Explore the Beauty of Cam Geometry: The Necessary and Sufficient Design Conditions for the Cam Mechanism With Flat Face Follower

Abstract

Abstract Cam, a mechanism usually used to transform a rotary motion into desired output motion, has been commonly used in modern industry. In practice, a variety of practical methods have been discussed to improve the cam mechanism. In theory, however, the mobility of cam mechanism is seldom mathematically addressed. This paper mathematically discusses the necessary and sufficient design conditions for two kinds of form-closed cam mechanism (a cam with a translating flat-faced follower and a cam with an oscillating flat-faced follower) to be mobile. For the former cam mechanism, the relation between the design conditions and the cam mobility is derived by proving the identical cam contour enveloped by the flat faces. The result shows that the cam mechanism is mobile if and only if it satisfies the design conditions: (a) distance between the two follower flat faces is a constant value (twice base circle radius + total stroke of follower) and (b) summation of the displacement functions being 180 degrees out of phase must be the total stroke of the follower. For the later cam mechanism, the relation is derived by transforming the cam contour into a geometric layout associated with orthoptic curves. The result shows that the cam mechanism is mobile if and only if it satisfies the design conditions: (a) the flat faces are orthogonal, (b) the cycle of the displacement function has to be 180 degrees, (c) low dwell period and high dwell period are identical, (d) difference of rising and returning period has to be twice the stroke of follower, and (e) only one of the rising or falling period can be designed.