Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices

[+] Author and Article Information
S. K. Saha

Department of Mechanical Engineering, I.I.T., Delhi, Hauz Khas, New Delhi 110 016, India

J. Appl. Mech 66(4), 986-996 (Dec 01, 1999) (11 pages) doi:10.1115/1.2791809 History: Received July 14, 1998; Revised June 17, 1999; Online October 25, 2007


Constrained dynamic equations of motion of serial multibody systems consisting of rigid bodies in a serial kinematic chain are derived in this paper. First, the Newton-Euler equations of motion of the decoupled rigid bodies of the system at hand are written. Then, with the aid of the decoupled natural orthogonal complement (DeNOC) matrices associated with the velocity constraints of the connecting bodies, the Euler-Lagrange independent equations of motion are derived. The De NOC is essentially the decoupled form of the natural orthogonal complement (NOC) matrix, introduced elsewhere. Whereas the use of the latter provides recursive order n—n being the degrees-of-freedom of the system at hand—inverse dynamics and order n3 forward dynamics algorithms, respectively, the former leads to recursive order n algorithms for both the cases. The order n algorithms are desirable not only for their computational efficiency but also for their numerical stability, particularly, in forward dynamics and simulation, where the system’s accelerations are solved from the dynamic equations of motion and subsequently integrated numerically. The algorithms are illustrated with a three-link three-degrees-of-freedom planar manipulator and a six-degrees-of-freedom Stanford arm.

Copyright © 1999 by The American Society of Mechanical Engineers
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