Solvability Of Reactions And Inverse Dynamics Problem For Complex Kinematic Chains

Driving forces and joint reactions for a known, prescribed motion of a robot have to be determined in a process of robot design. For robots with complex kinematical structure and/or redundantly actuated the inverse dynamic problem may have non-unique solution. Certain driving forces or selected reactions in some joints may still be unique, however. The paper presents a general method of detection of unique drives and joint reactions. The kinetostatic analysis with free-body diagram of the robot is used. Three variants of the method are proposed: rank comparison method, and QR and SVD based methods. Two simple robotic systems are considered as examples: planar gripper and spatial redundant manipulator.