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Volumn 41, Issue 1, 2006, Pages 41-52

An historical review of the theoretical development of rigid body displacements from Rodrigues parameters to the finite twist

Author keywords

Finite screw displacement; Finite twist; History; Mathematics; Review; Rigid body displacement; Rotations; Screw; Theoretical kinematics; Transformation group

Indexed keywords

HAMILTONIANS; MATHEMATICAL TRANSFORMATIONS;

EID: 27744485228     PISSN: 0094114X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mechmachtheory.2005.04.004     Document Type: Article
Times cited : (117)

References (97)
  • 1
    • 0011418022 scopus 로고
    • Problema algebraicum ob affectiones prorsis singulares memorabili, 1770
    • L. Euler Problema algebraicum ob affectiones prorsis singulares memorabili, 1770 Opera Omnia, I 6 1770 287 315
    • (1770) Opera Omnia, i , vol.6 , pp. 287-315
    • Euler, L.1
  • 2
    • 0000743406 scopus 로고
    • Formulae generales pro traslatione quacunque corporum rigidorum
    • L. Euler Formulae generales pro traslatione quacunque corporum rigidorum Novi Commentari Academiae Imperialis Petropolitanae 20 1775 189 207 Leonhardi Euleri Opera Omnia, Series Secunda, Opera Mechanica Et Astronomica, Basileae MCMLXVIII, 9, 84-98
    • (1775) Novi Commentari Academiae Imperialis Petropolitanae , vol.20 , pp. 189-207
    • Euler, L.1
  • 4
    • 0001525552 scopus 로고
    • Nova Methodus Motum Corporum Rigidorum Determinandi
    • L. Euler Nova Methodus Motum Corporum Rigidorum Determinandi Novi Commentari Academiae Imperialis Petropolitanae 20 1775 208 238 Leonhardi Euleri Opera Omnia, Series Secunda, Opera Mechanica Et Astronomica, Basileae MCMLXVIII, 9, 99-125
    • (1775) Novi Commentari Academiae Imperialis Petropolitanae , vol.20 , pp. 208-238
    • Euler, L.1
  • 5
    • 0004262125 scopus 로고
    • De Motu Corporum Circa Puncum Fixum Mobilium
    • L. Euler De Motu Corporum Circa Puncum Fixum Mobilium Commentatio 825 indicis ENESTROEMIANI, Opera postuma 2 1862 43 62 Leonhardi Euleri Opera Omnia, Series Secunda, Opera Mechanica Et Astronmica, Basileae MCMLXVIII, 9, 413-441
    • (1862) Commentatio 825 Indicis ENESTROEMIANI, Opera Postuma 2 , pp. 43-62
    • Euler, L.1
  • 6
    • 0003708995 scopus 로고
    • E.D. Wilson Scribner New York
    • J.W. Gibbs E.D. Wilson Vector Analysis 1901 Scribner New York and Yale University Press, New Haven, 1931
    • (1901) Vector Analysis
    • Gibbs, J.W.1
  • 11
    • 0037769058 scopus 로고    scopus 로고
    • The vectorial parameterization of rotation
    • O.A. Bauchau, and L. Trainelli The vectorial parameterization of rotation Nonlinear Dynamics 32 2003 71 92
    • (2003) Nonlinear Dynamics , vol.32 , pp. 71-92
    • Bauchau, O.A.1    Trainelli, L.2
  • 15
    • 0033876787 scopus 로고    scopus 로고
    • Screw axis defined by Giulio Mozzi in 1763 and early studies on helicoidal motion
    • M. Ceccarelli Screw axis defined by Giulio Mozzi in 1763 and early studies on helicoidal motion Mechanism and Machine Theory 35 2000 761 770
    • (2000) Mechanism and Machine Theory , vol.35 , pp. 761-770
    • Ceccarelli, M.1
  • 16
    • 0000758915 scopus 로고
    • Note sur le propriétés générales du systéme de deux corps semblables entr'eux et places d'une maniére quelconque dans l'espace; Et sur le déplacement fini ou infiniment petis d'un corps solide libre
    • M. Chasles Note sur le propriétés générales du systéme de deux corps semblables entr'eux et places d'une maniére quelconque dans l'espace; et sur le déplacement fini ou infiniment petis d'un corps solide libre Bulletin Des Sciences Mathematiques 14 1830 321 326
    • (1830) Bulletin des Sciences Mathematiques , vol.14 , pp. 321-326
    • Chasles, M.1
  • 18
    • 0000741026 scopus 로고
    • Des lois géométriques qui régissent les déplacements d'un systéme solide dans l'espace, et de la variation des coordonnées provenant de ces déplacements considérés indépendamment des causes qui peuvent les produire
    • O. Rodrigues Des lois géométriques qui régissent les déplacements d'un systéme solide dans l'espace, et de la variation des coordonnées provenant de ces déplacements considérés indépendamment des causes qui peuvent les produire Journal de Mathématiques 5 1840 380 440
    • (1840) Journal de Mathématiques , vol.5 , pp. 380-440
    • Rodrigues, O.1
  • 21
    • 0041852030 scopus 로고
    • On the composition of finite rotations
    • B. Paul On the composition of finite rotations American Mathematical Monthly 70 1963 949 954
    • (1963) American Mathematical Monthly , vol.70 , pp. 949-954
    • Paul, B.1
  • 24
    • 27744603163 scopus 로고
    • Gauss and the physical sciences
    • A.F. Monna Gauss and the physical sciences Nieuw Tijdschr. Wisk. 64 4 1976/1977 212 217 (in Dutch)
    • (1976) Nieuw Tijdschr. Wisk. , vol.64 , Issue.4 , pp. 212-217
    • Monna, A.F.1
  • 25
    • 27744525053 scopus 로고
    • Königliche gesellschaft der wissenschaften
    • Göttingen
    • C.F. Gauss, Königliche Gesellschaft der Wissenschaften, Göttingen, Werke 12 (1831) 1863-1929.
    • (1831) Werke , vol.12 , pp. 1863-1929
    • Gauss, C.F.1
  • 26
    • 27744607810 scopus 로고
    • On a new method of investigating the relations of surfaces to their normals, with results respecting the curvatures of ellipsoids
    • W.R. Hamilton On a new method of investigating the relations of surfaces to their normals, with results respecting the curvatures of ellipsoids Dublin University Review 1833 653 654
    • (1833) Dublin University Review , pp. 653-654
    • Hamilton, W.R.1
  • 27
    • 27744454774 scopus 로고
    • Quaternions
    • W.R. Hamilton Quaternions Math Papers III 1843 101 105 Reprinted in Cambridge University Press, 1967
    • (1843) Math Papers , vol.3 , pp. 101-105
    • Hamilton, W.R.1
  • 28
    • 27744571442 scopus 로고
    • Hamilton's entdeckung der quaternionen
    • Veröffentlichungen der Joachim Jungius-Gesellschaft Hamburg, Gottingen
    • B.L. van der Waerden, Hamilton's entdeckung der quaternionen, Vandenhoeck & Ruprecht, Veröffentlichungen der Joachim Jungius-Gesellschaft Hamburg, Gottingen, 1974.
    • (1974) Vandenhoeck & Ruprecht
    • Van Der Waerden, B.L.1
  • 29
    • 0001744133 scopus 로고
    • Hamilton's discovery of quaternions
    • Translated into English Adelphi University
    • Translated into English by F.V. Pohle, Adelphi University: Hamilton's discovery of quaternions, Mathematics Magazine 49(5) (1976) 227-234.
    • (1976) Mathematics Magazine , vol.49 , Issue.5 , pp. 227-234
    • Pohle, F.V.1
  • 30
    • 0000613202 scopus 로고
    • Letter to Graves on quaternions
    • W.R. Hamilton Letter to Graves on quaternions Philosophical Magazine XXV 1844 489 495 Reprinted in Math Papers, Cambridge University Press, 1967, pp. 106-110
    • (1844) Philosophical Magazine , vol.25 , pp. 489-495
    • Hamilton, W.R.1
  • 31
    • 0011566046 scopus 로고
    • Geometrical Optics
    • Cambridge University Press Cambridge
    • Edited for the Royal Irish Academy A.W. Conway J.L. Synge Geometrical Optics The Mathematical Papers of Sir William Rowan Hamilton vol. I 1931 Cambridge University Press Cambridge A.W. Conway, A.J. McConnell (Eds.), Dynamics, vol. II, 1940; H. Halberstam, R.E. Ingram (Eds.), Algebra, vol. III, 1967
    • (1931) The Mathematical Papers of Sir William Rowan Hamilton , vol.1
    • Conway, A.W.1    Synge, J.L.2
  • 32
    • 0000613202 scopus 로고
    • On quaternions; Or on a new system of imaginaries in algebra
    • W.R. Hamilton On quaternions; or on a new system of imaginaries in algebra (incl. Letter to J.T. Graves, 17 October 1843) Philosophical Magazine 25 Suppl., 3rd series 1844 489 495
    • (1844) Philosophical Magazine , vol.25 , Issue.3 , pp. 489-495
    • Hamilton, W.R.1
  • 33
    • 0004337740 scopus 로고
    • Olinde Rodrigues' Paper of 1840 on Transformation Groups
    • J.J. Gray Olinde Rodrigues' Paper of 1840 on Transformation Groups Archive for History of Exact Sciences 21 1980 375 385
    • (1980) Archive for History of Exact Sciences , vol.21 , pp. 375-385
    • Gray, J.J.1
  • 34
    • 0000318211 scopus 로고
    • Hamilton, Rodrigues, and the Quaternion Scandal
    • S.L. Altmann Hamilton, Rodrigues, and the Quaternion Scandal Mathematics Magazine 62 5 1989 291 308
    • (1989) Mathematics Magazine , vol.62 , Issue.5 , pp. 291-308
    • Altmann, S.L.1
  • 38
    • 0001710889 scopus 로고
    • On the motion of rotation of a solid body
    • A. Cayley On the motion of rotation of a solid body Cambridge Mathematics Journal III 1843 224 232
    • (1843) Cambridge Mathematics Journal , vol.16 , pp. 224-232
    • Cayley, A.1
  • 39
    • 27744548141 scopus 로고
    • Cambridge University Press
    • The Collected Mathematical Papers vol. I (Paper No. 6), Volumes plus Index 1889 Cambridge University Press 28 35
    • (1889) The Collected Mathematical Papers , vol.3 , pp. 28-35
  • 40
    • 0000369182 scopus 로고
    • On certain results relating to quaternions
    • A. Cayley On certain results relating to quaternions Philosophical Magazine 26 1845 141 145
    • (1845) Philosophical Magazine , vol.26 , pp. 141-145
    • Cayley, A.1
  • 41
    • 27744554770 scopus 로고
    • Cambridge University Press
    • The Collected Mathematical Papers vol. I (Paper No. 20) 1889 Cambridge University Press 123 126 Note 20, pp. 586
    • (1889) The Collected Mathematical Papers , vol.120 , pp. 123-126
  • 44
    • 27744474275 scopus 로고
    • Catalogue of Scientific Papers
    • Royal Society Cambridge
    • Catalogue of Scientific Papers Index of Pure Mathematics vol. I 1908 Royal Society Cambridge 1800 1900
    • (1908) Index of Pure Mathematics , vol.1 , pp. 1800-1900
  • 46
    • 0042906634 scopus 로고
    • Von den Bewegungen und Umlegungen
    • E. Study Von den Bewegungen und Umlegungen Mathematische Annalen 39 1891 441 564
    • (1891) Mathematische Annalen , vol.39 , pp. 441-564
    • Study, E.1
  • 48
    • 27744518550 scopus 로고
    • The theory of screws-a geometrical study of the kinematics, equilibrium, and small oscillations of a rigid body
    • R.S. Ball The theory of screws-a geometrical study of the kinematics, equilibrium, and small oscillations of a rigid body Transactions of the Royal Irish Academy XXV 1871 137 217
    • (1871) Transactions of the Royal Irish Academy , vol.25 , pp. 137-217
    • Ball, R.S.1
  • 49
    • 27744541323 scopus 로고
    • R.S. Ball, The theory of screws, Dublin, 1876; also extended abstract in Mathematische Annalen 1875 541 553
    • (1875) Mathematische Annalen , pp. 541-553
  • 51
    • 5644261015 scopus 로고
    • First supplement to an essay on the theory of systems of rays
    • W.R. Hamilton First supplement to an essay on the theory of systems of rays Transactions of the Royal Irish Academy XVI 1830 4 62
    • (1830) Transactions of the Royal Irish Academy , vol.16 , pp. 4-62
    • Hamilton, W.R.1
  • 53
    • 27744508295 scopus 로고
    • Sulle serie die sistemi di forze
    • G. Battaglini Sulle serie die sistemi di forze Napoli Rendiconto VIII 1869 87 94 also in Giornale di Matemax, X (1872) 133-140
    • (1869) Napoli Rendiconto , vol.8 , pp. 87-94
    • Battaglini, G.1
  • 54
    • 27744539138 scopus 로고
    • Zur theorie der linien-cómplexe des ersten und zweiten Grades
    • F. Klein Zur theorie der linien-cómplexe des ersten und zweiten Grades Mathematische Annalen II June 1869 198 226
    • (1869) Mathematische Annalen , vol.2 , pp. 198-226
    • Klein, F.1
  • 61
    • 0023566632 scopus 로고
    • Hamilton operators and dual-number quaternions in spatial kinematics
    • O.P. Agrawal Hamilton operators and dual-number quaternions in spatial kinematics Mechanism and Machine Theory 22 6 1987 569 575
    • (1987) Mechanism and Machine Theory , vol.22 , Issue.6 , pp. 569-575
    • Agrawal, O.P.1
  • 62
    • 0003779401 scopus 로고
    • Moscow English Translation, U.S. Department of Commerce, (N.T.I.S), No. AD
    • F.M. Dimentberg, The Screw Calculus and Its Application to Mechanics, Moscow, 1965, English Translation, U.S. Department of Commerce, (N.T.I.S), No. AD, 1969, pp. 680-993.
    • (1965) The Screw Calculus and Its Application to Mechanics , pp. 680-993
    • Dimentberg, F.M.1
  • 63
    • 85013917341 scopus 로고
    • Application of dual-number quaternion algebra to the analysis of spatial mechanisms
    • A.T. Yang, and F. Freudenstein Application of dual-number quaternion algebra to the analysis of spatial mechanisms Journal of Applied Mechanics, Transactions of ASME 86 2 1964 300 309
    • (1964) Journal of Applied Mechanics, Transactions of ASME , vol.86 , Issue.2 , pp. 300-309
    • Yang, A.T.1    Freudenstein, F.2
  • 65
    • 0015009060 scopus 로고
    • Kinematics analysis of spatial mechanisms by means of screw coordinates, Part I-screw coordinates
    • M.S.C. Yuan, and F. Freudenstein Kinematics analysis of spatial mechanisms by means of screw coordinates, Part I-screw coordinates ASME Journal of Engineering for Industry 93 1971 61 66
    • (1971) ASME Journal of Engineering for Industry , vol.93 , pp. 61-66
    • Yuan, M.S.C.1    Freudenstein, F.2
  • 68
    • 85024511428 scopus 로고
    • On the screw axes and other special lines associated with spatial displacements of a rigid body
    • B. Roth On the screw axes and other special lines associated with spatial displacements of a rigid body Transactions of the ASME B 89 1967 102 110
    • (1967) Transactions of the ASME B , vol.89 , pp. 102-110
    • Roth, B.1
  • 79
    • 0022676722 scopus 로고
    • Automatic computation of the screw parameters of rigid body motions, Part I. Finitely-separated positions
    • J. Angeles Automatic computation of the screw parameters of rigid body motions, Part I. Finitely-separated positions Journal of Dynamic Systems, Measurement, and Control, Transactions of ASME 108 1986 32 38
    • (1986) Journal of Dynamic Systems, Measurement, and Control, Transactions of ASME , vol.108 , pp. 32-38
    • Angeles, J.1
  • 80
    • 0025692640 scopus 로고
    • Coordinate transformations of screws with applications to screw systems and finite twists
    • I.A. Parkin Coordinate transformations of screws with applications to screw systems and finite twists Mechanism and Machine Theory 25 6 1990 689 699
    • (1990) Mechanism and Machine Theory , vol.25 , Issue.6 , pp. 689-699
    • Parkin, I.A.1
  • 81
    • 27744598907 scopus 로고
    • The finite displacement screws of a compound body
    • Prague
    • I.A. Parkin, The finite displacement screws of a compound body, in: Proceedings of the 8th IFToMM Congress, Prague (1991) 107-110.
    • (1991) Proceedings of the 8th IFToMM Congress , pp. 107-110
    • Parkin, I.A.1
  • 82
    • 0026838088 scopus 로고
    • A third conformation with the screw systems: Finite twist displacements of a directed line and point
    • I.A. Parkin A third conformation with the screw systems: finite twist displacements of a directed line and point Mechanism and Machine Theory 27 2 1992 177 188
    • (1992) Mechanism and Machine Theory , vol.27 , Issue.2 , pp. 177-188
    • Parkin, I.A.1
  • 83
    • 0028497313 scopus 로고
    • On the finite screw system of the third order associated with a revolute-revolute chain
    • C. Huang On the finite screw system of the third order associated with a revolute-revolute chain ASME Transactions, Journal of Mechanical Design 116 1995 875 883
    • (1995) ASME Transactions, Journal of Mechanical Design , vol.116 , pp. 875-883
    • Huang, C.1
  • 84
    • 0028532690 scopus 로고
    • The finite screw system associated with a prismatic-revolute dyad and the screw displacement of a point
    • C. Huang The finite screw system associated with a prismatic-revolute dyad and the screw displacement of a point Mechanism and Machine Theory 29 1994 1131 1142
    • (1994) Mechanism and Machine Theory , vol.29 , pp. 1131-1142
    • Huang, C.1
  • 85
    • 0031354618 scopus 로고    scopus 로고
    • The cylindroid associated with finite motion of the Bennett mechanism
    • C. Huang The cylindroid associated with finite motion of the Bennett mechanism Transactions of the ASME, Journal of Mechanical Design 119 1997 521 524
    • (1997) Transactions of the ASME, Journal of Mechanical Design , vol.119 , pp. 521-524
    • Huang, C.1
  • 88
    • 0025599267 scopus 로고
    • Geometry of screw systems-2, Classification of Screw Systems
    • C.G. Gibson, and K.H. Hunt Geometry of screw systems-2, Classification of Screw Systems Mechanism and Machine Theory 25 1 1990 11 27
    • (1990) Mechanism and Machine Theory , vol.25 , Issue.1 , pp. 11-27
    • Gibson, C.G.1    Hunt, K.H.2
  • 90
    • 0026895568 scopus 로고
    • Classification of screw systems-I. One- and Two-Systems
    • J.M. Rico Martinez, and J. Duffy Classification of screw systems-I. One- and Two-Systems Mechanism and Machine Theory 27 4 1992 459 470
    • (1992) Mechanism and Machine Theory , vol.27 , Issue.4 , pp. 459-470
    • Rico Martinez, J.M.1    Duffy, J.2
  • 91
    • 0026898846 scopus 로고
    • Classification of screw systems-II. Three-Systems
    • J.M. Rico Martinez, and J. Duffy Classification of screw systems-II. Three-Systems Mechanism and Machine Theory 27 4 1992 471 490
    • (1992) Mechanism and Machine Theory , vol.27 , Issue.4 , pp. 471-490
    • Rico Martinez, J.M.1    Duffy, J.2
  • 92
    • 0035341552 scopus 로고    scopus 로고
    • Interrelationship between screw systems and corresponding reciprocal systems and applications
    • J.S. Dai, and J. Rees Jones Interrelationship between screw systems and corresponding reciprocal systems and applications Mechanism and Machine Theory 36 5 2001 633 651
    • (2001) Mechanism and Machine Theory , vol.36 , Issue.5 , pp. 633-651
    • Dai, J.S.1    Rees Jones, J.2
  • 94
    • 0038380887 scopus 로고    scopus 로고
    • A linear algebraic procedure in obtaining reciprocal screw systems
    • J.S. Dai, and J. Rees Jones A linear algebraic procedure in obtaining reciprocal screw systems Journal of Robotic Systems 20 7 2003 401 412
    • (2003) Journal of Robotic Systems , vol.20 , Issue.7 , pp. 401-412
    • Dai, J.S.1    Rees Jones, J.2
  • 95
    • 0028378003 scopus 로고
    • Analytical expressions for the finite screw systems
    • C. Huang, and B. Roth Analytical expressions for the finite screw systems Mechanism and Machine Theory 29 2 1994 207 222
    • (1994) Mechanism and Machine Theory , vol.29 , Issue.2 , pp. 207-222
    • Huang, C.1    Roth, B.2
  • 96
    • 0029251548 scopus 로고
    • Finite displacements of points, planes, and lines via screw theory
    • K.H. Hunt, and I.A. Parkin Finite displacements of points, planes, and lines via screw theory Mechanism and Machine Theory 30 2 1995 177 192
    • (1995) Mechanism and Machine Theory , vol.30 , Issue.2 , pp. 177-192
    • Hunt, K.H.1    Parkin, I.A.2


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