A flexure mechanism for an interface device that interfaces a user with a computer system. An interface device includes a manipulandum physically contacted by the user. A five-bar closed-loop mechanism is coupled to the manipulandum to provide two rotary degrees of freedom to the manipulandum. The mechanism includes members coupled to each other by flexible couplings allowing rotation of the members. In preferred embodiments, four or five of the members are coupled together by flexible couplings that allow bending, thereby forming a unitary piece, where the couplings are oriented along axes of rotation of the mechanism. A senor senses a position of the manipulandum outputs a sensor signal, and in some embodiments actuators are coupled to the mechanism to output a force to the manipulandum in particular degrees of freedom. The manipulandum can be a joystick handle or portion of a sphere, where the device in one embodiment can be a handheld gamepad or similar controller.