In this paper, we study the effect of the wing to motor connection mechanism on generated lift in flapping wing hovering robots. We also propose a series compliance mechanism for the wing to motor connection and compare its performance against the existing mechanisms. In the first mechanism, the wing is directly connected to the motor with no compliance attached to the wing or motor. The second mechanism has a compliance in parallel to the wing while it, the wing, is directly connected to the motor. This mechanism resembles the well-known spring-mass system in which a spring is in parallel to the motor force, and the inertia of the wing and motor move together. The possibility of producing resonance with this mechanism is a great advantage that increases the produced lift around the resonant flapping frequency. Our proposed mechanism, the third mechanism, is inspired by the existence of tendons and muscles in animal wings. Therefore, there is an elastic spring (tendon) exist between the motor (muscle) and the wing. In this wing-motor mechanism, one end of the spring (or compliance) is connected to the wing and the other end is connected to the motor. We construct trajectory optimization to find the maximum lift production in each mechanism given the geometrical and physical limitations. The results show that the series and parallel compliance mechanisms have the potential to produce more lift with respect to the non compliance mechanism. Moreover, the series compliance mechanism can produce the highest lift depending on the inertia distribution between the wing and the motor.