Compliant mechanism based amplifiers have been extensively studied with particular attentions to achieving a high amplification ratio. However, a constant amplification ratio is less investigated, which is much desired for a simple and quick prediction of outputs. In this research, we aim to address this need. Thereby, we present an overconstraint based constant amplification ratio compliant mechanism (OCARCM) that alleviates the change of the amplification ratio. Comparative analysis is provided between the proposed OCARCM and the widely-used bridge-type compliant amplifier in terms of the ability to remain constant amplification ratio with and without payload. The free-body diagram (FBD) combined with the beam constraint model (BCM) method is employed to obtain the closed-form solutions that accurately and insightfully elaborate the nonlinearities in the force-displacement characteristics of the OCARCM. The closed-form results are verified by the nonlinear finite element results (FEA) with a maximum error of 1%. Both models reveal that the amplification ratio of the proposed OCARCM decreases by 1%, while the amplification ratio of the bridge-type amplifier decreases by approximately 14% under the same conditions. An experiment based on the 3D-printed prototype is conducted, which provides some insights into the characteristics of the design and the potential for future improvement.