Static balancing of a four-bar linkage and its cognates

Motivated by the need to statically balance the inherent elastic forces in linkages, this paper presents three techniques to statically balance a four-bar linkage loaded by a zero-free-length spring attached between its coupler point and an anchor point on the ground. The number of auxiliary links and balancing springs required for the three techniques is less than or equal to that of the only technique currently in the literature. One of the three techniques does not require auxiliary links. In these techniques, the set of values for the spring constants and the ground-anchor point of the balancing springs can vary over a one-parameter family. Thrice as many balancing choices are available when the cognates are considered. The ensuing numerous options enable a user to choose the most practical solution. To facilitate the evaluation of the balancing choices for all the cognates, Roberts–Chebyshev cognate theorem is extended to statically balanced four-bar linkages.

► Three methods to statically balance a spring-loaded four-bar linkage are found.
► The methods use not more than two balancing springs and not more than two auxiliary links.
► One of the methods does not use auxiliary links at all.
► The balancing parameters of the cognates of a four-bar has a parametrization that elegantly relates to the cognate triangle.