Use of Bézier curves in the design of the displacement law of the cam-follower mechanism: Von Mises effective Stress

Abstract

Designing cams by BézierCurves has become increasingly common, since the mathematical development of this method is less complex. Bezier curves are Bernstein-based polynomials under a unitary domain, and in that sense, this article presents the design of a cam using Bezier curves of degrees 5, 7 and 9. And beyond, this article seeks to show the variation of the effective effort of Von Mises in a cam-follower mechanism composed of a disc cam and a roller follower with translation movement and force closure. The expressions that allow determining the variation of Von Mises' effort for each of the curves used are presented. This variation is presented by means of graphs in which it is observed that as the degree of the curve increases, the magnitude of the efforts is greater, and this increases the probability of failure in the mechanisms. In addition, it was found that there is an inverse relationship between the stress and the radius of the primary circle of the cam