Parameter synthesis for parallel kinematic machines from given process requirements

Parallel kinematic machines (PKM) are complex systems which kinematic properties vary in the workspace. Normally the machine's task implies requirements, e.g. size of the workspace and dexterity that must be taken into account for the design of the machine. In this paper we demonstrate geometrical parameter synthesis based on interval analysis for the parallel kinematic machine with constant leg length Linapod. The proposed algorithm enables us to determine all parameter sets that fulfil given process requirements like the size of the orientation workspace and a given upper bound on the kinematic dexterity of the machine. The use of interval analysis guarantees the validity of the results and makes the procedure robust against numerical instability. The method is extendable for additional process requirements