Journal of Parallel and Distributed Computing 62, 1001–1020 (2002) doi:10.1006/jpdc.2001.1820 A Unified Formulation for Massively Parallel Rigid Multibody Dynamics of O(log 2 n) Computational Complexity Andr ! es Jaramillo-Botero 1 Engineering Faculty, Pontificia Universidad Javeriana, Calle 18 #118-250 v ! ı a a Pance, Cali, Colombia E-mail: ajaramil@puj.edu.co and Alfons Crespo I. Lorente DISCA Department, Universidad Polit ! ecnica de Valencia, Camino de Vera, 14, E46022, Valencia, Spain E-mail: alfons@aii.upv.es Received August 4, 1999; revised November 27, 2001; accepted January 11, 2002 A novel algorithm for the solution of the inverse dynamics problem is presented and augmented to the solution of the equations of motion (EOM) for rigid multibody chains using explicit constraint components of force. The unified model corresponds to an optimal, strictly parallel, time, space, and processor lower bound solution to the dynamics of accelerated rigid multibodies, i.e., computation time of Oðlog 2 nÞ using OðnÞ processors for an n body system. Complex topological structures are supported in the form of multiple degree-of-freedom (DOF) joints/hinges, free-floating, hyper-branched, and/or closed-chain systems, with applications ranging from multibody molecular dynamics simulations and computational molecular nanotechnol- ogy, to real-time control and simulation of spatial robotic manipulators. In addition to the theoretical significance, the algorithms presented are shown to be very efficient for practical implementation on MIMD parallel architectures for large-scale systems. # 2002 Elsevier Science (USA) Key Words: strictly parallel computations; robotics; forward dynamics; inverse dynamics; multibody dynamics; molecular dynamics; computational molecular nanotechnology. 1. INTRODUCTION Two basic problems are tackled in considering the dynamic behavior of general systems. Bodies, which are subject to forces, undergo acceleration (motion) (referred 1 To whom correspondence should be addressed. 1001 0743-7315/02 $35.00 # 2002 Elsevier Science (USA) All rights reserved.