Examples of spatial positioning redundant robotic manipulators that are optimally fault tolerant

It is common practice to design a robot´s kinematics from the desired properties that are locally specified by a manipulator Jacobian. For the case of optimality with respect to fault tolerance, one common definition is that the post-failure Jacobian possesses the largest possible minimum singular value over all possible locked-joint failures. This work considers a Jacobian that has been designed to be optimally fault tolerant for a simple spatial positioning manipulator. It is shown that despite the fact that the Jacobian is “unique”, up to column permutations and multiplications by ±1, there are a large family of physical manipulators that correspond to the optimal Jacobian. Two example manipulators are presented and analyzed. It is shown that there is a large degree of variability in the global kinematic properties of these designs, despite being generated from the same Jacobian.