Computational kinematics of multibody systems: Two formulations for a modular approach based on natural coordinates

Multibody systems can be divided into an ordered set of kinematically determined modules, known as structural groups, in order to compute their kinematics more efficiently. In this work a procedure for the kinematic analysis of any kind of structural group is introduced, and two different methods for their solution in natural coordinates are presented: the time derivative (TD) and the third-order tensor (3OT) approaches. Moreover, the newly derived methods are compared in terms of efficiency with a global formulation, consisting in solving the kinematics of the multibody system as a whole using dense and sparse solvers. Two scalable case studies have been considered: a 2D four-bar linkage and a 3D slider-crank mechanism with an increasing number of constraint equations. The results show that the TD approach performs better in all cases with speed ups in a range of 27 to 61 times faster in 2D, and of 2.3 to 3.7 times faster in 3D with respect to the global sparse solution

A parallel simulator for multibody systems based on group equations

Multibody systems consist of a set of components connected through some joints, where the movement of the system is determined by those of its components. Their design is computationally demanding, and the group equations formulation facilitates the application of parallelism to reduce the simulation time. A simulator for the kinematic analysis of multibody systems on up-to-date computational nodes (multicore CPU+GPU) is presented. The movement of the components is simulated by repeatedly solving independent linear systems working on sparse matrices. The appropriate selection of the linear algebra library to be used and the degree of parallelism at each level (explicit with OpenMP and implicit with multithread libraries) help obtain important reductions in the simulation time.This work was supported by the Spanish MINECO and European Commission FEDER funds under grant TIN2015-66972-C5-3-R

Exploiting hybrid parallelism in the kinematic analysis of multibody systems based on group equations

Computational kinematics is a fundamental tool for the design, simulation, control, optimization and dynamic analysis of multibody systems. The analysis of complex multibody systems and the need for real time solutions requires the development of kinematic and dynamic formulations that reduces computational cost, the selection and efficient use of the most appropriated solvers and the exploiting of all the computer resources using parallel computing techniques. The topological approach based on group equations and natural coordinates reduces the computation time in comparison with well-known global formulations and enables the use of parallelism techniques which can be applied at different levels: simultaneous solution of equations, use of multithreading routines, or a combination of both. This paper studies and compares these topological formulation and parallel techniques to ascertain which combination performs better in two applications. The first application uses dedicated systems for the real time control of small multibody systems, defined by a few number of equations and small linear systems, so shared-memory parallelism in combination with linear algebra routines is analyzed in a small multicore and in Raspberry Pi. The control of a Stewart platform is used as a case study. The second application studies large multibody systems in which the kinematic analysis must be performed several times during the design of multibody systems. A simulator which allows us to control the formulation, the solver, the parallel techniques and size of the problem has been developed and tested in more powerful computational systems with larger multicores and GPU.This work was supported by the Spanish MINECO, as well as European Commission FEDER funds, under grant TIN2015-66972-C5-3-