthesis of Spatial Chains 240
11.1 The Geometry of a TS Spatial Chain 240
11.1.1 Perpendicular Bisectors 241
11.1.2 The Design Equations 242
11.1.3 Four Specified Spatial Positions 243
11.1.4 Seven Specified Spatial Positions 243
11.2 The Geometry of a CC Chain 245
11.2.1 Direction and Moment Equations 246
11.2.2 Five Specified Spatial Positions 248
11.2.3 The Transfer Principle 248
11.2.4 The Spatial Dyad Triangle 249
11.2.5 The Central Axis Theorem 250
11.2.6 Roth s Theorem 251
11.2.7 The Spatial Compatibility Platform 252
11.3 The Geometry of Spatial RR Chains 254
11.3.1 The Constraint Equations 254
11.3.2 Three Specified Spatial Positions 257
11.3.3 Bennett Linkage Coordinates 260
11.4 Platform Linkages 262
11.4.1 The 4C Spatial Linkage 263
11.4.2 The 5TS Spatial Linkage 263
11.4.3 Function Generation 263
11.5 Summary 264
11.6 References 264
11.7 Exercises 265
12 Platform Manipulators 266
12.1 Introduction 266
12.1.1 Twists and Wrenches 267
12.1.2 Virtual Work 270
12.2 The Jacobian of a Platform Manipulator 270
12.3 Conditions for Line Based Singularities 272
12.3.1 Locating the Lines of Action 272
12.4 Classification of Line Based Singularities 274
12.4.1 Type 1 Singularities 275
12.4.2 Type 2 Singularities 275
12.4.3 Type 3 Singularities 278
12.4.4 Type 4 Singularities 279
12.4.5 Type 5 Singularities 282
12.5 Examples 283
xviii Contents
12.6 Summary 284
12.7 References 284
12.8 Exercises 284
A Solving Constraint Equations 287
A.I The 4R Linkage Constraint 287
A. 2 The Platform Constraint Equations 288
B Graphical Constructions 290
B.I Perpendicular Bisector 290
B.2 Circle Through Three Points 290
B.3 Duplication of an Angle 291
B.4 Reflection of a Point Through a Line 292
C Spherical Trigonometry 293
C.I The F Frame Formulas 294
C.2 The B Frame Formulas 296
C.3 Summary 297
D Operations with Dual Numbers 298
E Kinematics Equations 300
E.I The Planar RR Chain 300
E.2 The Spherical RR Chain 302
E.3 The CC Chain 303
References 305
Index 313
|
| any_adam_object | 1 |
| author | McCarthy, John Michael 1952- |
| author_GND | (DE-588)14316595X |
| author_facet | McCarthy, John Michael 1952- |
| author_role | aut |
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| callnumber-search | TJ182 |
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| dewey-ones | 621 - Applied physics |
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| dewey-search | 621.815 |
| dewey-sort | 3621.815 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Maschinenbau / Maschinenwesen Mathematik Maschinenbau |
| format | Book |
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| id | DE-604.BV013288201 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:43:11Z |
| institution | BVB |
| isbn | 0387989838 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009059990 |
| oclc_num | 247080104 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-703 DE-634 DE-11 |
| owner_facet | DE-91G DE-BY-TUM DE-703 DE-634 DE-11 |
| physical | XXI, 320 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series | Interdisciplinary applied mathematics |
| series2 | Interdisciplinary applied mathematics |
| spelling | McCarthy, John Michael 1952- Verfasser (DE-588)14316595X aut Geometric design of linkages J. Michael McCarthy New York u.a. Springer 2000 XXI, 320 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Interdisciplinary applied mathematics 11 Hebelgetriebe - Kinematische Kette - Diskrete Geometrie - Differentialgeometrie - Getriebesynthese Links and link-motion Machine design Roboterarm (DE-588)4507425-2 gnd rswk-swf Entwurf (DE-588)4121208-3 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Kinematische Kette (DE-588)4205924-0 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Hebelgetriebe (DE-588)4019928-9 gnd rswk-swf Diskrete Geometrie (DE-588)4130271-0 gnd rswk-swf Getriebesynthese (DE-588)4157216-6 gnd rswk-swf Hebelgetriebe (DE-588)4019928-9 s Kinematische Kette (DE-588)4205924-0 s Diskrete Geometrie (DE-588)4130271-0 s Differentialgeometrie (DE-588)4012248-7 s Getriebesynthese (DE-588)4157216-6 s DE-604 Roboterarm (DE-588)4507425-2 s Geometrie (DE-588)4020236-7 s Entwurf (DE-588)4121208-3 s 1\p DE-604 Interdisciplinary applied mathematics 11 (DE-604)BV004216726 11 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009059990&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | McCarthy, John Michael 1952- Geometric design of linkages Interdisciplinary applied mathematics Hebelgetriebe - Kinematische Kette - Diskrete Geometrie - Differentialgeometrie - Getriebesynthese Links and link-motion Machine design Roboterarm (DE-588)4507425-2 gnd Entwurf (DE-588)4121208-3 gnd Geometrie (DE-588)4020236-7 gnd Kinematische Kette (DE-588)4205924-0 gnd Differentialgeometrie (DE-588)4012248-7 gnd Hebelgetriebe (DE-588)4019928-9 gnd Diskrete Geometrie (DE-588)4130271-0 gnd Getriebesynthese (DE-588)4157216-6 gnd |
| subject_GND | (DE-588)4507425-2 (DE-588)4121208-3 (DE-588)4020236-7 (DE-588)4205924-0 (DE-588)4012248-7 (DE-588)4019928-9 (DE-588)4130271-0 (DE-588)4157216-6 |
| title | Geometric design of linkages |
| title_auth | Geometric design of linkages |
| title_exact_search | Geometric design of linkages |
| title_full | Geometric design of linkages J. Michael McCarthy |
| title_fullStr | Geometric design of linkages J. Michael McCarthy |
| title_full_unstemmed | Geometric design of linkages J. Michael McCarthy |
| title_short | Geometric design of linkages |
| title_sort | geometric design of linkages |
| topic | Hebelgetriebe - Kinematische Kette - Diskrete Geometrie - Differentialgeometrie - Getriebesynthese Links and link-motion Machine design Roboterarm (DE-588)4507425-2 gnd Entwurf (DE-588)4121208-3 gnd Geometrie (DE-588)4020236-7 gnd Kinematische Kette (DE-588)4205924-0 gnd Differentialgeometrie (DE-588)4012248-7 gnd Hebelgetriebe (DE-588)4019928-9 gnd Diskrete Geometrie (DE-588)4130271-0 gnd Getriebesynthese (DE-588)4157216-6 gnd |
| topic_facet | Hebelgetriebe - Kinematische Kette - Diskrete Geometrie - Differentialgeometrie - Getriebesynthese Links and link-motion Machine design Roboterarm Entwurf Geometrie Kinematische Kette Differentialgeometrie Hebelgetriebe Diskrete Geometrie Getriebesynthese |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009059990&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004216726 |
| work_keys_str_mv | AT mccarthyjohnmichael geometricdesignoflinkages |