A geometric approach to the static balancing of mechanisms constructed using spherical kinematic chain units

Abstract

A geometric method to the static balancing of mechanisms constructed using spherical chain units is presented. A (serial) spherical kinematic chain unit is composed of n moving links, whose masses are considered, connected by revolute (R) joints the axes of which intersect at a fixed point. The mass of each link can be balanced using one spring without any auxiliary parallelogram. The balancing can be achieved readily with almost no calculation. One end of each spring is fixed right above the intersection of the joint axes and the other end is attached to the point that is on the line defined by the intersection and the equivalent center of mass of the corresponding link (combining the masses of the link and the payload). This method is then applied to the mechanisms constructed using spherical kinematic chain units, and the ones constructed using spherical kinematic chain units and other types of kinematic chain units. By distributing the mass of a link onto its adjacent links, the static balancing of the mechanism is reduced to those of several spherical kinematic chain units, which can be balanced using the proposed method. Two examples are given, including a Bennett plano-spherical hybrid linkage and a 3-RRS parallel mechanism to illustrate the proposed method for static balancing.</p