Coordination of two crank angles and two acceleration poles for a slider crank mechanism using parametric equations

Abstract

The current article presents the parametric equations for the synthesis of a slider crank mechanism with a coupler point passing through two specified acceleration poles that accord with two specified crank angles. The parametric equations for the coordinates of the acceleration pole for the coupler with respect to the frame are shown to be functions of only the geometric configuration of the slider crank mechanism driven by the crank with a constant rotational speed. Moreover, a necessary condition for the crank angular interval corresponding to the two acceleration poles on a coupler curve generated by a slider crank mechanism is investigated. The desired coupler point of a given mechanism passing through two acceleration poles should be a double point on the locus of the acceleration pole described on the coupler plane. The transformed parametric equations on the fixed plane are then applied to synthesize the desired mechanism with a coupler point passing through two specified acceleration poles that accord with two specified crank angles.