An interval analysis based study for the design and the comparison of three-degrees-of-freedom parallel kinematic machines

This paper addresses an interval analysis based study that is applied to the design and the comparison of three-degrees-of-freedom (3-DoF) parallel kinematic machines. Two design criteria are used: (i) a regular workspace shape and (ii) a kinetostatic performance index that needs to be as homogeneous as possible throughout the workspace. The interval analysis based method takes these two criteria into account; on the basis of prescribed kinetostatic performances, the workspace is analyzed to find the largest regular dextrous workspace enclosed in the Cartesian workspace. An algorithm describing this method is introduced. Two 3-DoF translational parallel mechanisms designed for machining applications are compared using this method. The first machine features three fixed linear joints which are mounted orthogonally and the second features three linear joints which are mounted in parallel. In both cases, the mobile platform moves in the Cartesian x-y-z space with fixed orientation.