The Multiobjective Optimization of a Prismatic Drive

The multiobjective optimization of Slide-o-Cam is reported in this paper. Slide-o-Cam is a cam mechanism with multiple rollers mounted on a common translating follower. This transmission provides pure-rolling motion, thereby reducing the friction of rack-and-pinions and linear drives. A Pareto frontier is obtained by means of multiobjective optimization. This optimization is based on three objective functions: (i) the pressure angle, which is a suitable performance index for the transmission because it determines the amount of force transmitted to the load vs. that transmitted to the machine frame; (ii) the Hertz pressure used to evaluate the stresses produced on the contact surface between cam and roller; and (iii) the size of the mechanism, characterized by the number of cams and their width. NOMENCLATURE p: pitch of the transmission; e: distance between the axis of the cam and the line of centers of the rollers; r: radius of the roller; dcs: diameter of the camshaft (dcs = 2(e− r)); L: the width of the contact between the cams and the rollers; ψ: input of the mechanism, i.e., the angle of rotation of the cam; s: output of the mechanism, i.e., the displacement of the follower; μ: pressure angle; f: force transmitted from the cam to the roller; κc and κp: curvature of the cam profile and the pitch curve, respectively; ρc and ρp: radii of curvature of the cam profile and the pitch curve, respectively; m: number of cams mounted on the camshaft; n: number of lobes per cam; P: Hertz pressure; SM: size of the mechanism.