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.
Skip Nav Destination
Article navigation
March 2005
Article
Finding Geometric Invariants From Time-Based Invariants for Spherical and Spatial Motions
Bernard Roth
Bernard Roth
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305
Search for other works by this author on:
Bernard Roth
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305
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.
J. Mech. Des. Mar 2005, 127(2): 227-231 (5 pages)
Published Online: March 25, 2005
Article history
Received:
February 5, 2004
Revised:
May 9, 2004
Online:
March 25, 2005
Citation
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
Download citation file:
Get Email Alerts
Related Articles
The Composition of Bennett’s Hyperboloids From the Loop Itself
J. Mech. Des (September,2004)
Motion/Force Transmission Analysis of Parallel Mechanisms With Planar Closed-Loop Subchains
J. Mech. Des (June,2016)
Kinematics and Trajectory Planning of the Masonry Robot
J. Auton. Veh. Sys (July,2022)
Serial Metamorphic Manipulator Dynamics Formulation Implementing Screw Theory Tools
Letters Dyn. Sys. Control (October,2024)
Related Proceedings Papers
Related Chapters
Accuracy of an Axis
Mechanics of Accuracy in Engineering Design of Machines and Robots Volume I: Nominal Functioning and Geometric Accuracy
Pseudoinverse Method and Singularities Discussed
Robot Manipulator Redundancy Resolution
Feedback-Aided Minimum Joint Motion
Robot Manipulator Redundancy Resolution