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Article

Finding Geometric Invariants From Time-Based Invariants for Spherical and Spatial Motions

[+] Author and Article Information
Bernard Roth

Department of Mechanical Engineering, Stanford University, Stanford, CA 94305e-mail: broth@stanford.edu

J. Mech. Des 127(2), 227-231 (Mar 25, 2005) (5 pages) doi:10.1115/1.1828462 History: Received February 05, 2004; Revised May 09, 2004; Online March 25, 2005
Copyright © 2005 by ASME
Topics: Motion , Equations , Chain
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References

Bottema, O., and Roth, B., 1990, Theoretical Kinematics, Dover Publications, New York.
Roth,  B., and Yang,  A., 1997, “Application of Instantaneous Invariants to the Analysis and Synthesis of Mechanisms,” ASME J. Eng. Ind., 99(1), pp. 97–103.
Roth, B., 2004, “Time-Invariant-Properties of Planar Motions,” Advances in Robot Kinematics, edited by J. Lenarčič and C. Galletti, Kluwer Academic, Dordrecht.
Bottema, O., 1961, “Some Remarks on Theoretical Kinematics,” Proceedings of the International Conference for Teachers of Mechanisms, edited by F. Crossley, The Shoe String Press, North Haven, CT, pp. 157–167.
Veldkamp, G., 1963, Curvature Theory in Plane Kinematics, Doctoral dissertation, T. H. Delft, Delft, The Netherlands.
Veldkamp,  G., 1967, “Canonical Systems and Instantaneous Invariants in Spatial Kinematics,” J. Mech., 2(3), pp. 329–388.
Nayak,  J., and Roth,  B., 1981, “Instantaneous Kinematics of Multi-Degree-of-Freedom Motion,” ASME J. Mech. Des., 103, pp. 608–620.
McCarthy,  J., and Roth,  B., 1981, “The Curvature Theory of Line Trajectories in Spatial Kinematics,” ASME J. Mech. Des., 103, pp. 718–724.
McCarthy,  J., and Roth,  B., 1982, “Instantaneous Properties of Trajectories Generated by Planar, Spherical, and Spatial Rigid Body Motions,” ASME J. Mech. Des., 104, pp. 39–51.
Stachel, H., 2000, “Instantaneous Spatial Kinematics and the Invariants of the Axodes,” Proceedings Ball 2000 Symposium, Cambridge University Press, London, (23), p. 14.

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Grahic Jump Location
A two-degree-of-freedom R–R chain

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