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

[1]  A. Cayley.  The Collected Mathematical Papers: Galois , 2007 .

[2]  Joseph K. Davidson,et al.  Robots and Screw Theory: Applications of Kinematics and Statics to Robotics , 2004 .

[3]  Jian S. Dai,et al.  A Linear Algebraic Procedure in Obtaining Reciprocal Screw Systems , 2003, J. Field Robotics.

[4]  O. Bauchau,et al.  The Vectorial Parameterization of Rotation , 2003 .

[5]  J. R. Jones,et al.  Null–space construction using cofactors from a screw–algebra context , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[6]  H. Lipkin,et al.  Sir Robert Stawell Ball and methodologies of modern screw theory , 2002 .

[7]  Jian S. Dai,et al.  Interrelationship between screw systems and corresponding reciprocal systems and applications , 2001 .

[8]  M. Borri,et al.  On Representations and Parameterizations of Motion , 2000 .

[9]  Marco Ceccarelli,et al.  Screw axis defined by Giulio Mozzi in 1763 and early studies on helicoidal motion , 2000 .

[10]  C. Barus.  A treatise on the theory of screws , 1998 .

[11]  Chintien Huang,et al.  The Cylindroid Associated With Finite Motions of the Bennett Mechanism , 1997 .

[12]  D. R. Kerr,et al.  Finite Twist Mapping and its Application to Planar Serial Manipulators with Revolute Joints , 1995 .

[13]  I. A. Parkin,et al.  Finite displacements of points, planes, and lines via screw theory , 1995 .

[14]  Chintien Huang,et al.  The finite screw systems associated with a prismatic-revolute dyad and the screw displacement of a point , 1994 .

[15]  Chintien Huang,et al.  On the Finite Screw System of the Third Order Associated with a Revolute-Revolute Chain , 1994 .

[16]  Chintien Huang,et al.  Analytic expressions for the finite screw systems , 1994 .

[17]  Joseph Duffy,et al.  Classification of screw systems—I. One- and two-systems , 1992 .

[18]  Joseph Duffy,et al.  Classification of screw systems—II. Three-systems , 1992 .

[19]  Joseph Duffy,et al.  Orthogonal spaces and screw systems , 1992 .

[20]  I. A. Parkin,et al.  A third conformation with the screw systems: Finite twist displacements of a directed line and point☆ , 1992 .

[21]  Kenneth H. Hunt,et al.  Unifying Screw Geometry and Matrix Transformations , 1991, Int. J. Robotics Res..

[22]  Harvey Lipkin,et al.  Kinematics of complex joint angles in robotics , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[23]  J. Michael McCarthy,et al.  Introduction to theoretical kinematics , 1990 .

[24]  S. Altmann,et al.  Hamilton, Rodrigues, and the Quaternion Scandal , 1989 .

[25]  Jon M. Selig,et al.  Reuleaux Pairs and Surfaces That Cannot Be Gripped , 1989, Int. J. Robotics Res..

[26]  K. C. Gupta,et al.  An historical note on finite rotations , 1989 .

[27]  Joseph Duffy,et al.  A Theory for the Articulation of Planar Robots: Part I—Kinematic Analysis for the Flexure and the Parallel Operation of Robots , 1987 .

[28]  J. M. McCarthy,et al.  Dual Orthogonal Matrices in Manipulator Kinematics , 1986 .

[29]  Jorge Angeles,et al.  Automatic Computation of the Screw Parameters of Rigid-Body Motions. Part I: Finitely-Separated Positions , 1986 .

[30]  H. Mergler.  Introduction to robotics , 1985, Proceedings of the IEEE.

[31]  A. T. Yang,et al.  Application of Dual-Number Matrices to the Inverse Kinematics Problem of Robot Manipulators , 1985 .

[32]  Jeremy Gray,et al.  Olinde Rodrigues' paper of 1840 on transformation groups , 1980 .

[33]  M. Beatty.  Vector Analysis of Finite Rigid Rotations , 1977 .

[34]  Lung-Wen Tsai,et al.  Incompletely Specified Displacements: Geometry and Spatial Linkage Synthesis , 1973 .

[35]  O. Bottema,et al.  On a Set of Displacements in Space , 1973 .

[36]  Ferdinand Freudenstein,et al.  Kinematic Analysis of Spatial Mechanisms by Means of Screw Coordinates. Part 1—Screw Coordinates , 1971 .

[37]  K. E. Bisshopp.  Rodrigues’ Formula and the Screw Matrix , 1969 .

[38]  Bernard Roth,et al.  On the Screw Axes and Other Special Lines Associated With Spatial Displacements of a Rigid Body , 1967 .

[39]  A. T. Yang,et al.  Application of Dual-Number Quaternion Algebra to the Analysis of Spatial Mechanisms , 1964 .

[40]  B. Paul.  On the Composition of Finite Rotations , 1963 .

[41]  A. S. Ramsey.  The Mathematical Papers of Sir William Rowan Hamilton , 1931, Nature.

[42]  E. Study.  Von den Bewegungen und Umlegungen , 1891 .

[43]  Cayley.  On Three‐Bar Motion , 1875 .

[44]  Clifford,et al.  Preliminary Sketch of Biquaternions , 1871 .

[45]  Matthew Prior,et al.  Letter from “J” , 1863, The Dental register.

[46]  William Rowan Hamilton,et al.  ON QUATERNIONS, OR ON A NEW SYSTEM OF IMAGINARIES IN ALGEBRA , 1847 .

[47]  J. A Parkin,et al.  Co-ordinate transformations of screws with applications to screw systems and finite twists☆ , 1990 .

[48]  K. H. Hunt,et al.  Geometry of screw systems1Screws: Genesis and geometry , 1990 .

[49]  K. H. Hunt,et al.  Geometry of screw systems—2: classification of screw systems , 1990 .

[50]  Om P. Agrawal,et al.  Hamilton operators and dual-number-quaternions in spatial kinematics , 1987 .

[51]  S. Altmann.  Rotations, Quaternions, and Double Groups , 1986 .

[52]  J. Denavit,et al.  A kinematic notation for lower pair mechanisms based on matrices , 1955 .

[53]  J. L. Coolidge,et al.  A history of geometrical methods , 1947 .

[54]  Felix Klein.  Elementary Mathematics from an Advanced Standpoint: Geometry , 1941 .

[55]  Halphen.  Sur la théorie du déplacement , 1882 .

[56]  J. Plücker,et al.  Neue Geometrie des Raumes : gegründet auf die Betrachtung der geraden Linie als Raumelement , 1868 .

[57]  Julius Plucker,et al.  XVII. On a new geometry of space , 1865, Philosophical Transactions of the Royal Society of London.