Efficient parallelizable algorithm for the motion simulation of general multi-rigid-body mechanical systems

A novel parallel procedure for the formulation and numerical solution of the equations of motion associated with multibody mechanical systems is presented. Specifically, the formation of the equations of motion, with their solution for system state derivatives and subsequent temporal integration is performed on parallel computing systems. Based on the explicit determination of constraint forces at certain key joint locations and the subsequent highly efficient determination of system state time derivatives, this novel procedure may be viewed as hybridizations between more traditional methods in a number of ways. First, the procedure takes advantage of elements of improved computing efficiency from both parallel computations and the sequential order-N ( O(N)) algorithm to achieve the higher overall computing efficiency. Second, the algorithm uses a hybrid direct and iterative solution scheme which allows a substantially higher degree of parallelization than is generally obtainable using the more conventional recursive O( N) procedures. Third, the dynamical formulation is a hybrid form of state space and descriptor representations. Finally, a theoretical time optimal O(log2N) performance on computational turnaround with a processor optimal O( N) processors can be achieved on a Multi-Instruction, MultiData (MIMD) architecture processing system.; The algorithm should more easily accommodate the available (often sub-optimal) number of processors while still maintaining higher efficiency than other parallel procedures. At one extreme, the new procedure will produce true non-iterative O(N) performance when used sequentially on a single processor. At the other extreme, the algorithm will provide coarse grain parallelization of an N body system to O(N) processors potentially and theoretically providing O( log2N) computational performance. The approach maintains many of the desirable characteristics of the sequential O( N) procedures which allow it to perform well when the number of bodies in the simulation is significantly greater than the number of available processors.; Theoretical formulations are derived by means of methods developed in dynamics, numerics and computer science. Numerical programs based on the theoretical formulations are presented for validation, and along with typical case studies and performance comparison.