Determination Of Space Centrode Of A Coupler Link

In kinematics, the velocity center of the coupler link of a four-bar linkage in a collinear configuration cannot be determined solely by the traditional method of velocity center. Such a difficulty is a singularity and a baffling situation in the teaching of dynamics. This paper points out that three alternative approaches can be used to resolve this difficulty. The determination of the space centrode of the coupler link of the system considered involves the solution of two simultaneous transcendental equations ematica. Introduction Suppose that the crank AB of the four-bar linkage shown in and is carried out by using the software MathFig. 1 rotates with a given angular velocity COAB = -81 k radls We note that such a linkage has no range of lockup positions. It was shown in earlier studies by Jongl’z that the angular velocities of the coupler link BD and the output link DE in a collinear configuration, as shown in Fig. 2, are not amenable to solutions by the traditional method of veloci~ center alone, or by the method of linkage eqw.tion for velocities alone. These angular velocities were first solved by the usage of a perturbation method,l and then by the combined usage of the method of linkage equation for velocities and the method of linkage equation for accelerations.2 Based on the studies of Jongla, it is clear that the velocity center C of the coupler link BD in a collinear configuration can be determined by the following two alternative approaches: (1) usage of a perturbation method, (2) combined usage of the method of linkage equation for velocities and the method of linkage equation for accelerations. A third alternative approach to determine such a velocity center C is presented in this paper. Specifically, this one is termed approach (3): combined usage of the method of velocity center and the method of linkage equation for velocities. Notice that approaches (2) and (3) differ in the combination of methods used.