Analysis of a tripod flexure mechanism (TFM) for mirror sub-assemblies

This paper presents the analytical compliance analysis and type synthesis for a tripod flexure mechanism (TFM) which is used in the design of the mirror sub-assembly (MSA) of future inertia-confinement-fusion (ICF) facilities. To reveal the compliance characteristics of the TFM, the static compliance analysis is conducted. The analytical compliance matrix of the TFM is obtained by using the coordinate transformation method (CT-method) of compliance matrices. The parameterized compliance matrix of the TFM is derived, and it is significantly influenced by its legs' mounting angle θ. Different θ values generate different degree-of-freedom (DOF) characteristic of types. The finite element analysis (FEA) results are compared with analytical compliance elements results for different θ values. As to the linear linear-elastic deformations, the maximum compliance error of analytical model is less than 1% compared to the FE model. Enlightened by the compliance analysis of the TFM, a compliance-based type synthesis of the TFM is introduced in detailed processes, illustrating how θ affects the DOF characteristics. According to the results of the compliance analysis and type synthesis, a TFM was designed and fabricated for the MSA prototype, and it is experimentally verified. It is demonstrated that the parameterized compliance matrix provided is beneficial to design, analysis and type synthesis tasks of TFMs.