Dynamic Synthesis of a Crank-Rocker Mechanism Minimizing its Joint-Forces

Abstract

Dynamic Joint-Forces in a mechanism produce vibration and wear, decreasing its life span. Many studies have been carried out on optimization of mechanisms dynamic behaviour; however, few of it are focused on the reduction of Joint-Forces. Therefore, this work presents a method to obtain the link lengths of Function Generation Four-Bar Linkages, minimizing the maximum dynamic force in the joints. The study assumes that the crank rotates with constant angular velocity and the rocker moves a high amount of inertia between two positions. Hence, the mechanism mass and inertia is considered negligible. The equations of motion are set up together with Dead-Center Construction method after Alt. To analyze the behaviour of the Joint-Forces, all the equations are parametrized, finding out that the maximum Joint-Force is minimizable for every task given. The minimization of the Joint-Forces is achieved by using simple algorithms as Bisection and Regula-Falsi Illinois. The results show that this method reduces the maximal Joint-Force by a mean value of 8.5%, with respect to the Dead-Center Construction method with Transmission Angle Minimization. Moreover, for some tasks, the force reduction could reach up to 60%. Furthermore, this method solves the problem of null-length crank and rocker for centric crank-rocker mechanisms, generated by the Transmission Angle minimization.