Premium
Projection methods in flexible multibody dynamics. Part II: Dynamics and recursive projection methods
Author(s) -
Wehage R. A.,
Shabana A. A.,
Hwang Y. L.
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620351003
Subject(s) - multibody system , kinematics , projection (relational algebra) , projection method , mathematics , inertia , sylvester's law of inertia , equations of motion , newton's method , computer science , control theory (sociology) , algorithm , dykstra's projection algorithm , classical mechanics , nonlinear system , symmetric matrix , physics , quantum mechanics , artificial intelligence , eigenvalues and eigenvectors , control (management)
In Part I of this paper the kinematic relationships between the absolute, elastic and 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 co‐ordinates. 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.