On the Internal Counter-Torque between Springs in Serially Connected Statically Balanced Manipulators

Serially connected statically balanced manipulators with springs have been used in many applications. However, a portion of the torques caused by springs countering each other lead to an imbalance in gravitational torques and, therefore, are deemed as waste torques for springs to achieve static balance. In this paper, the torque contribution of a typical spring is classified as gravity-balancing torque and counter-torque based on the accumulated joint angle of the gravitational torque. Then, the internal counter-torque is defined as the sum of the magnitude of the terms of these counter-torques at each joint. Through the adjustment of spring attachment parameters, the internal counter-torque can be minimized with preferable spring attachment parameters while maintaining a static-balancing condition. A typical four-link manipulator with a preselected spring configuration is shown as an illustrative example. The results show that there are 28% and 50% reductions in the internal counter-torque at joints 2 and 3, respectively, through the adjustment of spring attachment parameters. Hence, the waste torques in statically balanced serially connected manipulators are reduced to the lowest quantity.