A Synthesis Approach of XYZ Compliant Parallel Mechanisms Toward Motion Decoupling With Isotropic Property and Simplified Manufacturing

Decoupled compliant parallel mechanisms with isotropic legs possess many excellent performances, including ease of actuation, control, manufacture and mathematical analysis, as well as effective error compensation. Despite the advent of numerous isotropic compliant parallel mechanisms, their synthesis process predominantly relies on the empirical knowledge of engineers, with an absence of dedicated synthesis methodologies. This paper proposes the constraint algebra method, a novel synthesis method capable of autonomously exploring feasible constraint space for the synthesis. This method involves algebraic formulation of the constraints for the compliant modules, followed by solving constraint equations to find the feasible constraints and orientations, thereby facilitating the synthesis with intended performance characteristics. The multiplicity of solutions to the constraint equations enables the generation of diverse designs, including innovative configurations that are challenging to obtain via other methods and experience. Furthermore, by the consideration of machinability in several steps of synthesis, the optimal configuration can be selected for simplified manufacture. A design case has been monolithically prototyped and experimentally tested. The proposed methodology holds promise for potential extension to the synthesis of other types of compliant mechanisms.