A decade ago Roth [1] presented a kinematic analogy between angular and linear kinematic quantities which is of ‘general application’ in the sense that the analogy does not require a ‘special’ type of angular motion. Unfortunately, the analogy seemed to hold only at the velocity analysis. More precisely, when the equations for the acceleration analysis are presented, the analogy breaks down. Since that paper was presented, newer results in kinematics allow us to show that, redefining a few terms, the analogy can be extended to higher order analyses. Furthermore, it is shown that the analogy is at the heart of the theory of screws proposed by Ball one hundred years ago.
RothR., ‘Kinematic analogues’, International Journal of Mechanical Engineering Education, 18(4), 294–300, 1990.
2.
KaneT. R. and LevinsonD. A., Dynamics: Theory and Applications, McGraw Hill, New York, 1985.
3.
RicoJ. M. and DuffyJ., ‘An application of screw algebra to the acceleration analysis of serial chains’, Mechanism and Machine Theory, 31 (4), 445–457, 1996.
4.
BallR. S.A Treatise on the Theory of Screws, Cambridge University Press, Cambridge, UK, 1900. Reprint 1998.
5.
RicoJ. M.GallardoJ. and DuffyJ., ‘Screw theory and higher order kinematic analysis of open serial and closed chains’, Mechanism and Machine Theory, 34(4), 559–586, 1999.
6.
BrandL., Vector and Tensor Analysis, John Wiley, New York, 1947.
7.
GallardoJ., ‘Higher-order kinematic analyses of spatial chains, through screw algebra, and their applications’, Ph.D. Dissertation, Instituto Tecnológico de la Laguna, ISSN:0188–9060, México (in Spanish).
