Rodrigues’ spatial kinematics

Abstract In this paper, we detail Rodrigues’ often overlooked treatment of spatial kinematics. In particular we discuss his use of midpoints, his general method of composition of displacements, and what we propose could be referred to as Rodrigues–Parkin twist coordinates. We show that the results that follow easily from application of his methods are identical to those published more than 150 years later.

[1]  J. Willard Gibbs,et al.  The scientific papers of J. Willard Gibbs , 1907 .

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

[3]  L. Brand,et al.  Vector and tensor analysis , 1947 .

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

[5]  Harvey Lipkin,et al.  Time derivatives of screws with applications to dynamics and stiffness , 2005 .

[6]  Chintien Huang,et al.  The Linear Representation of the Screw Triangle—A Unification of Finite and Infinitesimal Kinematics , 1995 .

[7]  Chintien Huang Notes on screw product operations in the formulations of successive finite displacements , 1997 .

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

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

[10]  Jorge Angeles,et al.  Rational kinematics , 1989 .

[11]  McCarthy,et al.  Geometric Design of Linkages , 2000 .

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

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

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

[15]  K Yagasaki,et al.  Analytical Mechanics: A Comprehensive Treatise on the Dynamics of Constrained Systems; For Engineers, Physicists, and Mathematicians , 2002 .

[16]  D. Chevallier,et al.  Lie algebras, modules, dual quaternions and algebraic methods in kinematics , 1991 .

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

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

[19]  J. Dai An historical review of the theoretical development of rigid body displacements from Rodrigues parameters to the finite twist , 2006 .

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

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

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

[23]  J. G. Papastavridis Analytical Mechanics: A Comprehensive Treatise on the Dynamics of Constrained Systems , 2014 .

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

[25]  Edward John Routh,et al.  The elementary part of A treatise on the dynamics of a system of rigid bodies , 2009 .

[26]  D. P Chevallier On the transference principle in kinematics: its various forms and limitations , 1996 .