Design of cams with negative radius follower using Bézier curves

• An optimization procedure for cam design using Bézier curves is proposed.
• This optimization method uses a Bézier ordinate as optimization parameter.
• As example, the follower lift is maximized avoiding the undercutting problem.
• The optimum ordinate is independent of the dimensionless base circle radius.
• We compare our results with the modified trapezoidal acceleration curve.

This paper discusses the application of Bézier curves for designing cams with a follower of negative radius |Rf|. This kind of cam-follower mechanisms is recommended in applications where the space is restricted and very high forces are involved. In particular, we propose a numerical method for optimizing the design of the cam profile using a Bézier ordinate as an optimization parameter. For the optimization problem addressed in this work, the follower lift is maximized avoiding the undercutting problem, but keeping the pressure angle lower than 41°. To that end, a parametric study has been performed using Bézier curves of orders n = 6 and n = 8, to ensure continuity for the second and third derivatives, respectively. It is found, for both orders n = 6 and n = 8, that the Bézier ordinate that maximizes the follower lift, for a given total rise angle β, is practically independent of the dimensionless prime circle radius α = Ra/|Rf|.