Abstract: The errors exist in the currently used method to calculate radius of curvature of an oscillating follower conical cam’s expansion pitch curve are analyzed. Space coordinates of the follower’s motion track are utilized, and with the consideration of deviation angle, polar equation of 3D expansion pitch curve is established, which is error free and can be easily plotted and used to analyze and design a conical cam. The deduced expression of radius of curvature is based on motion law of the mechanism and prime polar radius of the cam, and the function of minimum prime polar radius of conical cam with respect to allowable radius of curvature is established through this expression. Through example analysis, the relation curve between the minimum radius of curvature and the prime polar radius is described, and geometric parameters of a conical cam are designed. The feasibility of our methodology is validated by comparing with the currently used oscillating follower conical cam’s design method, with great theoretical value.

Key words: 3D expansion, conical cam, prime polar radius, radius of curvature