Force Analysis of Statically Balanced Serially Connected Manipulators Using Springs Based on Torque Compatibilities Associated With Accumulative Joint Angles

Force analysis with regard to serial connected manipulators is discussed thoroughly in the past. However, force analysis of statically balanced manipulator using springs has not been widely addressed because spring forces and motions do not share an immediate association. In this article, spring forces are represented as accumulative joint angles of links crossed by springs and attached angles/lengths of springs. Torque equilibrium equations regarding the preconnected joint of a typical link as contributed by gravity force and spring force can be inwardly formed link by link from the end link. Compatibility with the same accumulative joint angle can be formulated under static balance conditions. Hence, spring attachment parameters such as spring stiffness and attachment lengths are constrained by given link properties and spring attachment angles. Thus, spring forces can be determined by a chosen set of stiffness and attached lengths of springs, and the joint reaction force can then be determined. Example figures of 3-degrees-of-freedom (DOFs) manipulators show that joint reaction forces are reduced by 22.6%, 40.1%, and 75.7% at joints 1, 2, and 3, respectively, than those without springs. It is found that besides balancing gravity, the statically balanced manipulator is with lower joint reaction forces. Hence, the manipulator can be more lightweight by using compact joints and links with the same material. Furthermore, the static and dynamic performance of the manipulator can be improved by the effect of reduced joint reaction forces as well.