Tetrobot family tree: modular synthesis of kinematic structures for parallel robotics

Parallel robots can be built by linking together unit cells in configurations which retain the static determinacy of the overall structure. In the Tetrobot system, the kinematics of these concatenated structures can be solved by propagation of solutions through connected graphs of linked modules. In this paper, we examine the synthesis of unit cells which could be used in creating these structures and retain the ability to compute the kinematics for control of the actuated system. Admissible unit cells are shown to form families in two- and three-dimensions, and a set of synthesis rules is described which generates the members of these families recursively for each generations. The resulting set of modules comprises a broad set of useful cells which can be used to design parallel robots and guarantee the computability of their kinematics on a cell-by-cell basis.