Method of the Generalized Approach to the Synthesis of Cam Mechanisms

Abstract

The technique of applying the equation of the geometric connection of links in the higher kinematic pair of a cam mechanism for the complete synthesis of a mechanism with a flat translationally moving pusher with an arbitrary angle of inclination of the plate is considered. A distinctive feature of the technique is that the equation of the cam profile envelope is derived from the equation of the geometric relationship of the cam and the pusher in the Cartesian coordinate system. All transformations, the solution of the original coupling equation and the envelope equation are carried out by the matrix method in the same coordinate system without switching to other coordinate systems and to graphical methods of their interpretation. As a result of the performed studies, calculated relations for determining the coordinates of the cam profile points at an arbitrary angle of inclination of the pusher plate were obtained. The formula for determining the curvature radius of the cam at an arbitrary inclination angle of the plate is derived. The procedure for determining the radius of the main cam circumference is proposed, taking into account the identified features of the cam profile plotting. Based on the developed methodology, software in the MathCad package has been created. The correctness of the methodology and software was tested on a numerical test case. In the course of computer modeling, the reason for the need to limit the value of the inclination angle of the plate is established, due to the phenomenon of cam profile self-intersection, which does not depend on the pressure angle and is not tracked by the condition of the convexity of its profile. The test results allow us to assert that the generalized method of flat cam mechanisms synthesis is correct and effective, therefore it has prospects of application, for example, for a cam mechanism with a flat rotating pusher.