Acceleration-driven cam profile synthesis for a cam-type vibration exciter with an elastically coupled oscillating mass

This paper addresses the inverse synthesis of a disk-cam mechanism used as a cam-type vibration exciter with an elastically coupled oscillating mass. The primary aim is to determine the cam geometry directly from a prescribed acceleration program of the working body. The mechanism is modelled as an in-line translating flat-faced follower driven by a rotating cam and coupled to the oscillating mass through a spring, while a return spring provides force closure. The cam profile is obtained as the envelope of follower-face lines, yielding closed-form parametric equations for the working profile as well as analytical expressions for pressure angle and curvature radius. An acceleration-driven synthesis chain is formulated, where the required follower motion is computed from an inverse elastic model (algebraic for undamped coupling). Design inequalities for the base-circle radius are proposed to satisfy pressure-angle limits and prevent undercutting. A near vibro-impact case study is simulated in Wolfram Mathematica. In contrast to direct kinematic studies of predefined excitation mechanisms, the present work solves an inverse design problem in which the disk-cam profile is synthesized from a prescribed acceleration law of an elastically coupled oscillating mass. The practical outcome is an explicit analytical link between the target output acceleration, follower motion, admissible base-circle radius, pressure angle, and curvature constraints.