Inherently balanced double Bennett linkage

For fast moving mechanisms shaking force balance is important to reduce base vibrations. When mechanisms are force balanced, they are also gravity balanced which is important for reduced actuation effort and increased safety. It has been shown that from planar inherently balanced linkage architectures a variety of new and interesting force balanced mechanism solutions can be synthesized. The goal of this paper is to derive the balance conditions of one special solution consisting of two similar 4R four-bar linkages connected by a parallelogram, based on two sets of principal vectors. It is shown that also here the balance conditions can be derived from the linear momentum equations of each relative degree of freedom. Subsequently it is shown how the planar version can be transformed into a spatial version becoming an inherently balanced linkage of two similar Bennett linkages connected by a planar parallelogram. The balance conditions for both the planar and spatial version are exactly equal.