A contact aided compliant mechanism called twist compliant mechanism is presented in this paper. This mechanism has nonlinear stiffness when it is twisted in both directions along its axis. The inner core of the mechanism is responsible for its flexibility in one twisting direction. The contact surfaces of the cross-members and compliant sectors are responsible for its high stiffness in the opposite direction. A twist compliant mechanism with desired twist angle and stiffness can be designed by choosing the right thickness of its cross-members, thickness of the core and thickness of its sectors. A multi-objective optimization problem with three objective functions is proposed in this paper, and used to design an optimal twist compliant mechanism with desired deflection. The objective functions are to minimize the mass and maximum von Mises stress observed, while minimizing or maximizing the twist angles under specific loading conditions. The multi-objective optimization problem proposed in this paper is solved using an ornithopter flight research platform as a case study, with the goal of using the twist compliant mechanism to achieve passive twisting of the wing during upstroke, while keeping the wing fully extended and rigid during the downstroke. Prototype twist compliant mechanisms have been fabricated using a waterjet cutter and will be tested as part of future work.