Linearization of the Dynamics of Closed-Chain Mechanical Systems*

*Communicated by E.J. Haug

ABSTRACT

This paper presents an analytical-numerical method for linearizing the equations of motion of mechanical systems with closed chains. The algorithm developed here linearizes basic recursive kinematic relationships and then applies the chain rule to the derivation of the equations of 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 computation. Since the proposed algorithm uses no numerical differentiation, its accuracy is comparable to a symbolic, closed-form linearization. Moreover, without needing repetition computation in search of proper perturbation quantity, this method is computationally more efficient than the finite difference method

Notes

*Communicated by E.J. Haug