Static balancing of 3-DOF planar parallel mechanisms

The static balancing of planar 3-DOF parallel mechanisms is addressed in this paper. Static balancing is defined as the set of conditions on mechanism dimensional and inertial parameters which, when satisfied, ensure that the weight of the links does not produce any torque (or force) at the actuators for any configuration of the mechanism, under static conditions. For the mechanisms studied here, conditions for static balancing are obtained, and 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. Then, the conditions for the static balancing of the same mechanisms are derived for designs in which elastic elements are included. Finally, examples of balanced mechanisms are given. A dynamic study is performed