Planar four-bar mechanism including revolute joints with clearance

The equations of motion of a four-bar mechanism are derived, which includes the joint clearance and is under the condition of constant crank rotate speed. The contact model for planar revolute joints is based on a continuous contact force model related to the contact conditions. Simulations are performed based on the model for the four bar mechanism built in MATLAB, for cases at different crank speeds and with different clearance sizes. The results show that the number of impacts and the penetration depth are highly nonlinearly related with the radial clearance and crank speed in low crank rotate speed cases, while the changes of number of impacts and the penetration depth with crank rotate speed become stable when the crank rotate speed is higher than a specific value. The effect of energy loss represented by restitution and friction on penetration depth is also carefully studied. Based on the simulation results, the idea of "Constrain belt" is presented and discussed. Furthermore, the relationship of the value of "Constrain belt" versus stiffness and operating load is plotted and their proportion relation is obtained. At last, two applications of "Constrain belt", namely, accuracy analysis and clearance design, are pointed out.