A study of the instantaneous centers of velocity for two-degree-of-freedom planar linkages

The secondary instantaneous centers of velocity for two-degree-of-freedom planar linkages must lie on straight lines. For many of these linkages, however, some of these lines cannot be obtained by a direct application of the Aronhold–Kennedy theorem. This paper, therefore, will present both graphical and analytical techniques to locate these unknown lines of centers for certain types of two-degree-of-freedom linkages. First the techniques are applied to the three topologies of the seven-bar linkage, two of which contain a four-bar chain, and the unknown lines of centers are obtained for each topology. Then the techniques are applied to the 35 topologies of the nine-bar linkage. The paper includes a discussion of these topologies and presents three examples for illustrative purposes. The techniques can locate the unknown lines of centers for all, but one, of the 35 topologies. The techniques presented in this paper provide geometric insight into the first-order instantaneous kinematics of two-degree-of-freedom planar linkages.