Stiffness Design for a Spatial Three Degrees of Freedom Serial Compliant Manipulator Based on Impact Configuration Decomposition

Abstract

This paper proposes a method of stiffness design for a spatial Three Degrees of Freedom (3DOF) serial compliant manipulator with the objective of protecting the compliant joint actuators when the manipulator comes up against impact. System dynamic equations of serial compliant manipulators integrated with an impact model are linearized to identify the maximum joint torques in the impact. Based on this, a general procedure is given in which maximum joint torques are calculated with different directions of end-effector velocity and impact normal in the manipulator workspace based on a given magnitude of end-effector velocity. By tuning the stiffness for each compliant joint to ensure the maximum joint torque does not exceed the maximum value of the actuator, candidate stiffness values are obtained to make the compliant actuators safe in all cases. The theory and procedure are then applied to the spatial 3DOF serial compliant manipulator of which the impact configuration is decomposed into a 2DOF planar serial manipulator and a 1DOF manipulator with a 2DOF link based on the linearized impact-dynamic model. Candidate stiffness of the 3DOF serial compliant manipulator is obtained by combining analysis of the 2DOF and 1DOF manipulators. The method introduced in this paper can be used for both planar and spatial compliant serial manipulators.