A constraint-flow based method of synthesizing XYθ compliant parallel mechanisms with decoupled motion and actuation characteristics

It is an open challenge to synthesize XYθ compliant parallel mechanisms (CPMs) with decoupled motion and actuation characteristics for increasing applications from semiconductor manufacture to bio-nanotechnology. The key issue in the synthesis is to obtain the permitted constraints of the constituent compliant modules. In this paper, a constraint-flow based method is proposed to address this need, and up to 6859 constraint combinations are derived for the compliant modules, leading to a great number of possible synthesis schemes. Two case studies of schemes are presented to demonstrate the proposed synthesis method. One of the designs is analytically modelled, with less than 6.45% difference compared with the FEA results. A prototype of the design is also fabricated and experimentally tested. The analytical, FEA and/or experimental results show that the couplings are less than 3.9%, the translation resolution is 5 nm, and the rotation resolution is 50 nrad. The introduced constraint flow concept is not limited to the application of synthesizing decoupled XYθ CPMs, but also is an alternative and effective method in synthesizing other types of CPMs.