Design of Perfectly Statically Balanced One-DOF Planar Linkages With Revolute Joints Only

A systematic methodology for the design of a statically balanced, single degree-of-freedom planar linkage is presented. This design methodology is based on the concept of conservation of potential energy, formulated by the use of complex number notations as link vectors of the linkage. By incorporating the loop closure equations and the kinematic constraints, the gravitational potential energy of the system can be formulated as the function of the vectors of all ground-adjacent links. The balance of the gravitational potential energy of the system is then accomplished by the elastic potential energy of a zero free-length spring on each ground-adjacent link of the linkage. As a result, spring constants and installation configurations of the ground-attached springs are obtained. Since the variation in the gravitational potential energy of the linkage at all configurations can be fully compensated by that of the elastic potential energy of the ground-attached springs, this methodology provides an exact solution for the design of a general spring balancing mechanism without auxiliary parallel links. Illustrations of the methodology are successfully demonstrated by the spring balancing designs of a general Stephenson-III type six-bar linkage and a Watt-I type six-bar linkage with parallel motion.