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Projection Methods in Flexible Multibody Dynamics. Part 2. Dynamics and RecursiveProjection Methods

机译：柔性多体动力学中的投影方法。第2部分。动力学和递归投影方法

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In Part I of this paper the kinematic relationships between the absolute, elasticand joint accelerations are developed. In this paper, these kinematic equations are used with the generalized Newton Euler equations and the relationship between the actual and generalized reaction forces to develop a recursive projection algorithm for the dynamic analysis of open-loop mechanical systems consisting of a set of interconnected rigid and deformable bodies. Optimal matrix permutation, partitioning and projection methods are used to eliminate the elastic accelerations while maintaining the inertia coupling between the rigid body motion and the elastic deformation. Recursive projection methods are then applied in order to project the inertia of the leaf bodies onto their parent bodies. This leads to an optimal symbolic factorization which recursively yields the absolute and joint accelerations, and the joint reaction forces. The method presented in this paper avoids the use of Newton Raphson algorithms in the numerical solution of the constrained dynamic equations of open-loop kinematic chains since the joint accelerations are readily available from the solution of the resulting reduced system of equations. Furthermore, the method requires only the inversion or decomposition of relatively small matrices and the numerical integration of a minimum number of coordinates. Open-loop multibody robotic manipulator systems are used to compare the results and efficiency of the recursive methods with that of the augmented formulations that employ Newton Raphson algorithms.

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