On Extreme Velocity Ratios in Spherical Four-Link Mechanisms

The conditions for the existence of extreme velocity ratios in spherical four-link mechanisms have been investigated by algebraic means. It is shown that, in the general case, all such extreme velocity ratios must be among the real roots of a 10th-degree algebraic polynomial. The results make it possible to obtain the extreme velocity ratios of any given spherical four-link mechanism. The method of the paper has been illustrated by several numerical examples. Special formulations of the general case have also been considered and applications to some practical spherical mechanisms have been discussed. The results can also be used for synthesizing spherical four-link mechanisms with prescribed extreme velocity ratios.