Considering Passive Joints in Cooperative Manipulation As Functional Redundancy

In this paper, it is studied how a certain class of physical constraints can be represented by a continuous set of orientations and how this representation is especially suitable for representing the constraints imposed by revolute and spherical joints. Further, it is shown how this can be used to represent the freedom of passive joints. It is recognised that in cooperative manipulation, the representation developed can be used to show how the introduction of passive joints at the end of a kinematic chain gives the same advantages as functional redundancy for single manipulators. This is used to improve manipulability and performance. Similar to functional redundancy the freedom of the passive joint is task dependent and the type of the passive joint must be chosen with the task in mind. Due to this observation, this paper proposes to consider the last passive joint a part of the tool. The manipulator can then be a standard industrial manipulator with functional redundancy in the specifications of the orientation of the last joint. It is shown that by introducing a passive joint at the end of the manipulator chain the workspace is increased, the dynamic load carrying capacity is maintained or increased while each manipulator is given a freedom equal to functional redundancy.