Series elastic actuators with increasing nonlinear stiffness(NlSEA) have promising applications in human-machine interactions for the existence of a nonlinear elastic mechanism that supplies inherent safety and can implement high torque resolution under low load and quick dynamic response under high load. In this study, a novel design method for a nonlinear elastic mechanism that can be applied in NlSEA is proposed. By combining the S-shaped cantilever beam and specialized cam surface, this study proposed an analytical approach to design a nonlinear elastic mechanism satisfying a given stiffening torque-deformation relationship. The geometric parameters constraints were discussed to support parameter determination. Two kinds of cases of nonlinear elastic mechanisms with increasing and constant stiffness characteristics were conducted to verify the effectiveness and generalizability of the proposed design method by simulations. Moreover, a nonlinear elastic mechanism with an increasing stiffness characteristic was designed and a prototype was fabricated. A torque-deformation verification experiment, regulation response experiments, and sinusoidal tracking experiments were conducted to verify the accuracy, response performance, and tracking performance of the prototype. The designed nonlinear elastic mechanism has a large torque-to-mass ratio in a compact and lightweight structure.