A Unified Approach to Teaching Analytical Cam Design Using Conjugate Geometry

Abstract

While graphical techniques for synthesizing cam profiles are useful for teaching the fundamentals of cam design, they can be laborious when considering the iterative nature of design. Analytical techniques are better suited to take advantage of the powerful computation tools so readily available. However, the techniques for deriving the governing equations can be cumbersome and difficult to follow for students because many of the analytical formulations require the knowledge of a ‘trick’ specific to each problem. Presented here is a procedure that uses two simple concepts of conjugate geometry to derive the governing vector equation for the cam profile. The first concept is that of forming a closed vector loop within the cam and follower. The second is the principle that the relative velocity between the cam and follower is purely along the common tangent of the two surfaces at the point of contact. The authors believe that this approach is more intuitive and easier to learn. The same approach can be used for any cam-and-follower system where the surface of the follower can be described parametrically.