To introduce a passive compliant mechanism for robot joints is an effective way for impact absorption. However, because robot joints also require high torque transmission characteristic, the simultaneous implementation of stiffness and softness is a significant issue. In this paper, we develop a torque transmission mechanism with nonlinear passive stiffness that realizes from zero to extremely high stiffness based on mechanical singularity. The analysis of nonlinear stiffness is established and the experimental evaluation is shown. A four-legged robot with the proposed mechanism is designed and the effectiveness of high nonlinearity of the proposed mechanism is shown by simulation.