Static Balancing of Spatial and Planar Parallel Manipulators With Prismatic Actuators

In this paper, the static balancing of existing spatial and planar parallel manipulators by the addition of balancing elements 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 spatial six-degree-of-freedom parallel manipulators and it is shown that planar three-degree-of-freedom parallel manipulators can be treated as a particular case of the spatial 6-dof mechanisms. The static balancing conditions associated with planar mechanisms can therefore easily be found, but are not given here because of space limitations. A brief geometric interpretation of the balancing conditions which are associated with statically balanced spatial mechanisms is then carried out. 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 and spatial 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. Moreover, the possibility of balancing existing systems by introducing additional elements, as demonstrated here, is of interest for retrofitting existing parallel mechanisms.