The 6×6 stiffness formulation and transformation of serial manipulators via the CCT theory

This paper presents systematic methods to approach the conservative congruence transformation, CCT, via the geometrical analysis for the stiffness control transformation of serial manipulators. Through the strategy of changing basis, the 6×6 Cartesian stiffness of manipulators is shown to be basis dependent. The generalized formulation and symmetric property of the 6×6 Cartesian stiffness matrix are presented via the CCT theory in the presence of external loads. Examples of the serial manipulators are conducted to verify the conservative stiffness mapping.