Inverse dynamics of a toggle mechanism

The inverse dynamics problem aimed at determining the driving forces that produce a specific motion is presented. It is necessary to know the velocities and accelerations to be able to estimate the inertia forces which provide the basis to calculate the required actuating forces. A constrained multibody technique is employed to calculate the position, velocity and acceleration of the toggle mechanism. For the multibody dynamic analysis, Hamilton's principle and Lagrange multiplier method are applied to formulate the equations of motion. By using geometric relationships the differential-algebraic equations can be reduced to pure differential equations form and Runge-Kutta numerical method is used to perform numerical simulations. The results of kinematic and dynamic analysis are presented and compared for the four-point type and the five-point toggle mechanisms.