This paper shows how the instantaneous invariants for time-independent motions can be obtained from time-dependent motions. Relationships are derived between those parameters that define a time-dependent motion and the parameters that define its geometrically equivalent time-independent motion. The time-independent formulations have the advantage of being simpler than the time dependent ones, and thereby lead to more elegant and parsimonious descriptions of motions properties. The paper starts with a review of the choice of canonical coordinate systems and instantaneous invariants for time-based spherical and spatial motions. It then shows how to convert these descriptions to time-independent motions with the same geometric trajectories. New equations are given that allow the computation of the geometric invariants from time-based invariants. The paper concludes with a detailed example of the third-order motion analysis of the trajectories of an open, spatial chain.
Finding Geometric Invariants From Time-Based Invariants for Spherical and Spatial Motions
Contributed by the Mechanisms and Robotics Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 5, 2004; revised May 9, 2004. Associate Editor: G. R. Pennock.
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Roth, B. (March 25, 2005). "Finding Geometric Invariants From Time-Based Invariants for Spherical and Spatial Motions ." ASME. J. Mech. Des. March 2005; 127(2): 227–231. https://doi.org/10.1115/1.1828462
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