References to Additional Literature 1. Angeles J (1982) Spatial kinematic chains, analysis, synthesis, optimisation. Springer, New York 2. Angeles J (1988) Rational kinematics. Springer Tracts in Natural Philosophy 34, New York 3. Angeles J, Hommel G, Kov´acs P (1993) Computational kinematics. Kluwer, Dordrecht 4. Angeles J (2003) Fundamentals of robotic mechanical systems: Theory, methods and algorithms. 2nd ed. Springer, New York 5. Artobolevski I I (1986) Mechanisms in modern engineering design. v.1–3, Mir, Moscow 6. Beggs J S (1966) Advanced mechanism. Macmillan, New York 7. Beggs J S (1983) Kinematics. Springer, Berlin, Heidelberg, New York 8. Beyer R (1931) Technische Kinematik. Barth, Leipzig 9. Beyer R (1953) Kinematische Getriebesynthese. Springer, Berlin (Engl. trans. Kuenzel H (1963) The kinematic synthesis of linkages. Chapman and Hall, London) 10. Beyer R (1963) Technische Raumkinematik. Springer, Berlin 11. Bogolyubov A N (1967) Razvitie problem mekhaniki mashin (Bibliografiya) [Develop- ment of problems of mechanics in machines (Bibliography)], Naukova Dumka, Kiev 12. Crelier L (1911) Syst`emes cin´ematiques. Gauthier-Villars, Paris 13. de Groot J (Ed.) (1970) Bibliography on kinematics. v.1,2. Eindhoven Univ. of Techn. 14. Dizio˘glu B (1965,1967) Getriebelehre v.1: Grundlagen, v.2: Massbestimmung. Vieweg, Braunschweig 15. Dresig H, Naake S, Rockhausen L (1994) Vollst¨andiger und harmonischer Ausgleich ebener Mechanismen. Fortschritt-Berichte VDI, Reihe 18, 155,71 pp. D¨usseldorf 16. Dresig H, Sch¨onherr J, Peisach E E (2000) Typ- und Masssynthese von ebenen Kop- pelgetrieben mit h¨oheren Gliedergruppen. Abschlussbericht DFG-Forschungsvorhaben Dr234/7-2, Bonn 17. Giering O, Hoschek J (eds.) (1994) Geometrie und ihre Anwendungen. Hanser, M¨unchen 18. Hall A S (1966) Kinematics and linkage design. Prentice-Hall, Englewood Cliffs, New Jersey 19. Heun K (1906) Lehrbuch der Mechanik. Teil 1: Kinematik. G¨oschen, Leipzig 20. Jones F D, Horton H L, Newell J A (eds.) (1968) Ingenious mechanisms for designers and inventers, vol.1,2,3,4 Industrial Press, New York 21. Julia G (1936) Cours de cin´ematique (r´edig´e par J. Dieudonn´e). 2nd. ed. Gauthier- Villars, Paris 22. Klein F, M¨uller C (eds.) (1901-1908) Enzyklop¨adie der Math. Wissenschaften. v.IV: Mechanik. Teubner, Leipzig © Springer-Verlag Berlin Heidelberg 2016 677 J. Wittenburg, Kinematics, DOI 10.1007/978-3-662-48487-6 678 References to Additional Literature 23. Koenigs G (1905) Introduction `a une th´eorie nouvelle des m´echanismes. Hermann, Paris 24. Lebedev P A (1966) Kinematics of spatial mechanisms (Russ.). Isdat. Maschinostr., Moscow (with references to 115 Russian titles) 25. Lenarˇciˇc J, Ravani B (eds) (1994) Advances in robot kinematics and computational geometry. Kluwer, Dordrecht 26. Lenarˇciˇc J, Parenti-Castelli V (eds.) (1996) Advances in robot kinematics. Kluwer, Dordrecht 27. 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Wiley, New York Index (4 × 4) transformation matrix, 85 binary link, 658 Π-points, 435 Bobillier’s theorem, 484 Bresse circle, 473 acceleration, 350, 413, 497 Bryan angles, 9, 38, 40, 333, 660 complex formulation, 470 Burmester point, 632 acceleration distribution, 309 Burmester theory, 629 accelerometer, 318 active height, 536, 545, 550 cam mechanism, 240, 455 addendum, 536, 545 canonical reference frame, 80, 303, 310 addendum circle, 546, 550 Cardan angles, 9 addendum modification, 547 cardinal point, 437, 489 affine transformation, 238 cardioid, 460, 501 angle of pressure, 544, 547, 552 carrier body, 664 angular acceleration, 289, 350 cartesian base, 1 angular momentum, 666 Cayley-Klein parameters, 28, 337 angular velocity, 289, 329, 350 center angular velocity ratio, 509 of acceleration, 309 angular velocity triangle, 360 of curvature, 414 animation of motion, 46 of rotation, 521, 575, 577 antiparallelogram mechanism, 465 center point, 629, 630 Archimedes’ spiral, 508 center point curve, 630, 632, 653 articulation point, 350, 671 centrifugal acceleration, 356 astroid, 501, 520 centrode, 451, 464, 485, 488, 530, 577, 600 Chebychev’s optimality criterion, 509, 619 Ball’s point, 492, 618 Chinese southpointing chariot, 307 ball-in-track joint, 404 circle of singular foci, 598, 606, 648 base circle, 543, 552 circle of vertices, 504 base cylinder, 552, 556 circle point, 425, 629 base helix, 553, 556 circle point curve, 632 base helix angle, 560 circular pitch, 535, 545 Bennett mechanism, 180, 207, 663 closed kinematic chain, 400 Besicovitch, 503 closure condition, 166, 168, 177, 674 bevel differential, 307 co-factor, 3, 5, 35, 41 bevel gear, 306 cognate four-bars, 590, 604, 617, 625 Bezout, 281 cognate slider-crank, 593, 608 bicursal, 633, 653 commutativity conditions, 418, 424 © Springer-Verlag Berlin Heidelberg 2016 679 J. Wittenburg, Kinematics, DOI 10.1007/978-3-662-48487-6 680 Index complex (of lines), 70 Darboux motion, 457 complex line, 71, 141, 296 decomposition complex number, 411, 431, 497, 590 of a rotation, 55, 299 composite system center of mass, 634, 665, of a screw displacement, 116 667 of force screw, 368 conchoid, 459 dedendum, 546 congruence, 70, 77, 206 defect, 138 conjugate screws, 124, 374 degree of freedom, 137, 515, 664, 674 conjugate tooth flanks, 374, 532, 534, 537, Denavit-Hartenberg parameters, 161, 235, 544, 553, 558, 560 271 conservation of kinetic energy, 664 differential equations of motion, 665 constraint force, 665, 671 direct kinematics, 278, 350 contact direct path, 354 force, 544, 554 direction cosine matrix, 1, 13, 17, 33, 34, normal, 536, 542, 561 37, 318, 350, 660 point, 538 direction cosines, 1, 329, 335 ratio, 546, 556, 564 directrix, 77, 125, 132, 379, 487, 489 coordinate matrix, 3 discriminant, 311, 382 Coriolis acceleration, 292, 356 displacement coupler, 567, 639 elementary, 415 centrode, 464 in a plane, 411 coupler curve, 482, 567, 584, 590, 594, 595, sense-preserving, 416, 420 607, 616, 634, 643, 656, 658 sense-reversing, 416, 420 bicursal, 595, 606 displacement group, 443 double points, 599, 648 distribution parameter, 78, 83, 125, 301, straight-line approximation, 617 364, 553, 558 symmetrical, 603, 646 door mechanism, 466 unicursal, 595 double helical gearing, 554 coupler triangle, 590, 643, 656 double-crank, 570, 593, 643 coupling double-rocker, 570, 643 ball-in-track, 405, 407 first kind, 571 bicardanic, 402 second kind, 571, 593 Clemens, 403 draw-bar, 42 Devos, 405 dual angle, 99 Hebson, 401 dual basis, 102 Oldham, 387, 394, 409 dual Bryan angles, 108 Tracta, 401 dual derivative, 98 tripod, 407 dual differentiation, 98, 108, 167, 178, 268 Unitru, 403 dual direction cosine matrix, 102, 108 crank, 570 dual direction cosines, 103 crank-rocker, 570, 593, 623, 632, 643 dual Euler angles, 108 crowning, 531 dual Euler-Rodrigues parameters, 110 cubic of stationary curvature, 487 dual number, 97 curvature, 414, 473, 476, 485, 510 dual quaternion, 110, 112, 278 curvilinear coordinates, 321 dual Rodrigues vector, 110 cusp, 303, 311, 460, 463, 481, 501, 517, 542, dual transformation matrix, 269 548, 654 dual vector, 99 cycloid, 500, 501, 521 dwell mechanism, 509 ordinary, 506 dynamics of mechanisms, 663 cylindroid, 122, 132, 359, 373 principal axes, 123, 124 eigenvalue, 4, 14, 124, 311, 382 principal pitches, 124 eigenvector, 5, 15, 59, 311, 382 Index 681 elliptic trammel, 455, 475, 494, 497, 501, generator, 78, 237 514, 629 gimbal lock, 8, 54 envelope, 517 gimbal suspension system, 8, 51 epicycloid, 500, 508, 535, 541 glide reflection, 419, 421, 441 epitrochoid, 500, 508 Goldberg mechanism, 212 prolate, 542 gorge circle, 363, 558 equilibrium condition, 587 Gr¨ubler’s formula, 139, 205, 298, 401 Euler angles, 7, 19, 38, 333, 336 graph theory, 672 Euler vector, 33, 339 Grashof condition, 568, 641 Euler’s equation, 671 group, 4, 21, 30 Euler’s formula, 412 Euler-Rodrigues parameters, 16, 19, 21, 28, half-angle equations, 175 36, 38, 270, 319, 334 helicoid, 556 correction formulas, 345 helix, 367, 374 Euler-Savary equation, 479 herpolhode cone, 305, 332, 342, 390, 395 evolute, 517 Heureka octahedron, 242 external force, 664 homokinetic shaft coupling, 153, 387, 400 homologous points, 425, 629, 630 Fayet’s equation, 481 Hooke’s joint, 154, 205, 305, 388, 663 Fenyi’s joint, 302 angular acceleration, 390 fillet, 536, 546 angular velocity ratio, 389 fixed axode, 301 herpolhode cone, 390 fixed centrode, 452 polhode cone, 390 fixed cone, 305 series-connected, 397