Theoretical Kinematics

Oene Bottema, B. Roth

Dover Publ., 1979 - Science - 558 pages

Classic, comprehensive treatment covers Euclidean displacements; instantaneous kinematics; two-position, three-position, four-and-more position theory; special motions; multiparameter motions; kinematics in other geometries; and special mathematical methods. Rigorous, elegant study. Over 800 examples. Bibliography. "...the finest treatment yet written..." — American Scientist.

Contents

• EUCLIDEAN DISPLACEMENTS 1 Displacements: 1
• Orthogonal matrices: 3
• The eigenvalues of an orthogonal matrix: 4
• Standard representations of a displacement: 7
• Cayleys formula for an orthogonal matrix: 9
• A displacement as the product of two reflections: 11
• Indirect displacements: 12
• Transformations and operators: 13
• INSTANTANEOUS KINEMATICS: 17
• The Taylor expansion of an orthogonal matrix: 18
• The angular velocity matrix: 20
• The case n3: 23
• Canonical systems: 27
• Geometrical invariants: 31
• TWO POSITIONS THEORY: 35
• Homologous points: 36
• The complex of lines joining homologous points: 37
• Normal planes: 39
• Homologous planes: 41
• The midpoint plane: 43
• Homologous lines: 45
• The linear complex P: 47
• The midpoint line: 48
• The linebisectors: 51
• The instantaneous case: 55
• Another method to derive the screw displacement equations: 56
• THREEPOSITIONS THEORY: 63
• The plane at infinity: 68
• The planes through three homologous points: 70
• Collinear homologous points: 72
• Lines through three homologous points: 74
• The intersection of three homologous planes: 76
• Three homologous lines: 78
• The circle axes: 91
• The radius of a circle: 94
• An oblique coordinate system: 96
• Applications: 99
• Three mutually orthogonal screw axes: 102
• Three screw axes with a common perpendicular: 106
• The instantaneous case: 111
• FOUR AND MORE POSITIONS: 113
• The configuration of the screw axes: 114
• The screw cone: 117
• The correspondence between axis direction and rotation angle: 118
• The distance condition: 119
• The screw congruence: 121
• Homologous points: 125
• Homologous planes and lines: 128
• A special case of four positions: 132
• More than four positions: 135
• The instantaneous case: 140
• CONTINUOUS KINEMATICS: 147
• Studys soma: 150
• Eulerian angles: 153
• Oneparametermotions: 156
• The axodes: 157
• The pointpaths: 162
• The motion of a plane: 173
• The motion of a line: 177
• A generalization of the EulerSavary formula: 186
• Some general remarks: 189
• The velocity distribution: 191
• The acceleration distribution: 193
• SPHERICAL KINEMATICS: 199
• The lines joining homologous points: 200
• Three positions: 201
• Four and five positions: 203
• Instantaneous spherical properties: 206
• Third order properties: 211
• Fourth order properties: 214
• Time dependent motion: 217
• PLANE KINEMATICS: 219
• Two positions theory: 221
• Three positions theory: 223
• Four positions theory: 235
• Five positions theory: 249
• Six and more positions: 255
• Continuous displacements: 257
• Instantaneous geometric kinematics: 263
• Second order properties: 267
• Third order properties: 279
• Fourth order properties: 284
• Translations: 290
• Time as a parameter: 295
• SPECIAL MOTIONS: 299
• The FrenetSerret motion: 301
• Darbouxs motion: 304
• Mannheims motion: 310
• Schoenflies motion: 312
• Analytically determined motions: 315
• Linesymmetric motions: 317
• Planesymmetric motions: 329
• Motions defined by geometrical conditions: 330
• Special spherical motions: 331
• Special plane motions: 334
• nPARAMETER MOTIONS: 355
• First order properties: 360
• Second order properties: 364
• Continuous twoparameter spatial motions: 373
• Twoparameter spherical motions: 379
• Twoparameter plane motions: 380
• Examples of threeparameter motions: 385
• A MAPPING OF PLANE KINEMATICS: 393
• The geometry of the image space: 397
• Straight lines in the image space: 401
• Curves in the image space: 403
• Plane image curves: 407
• Quadratic motions: 409
• The general fourbar motion: 413
• Folding fourbars: 418
• The slidercrank motion: 423
• Elliptic motion: 425
• The inverse of a fourbar motion: 427
• Cycloidal motions: 428
• The inverse motion: 432
• The centrodes: 434
• Instantaneous kinematics: 436
• Motions with two degrees of freedom: 437
• Algebraic motions with two given paths: 441
• The mapping of indirect displacements: 442
• KINEMATICS IN OTHER GEOMETRIES: 447
• SPECIAL MATHEMATICAL METHODS IN KINEMATICS: 501
• BIBLIOGRAPHY: 533
• INDEX: 545

Popular passages

Page 533 - Treatise on the Theory of Screws (gr. 8°, 26 chapt., 544 p., 50 fig. and 3 plates; 18 sh.). Cambridge, University press, 1900. — Since the author's celebrated publication ,,The Theory of Screws: A study in the Dynamics of a Rigid Body...‎

Bibliographic information

• Title: Theoretical Kinematics; Dover Books on Engineering Series
• Authors: Oene Bottema, B. Roth
• Contributor: B. Roth
• Edition: reprint, illustrated
• Publisher: Dover Publ., 1979
• ISBN: 0486663469, 9780486663463
• Length: 558 pages
• Subjects: Science / Mechanics / Dynamics; Science / Mechanics / General; Science / Physics / General; Technology & Engineering / Civil / General; Technology & Engineering / Mechanical