Static Equilibrium Position Analysis of Planar Multibody Systems Based on the Reduced Multibody System Transfer Matrix Method

The static equilibrium configuration of a multibody system is often used as the initial condition for dynamics analyses. However, for complex multibody systems, determining the static equilibrium configuration is challenging. An approach for analyzing the static equilibrium configuration is developed using the planar reduced multibody system transfer matrix method in this paper. By incorporating the direct differentiation method, a systematic procedure is established to construct the Jacobian matrix of the dynamic equations. The Newton-Raphson iteration method is applied to solve the nonlinear system of equations under the condition of zero generalized acceleration, thereby obtaining the static equilibrium configuration. Compared to the conventional approach of dynamic simulation until the generalized velocities and generalized accelerations converge to zero, the proposed method offers significantly higher computational efficiency and accuracy.