LINEARIZATION OF THE DYNAMICS OF CLOSED-CHAIN MECHANICAL SYSTEMS

This paper presents an analytical-numerical method for linearizing the equations of motion of mechanical systems with dosed chains. The algo rithm developed here linearizes basic recursive kinematic relationship s and then applies the chain rule to the derivation of the equations o f motion under the framework of recursive formulation. This method can be incorporated into the formulation of recursive equations of motion for general multibody dynamic systems to handle large-scale systems. The method is directly applicable to system Jacobian matrix computatio n. Since the proposed algorithm uses no numerical differentiation, its accuracy is comparable to a symbolic, closed-form linearization. More over, without needing repetition computation in search of proper pertu rbation quantity, this method is computationally more efficient than t he finite difference method.