New Complex-Number Form of the Cubic of Stationary Curvature in a Computer-Oriented Treatment of Planar Path-Curvature Theory for Higher-Pair Rolling Contact

[+] Author and Article Information
G. N. Sandor

Mechanical Engineering Design and Rotordynamics Laboratories, University of Florida, Gainesville FL 32611

A. G. Erdman, L. Hunt

Dept. of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455

E. Raghavacharyulu

Indian Institute of Technology, New Delhi, India

J. Mech. Des 104(1), 233-238 (Jan 01, 1982) (6 pages) doi:10.1115/1.3256316 History: Received June 01, 1980; Online November 17, 2009


New complex number forms of the Euler-Savary Equation (ESE) for higher-pair rolling contact planar mechanisms were derived in a former paper by the authors. The present work, based on the former, deals with the derivation of the cubic of stationary curvature (CSC) in complex-vector form, suitable for digital computation. The CSC or Burmester’s circlepoint curve and its conjugate, the centerpoint curve for four infinitesimally close positions of the moving plane requires taking into account not only the curvature but also the rate of change of curvature of the rolling centrodes in the immediate vicinity of the position considered. The analytical procedure based on the theory developed in the present paper, when programmed for digital computation using complex arithmetic, takes care of the algebraic signs automatically, without the need for observing traditional sign conventions. The analysis is applicable to both higher-pair and lower-pair planar mechanisms. An example using the complex-number approach illustrates this.

Copyright © 1982 by ASME
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