Synthesis of Linkages to Generate Specified Histories of Forces and Torques: The Planar 4R Four-Bar Mechanism

Abstract

Abstract Analytical precision position and optimum synthesis methods for linkages to generate specified force and torque histories are presented and applied to the planar four-bar mechanism. Mechanical advantage method (MAM) and integration of power equilibrium method (IPEM) are used to develop design equations. MAM yields design equations to use when the torque multiplication factor is defined at discrete number of design positions, as well as in continuous forms. IPEM requires continuous forms, but it reduces the torque generation problem into a function generation problem. Design equations with one, two, three, and four unknowns are developed for precision position synthesis; and they are used to formulate optimum synthesis process using many design positions that requires no iteration. Generation of infinite torque multiplication factor and synthesis of quick-return four-bar mechanism to generate specified advance-to-return time ratio are also considered. The synthesized four-bar mechanisms replace circular and non-circular external and internal gear drives. Several industrial application examples are included. The second part of the article considers the slider-crank mechanism.