Compliant folded beam suspension mechanism control for rotational dwell function generation using the state feedback linearization scheme

The control of a slider–crank mechanism driven by a compliant, folded beam mechanism is investigated in this study. The compliant folded beam mechanism, also called the compliant double arm mechanism, has application areas at both the micro and macro levels. The compliant folded beam mechanism control in micro dimensions, driven by a force actuator is investigated here. The kinematic synthesis of the mechanism has been studied using mathematically exact nonlinear Elastica theory. The equivalent stiffness of the large deflecting fixed-free flexible beam, the single arm beam and the complete folded beam mechanism (double arm mechanism) are computed and, the complete mechanism stiffness is represented by a polynomial function that is curve fitted to the nonlinear inextensible exact beam theory solution. The dynamic response of the mechanism is obtained by solving the nonlinear equation of motion numerically using Runge–Kutta methods. The emphasis of the paper is placed on the subject of control of compliant mechanisms incorporating nonlinear stiffness (having large deflections) for function generation. The trajectory control of double cranks is achieved by considering linearization by the state feedback since the compliant folded beam mechanism (the double parallel arm mechanism) has a nonlinear stiffness. A PD controller is then applied to the feedback linearized system. The controller coefficients are determined to satisfy desired specifications on the output of the system.