A design method for tendon-driven serial manipulators using controllable block triangular form of structure null space matrix

This paper proposes a generalized method for designing tendon-driven serial-chained manipulators with an arbitrary number of tendon redundancy. First, a special class of tendon-driven structures is defined by introducing the controllable block triangular form (CBTF) of a null space matrix and its complementary CBTF of a structure matrix, satisfying physical constraints related to the minimal connection of tendons and to the placement of actuators. Then it is shown that any general design of tendon-driven serial manipulators can be reduced to the design of such a special class of tendon-driven structures. Two associated design problems are derived and solved. The first design problem is about finding a complementary CBTF structure matrix for a given CBTF null space matrix using algebraic relations, whereas the second one seeks the both matrices that optimize the wanted structural characteristics based on the result of the first design problem. Numerical design examples are provided to show the validity of the proposed method.