A study of the instantaneous centers of velocity for the 3-dof planar six-bar linkage (Q634975)

The graphical and analytical techniques for locating the instantaneous centers of velocity (secondary centers) for the planar linkage with two degrees of freedom, published by the authors [ibid. 45, No. 4, 641--657 (2010; Zbl 1254.70009)], are extended to locate the unknown secondary centers of a six-bar linkages with three degrees of freedom. The secondary centers can be single points or infinite lines. Several theorems are proven for the general six-bar linkage to obtain the number of double points and lines in the linkage, and several refinements are derived for special cases of the linkage geometry. The detailed discussion is useful in both the kinematic analysis and the kinematic synthesis of multi-degree of freedom planar linkages. For instance, the study provides insights as to where to pin certain links to obtain a particular motion of the coupler link. It provides also a better understanding of the first-order instantaneous kinematic properties of potentially useful linkages.