Inherently Balanced Spherical Pantograph Mechanisms

This paper investigates the possibilities for designing shaking force balanced spherical pantograph mechanisms. Three different spherical designs are presented, which are a balanced general spherical pantograph, a balanced double spherical pantograph and a double S-shaped mechanism with surrounding 4R four-bar linkage. Also variations of the balanced designs are presented. As compared to the planar balanced pantograph, the same underlying system of principal vectors exists, of which the geometries can be visualized in the orthogonal planes. The feasible variations of link lengths for which force balance is maintained are discussed.