DESIGN AND SYNTHESIS OF CAM MECHANISMS USING PARAMETRIC POLYNOMIALS

Abstract

The present study mainly focuses on the optimum design of planar cam mechanisms for general-purpose engineering applications. A new family of parametric polynomials is presented for cam mechanism designs using nonlinear programming techniques. The features of cam design using this new family of parametric polynomials are : (1) the use of use fewer parameters to produce general motion curves; (2) the simplification for the procedure of optimization as the relation between the kinematic features and the parameters can be easily established; (3) the boundary continuity of motion curves can be easily modified. In Chapter 2 the method to produce the parametric polynomials and the basic kinematic features of them is presented. Parametric polynomials that have the feature of antisymmetric acceleration and the method for motion curve optimization using parametric polynomials are presented. The problems of curvature optimization for the flat-face followers are analyzed in Chapters 3 and 4. In Chapter 3, parametric motion curves with non-antisymmetric acceleration property are developed to extend the flexibility of the parametric polynomials. The problems of cam-size optimization are analyzed in Chapters 5 and 6. In Chapter 7, examples are given to show the application of the parametric polynomials to solve the dynamic problems of the cam-follower systems. In addition, the dynamic behavior of a return spring under the excitation of a cam motion caused by a prescribed motion curve is studied and a simple expression of the response spectrum is presented to estimate the vibration of the spring for different rotational speeds of the cam and different prescribed cam motions. This spectrum provides a very useful tool for the dynamic synthesis of cam mechanism at high speed. Compared with the existing 'residual spectrum' developed by Chen and Wiederrich, the present spectrum is simpler in form and does not have the fluctuation in the spectrum.