In this paper, we first presented a four-bar linkage mechanism for actuating the wings in a flapping wing flying robot. After that, given the additional constraints imposed by the four-bar linkage, we parameterized the wing kinematics to provide sufficient control authority for stabilizing the system during 3D hovering. The four-bar linkage allows the motors to spin continuously in one direction while generating flapping motion on the wings. However, this mechanism constrains the flapping angle range which is a common control parameter in controlling such systems. To address this problem, we divided each wingbeat cycle into four variable-time segments which is an extension to previous work on split-cycle modulation using wing bias but allows the use of a constant flapping amplitude constraint for the wing kinematic. Finally, we developed an optimization framework to control the system for fast recovery while guaranteeing the stability. The results showed that the proposed control parameters are capable of creating symmetric and asymmetric motions between the two wings and, therefore can stabilize the hovering system with minimal actuation and flapping angle amplitude constraint.