With the use of springs, a method to balance the constant forces in arbitrary directions on a planar serial manipulator is developed in this study. Gravity balancing has been discussed a lot in the past. However, manipulators usually bear forces from various directions rather than only a fixed one as gravity. For instance, an industrial manipulator would bear forces from everywhere during the working process. Therefore, a method to balance these forces in arbitrary directions with springs is proposed. Based on the representation of energy, spring energy is the function of springs’ attachment points. Two spring systems with different attachment angles are needed to balance respectively forces in arbitrary directions and gravity. The spring installations of the above systems on 3-DoF manipulators are proposed. Finally, a resistive force-balanced manipulator with/without gravity balance in the grinding process is shown. In sum, this paper for the first time develops the balancing method for forces in arbitrary directions, expanding the spring balance theory to a broader application.

The kinematic control of a planar manipulator with several-degrees of redundancy has been a difficult problem because of the heavy computational burden and/or lack of appropriate techniques. The extended motion distribution scheme, which is based on decomposing a planar redundant manipulator into a series of nonredundant/redundant local arms (referred to as subarms) and distributing the motion of an end-effector to subarms at the joint velocity level, is proposed in this paper. The configuration index, which is defined as the product of minors corresponding to subarms in the Jacobian matrix, is used to globally guide the redundant manipulators. To enhance the performance of the proposed scheme, a self-motion control, which handles the internal joint motion that does not contribute to the end-effector motion, can be used optionally to guarantee globally optimal manipulation. The repeatability problem for the redundant manipulators is discussed using the proposed scheme. The results of computer simulations are shown and analyzed in detail for planar 8-DOF and 9-DOF manipulators, as examples.