A New Software Approach for the Simulation of Multibody Dynamics

Abstract

This paper introduces a new modular software approach combining symbolical and numerical methods for the simulation of the dynamics of mechanical systems. It is based on an exact, noniterative object-oriented algorithm, which is applicable to mechanisms with any joint type and any topology, including branches and kinematic loops. The simulation of big well-partitioned systems has complexity O(N), where N is the total number of simulated bodies. A new design software Virtual System Designer (VSD) integrates this method with the three-dimensional computer aided design tool Autodesk Inventor, which minimizes the cost of the development of models and the training of design engineers. The most time-expensive routine of the simulation process in VSD is the calculation of the accelerations of each body, which needs to find the roots of matrix equations. Accounting for the sparsity of matrices can significantly improve the numerical efficiency of the routine. The preprocessing module, developed using Maple software, performs the symbolic simplification of the matrix multiplication’s and QR decomposition’s procedures. The new coordinate projection method is demonstrated. The results of the simulation of the dynamics of a double insulator chain example show the method’s stability and effectiveness.

Simbody: multibody dynamics for biomedical research

“…Eqn. (2) can be used directly to eliminate this drift, and improve the solution overall, using the method of coordinate projection [31, 33–34]. Coordinate projection is superior to the more commonly-used Baumgarte stabilization method [35] for several significant reasons.…”

Integration Method of CAD Systems

“…where Q During the simulation of multibodies only the sparse matrices should be decomposed, that makes the method suitable for the implementation of sparse solvers or a special preprocessing module, performing a symbolic simplification of the decomposition of matrices [5]. The further integration of the preprocessing module with VSD will significantly increase the power of the software and the numerical efficiency of the software.…”

“…In this paper we show the modification of our method, which uses the decomposition of sparse matrices during the simulation of multibodies. It is suitable for the implementation of sparse solvers or a special preprocessing module, performing a symbolic simplification of decomposition of matrices [5].…”

Flight Dynamic Simulation for Multibody Aircraft Configurations

“…See [15,16] and the work cited within for a reasonably complete survey on methods and solution techniques. Although many detailed formulations are documented [17][18][19][20][21], the techniques roughly split along two lines pertaining to the manner in which motion is described (constrained or unconstrained coordinates) and how the fundamental dynamic equations are constructed (Newton-Euler or analytical mechanics approach). If unconstrained coordinates are employed, the final equations of motion tend to be quite involved and tedious to construct.…”