Geometrical Interpretation of the CCT Stiffness Mapping for Serial Manipulators

Abstract

Recent research results suggested a conservative transformation to correct the well-known congruence transformation between Cartesian and joint stiffness matrices of a serial manipulator. This paper utilizes screw geometry to interpret the conservative congruence transformation (CCT). The analysis using screw theory provides better geometric insights into the CCT. The effective geometrical stiffness matrix, due to the change of manipulator geometry under stiffness control in the presence of external force, is confirmed. This paper also points out several erroneous assumptions that may have led to the incorrect formulation of the conventional congruence transformation.