Synthesis of polynomial and other curves with the Bezier technique

Abstract

This paper discussed the application of the Bezier technique for motion program synthesis of cam-follower mechanisms. It shows that any polynomial curve can be obtained through the Bezier technique by selecting control points with a uniform θ increment and the simple and intuitive nature of the Bezier technique in computer graphics is fully preserved in motion program synthesis. The boundary control, including the situations with zero derivatives, non-zero derivatives, derivative continuity, and no derivative control, can be achieved without the troubles of differentiation, integration or derivation of equations. The use of basic and auxiliary control points adds more flexibility to control the peak velocity, acceleration, and jerk of motion programs. Compared to the traditional motion program synthesis techniques, the proposed Bezier technique is far more flexible and simpler, and readily adaptable for interior control. The Bezier technique allows one to apply his feeling and intuition to change the motion program. An excellent motion program difficult to achieve through the traditional techniques may be synthesized with little experience and training.