Static balancing of planar parallel manipulators

In this paper, the static balancing of planar parallel manipulators is addressed. Static balancing is defined here as the set of conditions on manipulator dimensional and inertial parameters which, when satisfied, ensure that the weight of the links does not produce any force (or torque) at the actuators for any configuration of the manipulator, under static conditions. These conditions are derived here for planar one-, two- and three-degree-of-freedom parallel manipulators. Subspaces of the parameter space which are associated with statically balanced mechanisms are then defined. It is shown that balancing is generally possible even when the dimensional parameters are imposed, which is a useful property since dimensional parameters are usually obtained from kinematic design or optimization. Finally, examples of balanced planar parallel manipulators are given. Static balancing leads to considerable reduction in the actuator forces (or torques), which in turn leads to less powerful actuators and more efficient designs