On the modelling of actuator dynamics and the computation of prescribed trajectories

The dynamics of actuator mechanisms is presented using a multibody modelling approach to concisely express the structure of the system equations. The Lagrange equations are used to obtain the Newton–Euler equations to which constraint equations are augmented to form a system of differential algebraic equations. The differential algebraic equations are cast as ordinary differential equations and computed using the numerical integrator LSODAR of Petzold and Hindmarsh. Constraint compliance is investigated to ensure the accuracy of the results. Animation of an excavator and wheel loader system is presented and graphs of constraint forces show the nature of the actuator dynamics involved in maintaining specified bucket trajectories. The model is general in nature and caters for arbitrary mechanism connectivity and physical properties.