Stability analysis of constrained multibody systems

✍ Scribed by S. K. Ider; F. M. L. Amirouche

• Publisher: Springer
• Year: 1990
• Tongue: English
• Weight: 879 KB
• Volume: 6
• Category: Article
• ISSN: 0178-7675
• DOI: 10.1007/bf00350416

✦ Synopsis

Automated algorithms for the dynamic analysis and simulation of constrained multibody systems usually assume the rows of the constraint Jacobian matrix to be linearly independent. But during the motion, at instantaneous configurations, the Jacobian matrix may become less than full rank resulting in singularities. This occurs when the closed-loop goes from 3D to 2D type of configuration. In this paper the linearly dependent rows are identified by an uptriangular decomposition process. The corresponding constraint equations are modified so that the singularities in the numerical procedure are avoided. The conditions for the validity of the modified equations are described. Furthermore, the constraint equations expressed in accelerations are modified by Baumgarte's approach to stabilize the accumulation of the numerical errors during integration. A computational procedure based on Kane's equations is presented. Two and three-link robotic manipulators will be simulated at singular configurations to illustrate the use of the modified constraints.