New Complex-Number Forms of the Euler-Savary Equation 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

Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455

E. Raghavacharyulu

Indian Institute of Technology, New Delhi, India

J. Mech. Des 104(1), 227-232 (Jan 01, 1982) (6 pages) doi:10.1115/1.3256315 History: Received June 01, 1980; Online November 17, 2009


It is well known from the theory of Kinematic Synthesis of planar mechanisms that the Euler-Savary Equation (ESE) gives the radius of curvature and the center of curvature of the path traced by a point in a planar rolling-contact mechanism. It can also be applied in planar linkages for which equivalent roll-curve mechanisms can be found. Typical example: the curvature of the coupler curve of a four-bar mechanism. Early works in the synthesis of mechanisms concerned themselves with deriving the ESE by means of combined graphical and algebraic techniques, using certain sign conventions. These sign conventions often become sources of error. In this paper new complex-number forms of the Euler-Savary Equation are derived and are presented in a computer-oriented format. The results are useful in the application of path-curvature theory to higher-pair rolling contact mechanisms, such as cams, gears, etc., as well as linkages, once the key parameters of an equivalent rolling-contact mechanism are known. The complex-number technique has the advantage of eliminating the need for the traditional sign conventions and is suitable for digital computation. An example is presented to illustrate this.

Copyright © 1982 by ASME
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