On the Synthesis of Cams with Roller or Irregular Followers

The paper extends the theory for plate cam geometry design for regular and irregular-surface follower system. Analytical description of cam profiles for general cam-follower system is obtained using the envelope theory. Usually during the analysis of cam geometry, it is common consider cam as the fixed member and to define the cam surface as envelope curve formed by inverting the follower from the initial position of the cam. The analytical description of cam geometry is show to be a non linear algebraic equation. This analytical approach constitutes a single variable, single nonlinear algebraic equation problem which may be avoided only for roller follower systems. On the other cases the problem can be solved by any reliable nonlinear equation solver. The results of the examples demonstrated in this paper show that the cam geometry can be significantly changed by choosing different types of follower for the same required motion. It is common to identify radius of curvature along the cam profile as fundamental parameter for cam design. Starting from the analytical description of the radius of curvature of cam profile, an algebraic relation between radius of curvature of cam, system geometry, cam revolution speed and follower position, velocity and acceleration is derived. This relation makes possible to obtain follower acceleration as function of the radius of curvature of cam. This relation can be used during follower motion design as control tool on radius of curvature of cam. Also, it can be used as comparison tool between different follower profiles or mechanisms geometry. Some examples are reported. For practical engineering design, this implies that the geometry of cams can be adjusted by selecting the follower profile so as to satisfy the design requirements. The development of this geometric analysis tool enables the search for optimal geometric design of general follower cam system.