Static balancing of spatial six-degree-of-freedom parallel mechanisms with revolute actuators

The static balancing of spatial 6-degree-of-freedom parallel mechanisms or manipulators with revolute actuators is studied in this article. Two static balancing methods, namely, using counterweights and using springs, are used. The first method leads to mechanisms with a stationary global center of mass while the second approach leads to mechanisms whose total potential energy (including the elastic potential energy stored in the springs as well as the gravitational potential energy) is constant. The position vector of the global center of mass and the total potential energy of the manipulator are first expressed as functions of the position and orientation of the platform. Then, conditions for static balancing are derived from the resulting expressions. Finally, examples are given to illustrate the design methodologies.