Displacement amplification ratio and input stiffness are significant design characteristics for an ultra-precision positioning flexure-based compliant mechanism. Early and accurate performance prediction models can significantly improve the reliability and availability of product in the field of ultra-precision positioning, but Existing theoretic models cannot predict its characteristics accurately and make it very difficult to error compensation by means of these models. This paper provides a set of uncanonical linear homogeneous equations for calculating a classic bridge-type mechanical amplifier performance, these closed-form equations are established based on the thought of statically indeterminate structure, including Force Method, Maxwell-Mohr Method and deformation compatibility. Subsequently, case studies involving the calculation results compared with FEA, geometric parameters' influence discussion and modal analysis using FEA simulation are presented. This proposed analytical model is applicable and reliable to the bridge-type micro-displacement amplifier design and verification. Furthermore, the present model can be used in any other over-constrained flexure-based amplifier.