On the dynamic behaviour of the "click" mechanism in dipteran flight

In this paper, the dynamic behaviour of the "click" mechanism is analysed. A more accurate model is used than in the past, in which the limits of movement due to the geometry of the flight mechanism are imposed. Moreover, the effects of different damping models are investigated. In previous work, the damping model was assumed to be of the linear viscous type for simplicity, but it is likely that the damping due to drag forces is nonlinear. Accordingly, a model of damping in which the damping force is proportional to the square of the velocity is used, and the results are compared with the simpler model of linear viscous damping. Because of the complexity of the model an analytical approach is not possible so the problem has been cast in terms of non-dimensional variables and solved numerically. The peak kinetic energy of the wing root per energy input in one cycle is chosen to study the effectiveness of the "click" mechanism compared with a linear resonant mechanism. It is shown that, the "click" mechanism has distinct advantages when it is driven below its resonant frequency. When the damping is quadratic, there are some further advantages compared to when the damping is linear and viscous, provided that the amplitude of the excitation force is large enough to avoid the erratic behaviour of the mechanism that occurs for small forces.