Stiffness control of a three-link redundant planar manipulator using the Conservative Congruence Transformation (CCT)

In this paper, the Conservative Congruence Transformation (CCT), K_θ-K_g=J_θ^TK_pJ_θ, is applied to a 3-link redundant planar manipulator. Since 3-link planar manipulator has one degree of redundancy, one constraint is allowed to be used to define the parameters of the system. Different constraints can be used to meet the specific requirements of manipulation. In this paper, two constraints are employed to obtain solution for redundant manipulation. One involves maintaining the most distal link along specific orientations; the other requires that the moment at the end-effector be always zero. In the latter case, the orientation of the distal link is decided in such a way that this constraint is satisfied. Numerical simulation and results are presented to illustrate that CCT is indeed a general and correct stiffness mapping in the analysis of redundant manipulators. The incorrect results of the conventional formulation, K_θ=J_θ^TK_pJ_θ, are also computed and compared with the results of the CCT theory.