RESEARCH PAPERS: Mechanisms and Design Automation Papers

The Curvature Theory of Line Trajectories in Spatial Kinematics

[+] Author and Article Information
J. M. McCarthy

FMC Corporation, Central Engineering Labs, Santa Clara, CA

B. Roth

Department of Mechanical Engineering, Stanford University, Stanford, CA 94305

J. Mech. Des 103(4), 718-724 (Oct 01, 1981) (7 pages) doi:10.1115/1.3254978 History: Received June 01, 1980; Online November 17, 2009


This paper develops the differential properties of ruled surfaces in a form which is applicable to spatial kinematics. Derivations are presented for the three curvature parameters which define the local shape of a ruled surface. Related parameters are also developed which allow a physical representation of this shape as generated by a cylindric-cylindric crank. These curvature parameters are then used to define all the lines in the moving body which instantaneously generate speciality shaped trajectories. Such lines may be used in the synthesis of spatial motions in the same way that the points on the inflection circle and cubic of stationary curvature are used to synthesize planar motion. As an example of this application several special sets of lines are defined: the locus of all lines which for a general spatial motion instantaneously generate helicoids to the second order and the locus of lines generating right hyperboloids to the third order.

Copyright © 1981 by ASME
Topics: Kinematics , Motion , Shapes
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