OBTAINING THE PARAMETRIC POSITION EQUATIONS OF A FOUR-BAR MECHANISM USING THE PARAMETRIC POSITION EQUATIONS OF THE PLANAR MANIPULATOR WITH 3 REVOLUTE JOINTS (3RM)

Abstract

In a four-bar mechanism, the crank link rotates at a constant angular velocity, while the other two links have constantly changing angular velocities. If it is desired to convert a 3RM into a four-bar mechanism, the variable angular velocities of the rotary actuators at both ends of the coupler link should be accurate. The general parametric set of equations that give the cartesian coordinates of 3RM can be arranged so that they can be used for the four-bar mechanism by limiting the degree of freedom. In this case, the angular velocities of the actuators on both ends of the coupler link should be determined while the crank link rotates at a constant angular speed. Angular velocities of actuators have been obtained using the WorkingModel2D (WM2D) "dynamic motion-simulation software" for a four-bar mechanism, whose geometric parameters have been selected as the crank-rocker. Using the angular velocity data, unknown coefficients in polynomials expressing the angular velocities of the rotary actuators connected to the coupler link have been found using Mathematica software. The trajectory and angular velocity data have been obtained from WM2D, the results of trajectory and angular velocity equations have been compared and the results have been at acceptable levels.