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

•A parameterized compliance matrix of the TFM is derived as functions of leg’s mounting angle θ.•The compliance and DOF properties of the TFM significantly rely on θ-vales.•Findings of θR=arctanrh that the TFM becomes a 3-DOF rotational mechanism, and a constant compliance relationship γ52γ1γ3=1, when flexure leg has negligible axial stiffness (β3 → 0).•A compliance-based type synthesis of the TFM with the parameter θ is performed.•The feasibility of the TFM for MSA design is proved by experimental measurements.