Design of decoupled, compact, and monolithic spatial translational compliant parallel manipulators based on the position space

The initial version of this paper was presented at 2014 Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators, Tianjin, China. The conceptual design of three types of decoupled, compact, and monolithic XYZ compliant parallel manipulators (CPMs) is taken into account in this paper using the position space concept. The CPMs are termed CUBEs due to the shape of their compact structures. The position space of a compliant module is the combination of all permitted positions in an XYZ CPM system where the constraint of this compliant module in the XYZ CPM system remains unchanged when the position of the compliant module changes within the position space. The position of each compliant P joint is considered relative to its adjacent compliant joint/module rather than being considered in insolation. A design method for obtaining monolithic XYZ CPMs is proposed in terms of both the kinematic substitution and position spaces. Three types of monolithic XYZ CPMs are then demonstrated using the proposed method, with the help of three classes of kinematically decoupled three degrees of freedom translational parallel mechanisms. These monolithic XYZ CPMs include a 3-PPP (P: prismatic) XYZ CPM, a 3-PPPR (R: revolute) XYZ CPM, and a 3-PPPRR XYZ CPM. The position space concept can enable the system configurations to be designed based on the chosen optimization requirements, which include considerations such as compactness or minimization of parasitic rotations. This provides an efficient and systematic method to arrange the relative position between any two compliant joints/modules so that one can easily generate practical and useful configurations for XYZ CPMs. The resulting XYZ CPM is the most compact one when the fixed ends of the three actuated compliant P joints thereof overlap or are as close to each other as possible.