Planar motion of sliding cams by computer algebraic manipulation

Abstract

The law of cosines, colinearity of tangents at the point of contact and Kennedy's Theorem have been used to derive a system of three first order differential equations and the planar motion of sliding cams. The construction and solution of these equations and of auxilliary quantities, such as higher derivatives of angular motions and torques, have been accomplished by a PL/I-Formac code. This code includes a symbolic application of Newton's method for determining initial conditions. A complete example and computer output is presented. The emphasis of this paper is the use of computer aided algebraic and symbol manipulation requiring only the equations for the cam profiles and other analytic information as input, and the exact constitutive equations are generated and used as opposed to approximate methods such as replacement mechanisms.