A Combined Penalty and Recursive Real-Time Formulation for Multibody Dynamics

Abstract

The continuously improved performance of personal computers enables the real-time motion simulation of complex multibody systems, such as the whole model of an automobile, on a conventional PC, provided the adequate formulation is applied. There exist two big families of dynamic formulations, depending on the type of coordinates they use to model the system: global and topological. The former leads to a simple and systematic programming while the latter is very efficient. In this work, a hybrid formulation is presented, obtained by combination of one of the most efficient global formulations and one of the most systematic topological formulations. It shows, at the same time, easiness of implementation and a high level of efficiency. In order to verify the advantages that the new formulation has over its predecessors, the following four examples are solved using the three formulations and the corresponding results are compared: a planar mechanism which goes through a singular position, a car suspension with stiff behavior, a 6-dof robot with changing configurations, and the full model of a car vehicle. Furthermore, the last example is also analyzed using a commercial tool, so as to provide the readers with a well-known reference for comparison.

Two implementations of IRK integrators for real‐time multibody dynamics

“…Analogously, Equation (37) shows the difference equations of the integrator which express the velocities and accelerations at the second stage as functions of the positions at the same stage, plus some positions, velocities and accelerations at the current time-step and the first stage. Therefore, Equations (36) and (37) possess the same form as the difference equations of Newmark-type integrators, which means that the strategy followed in the authors' previous works to combine the three dynamic formulations with those integrators at time-step level [1,4], may now be applied with SDIRK integrators at stage level. As said in Section 2, the motion equations for the two formulations in dependent co-ordinates were stated through an index-3 augmented Lagrangian scheme [3] …”

“…The three formulations being compared have previously shown an excellent aptitude for realtime purposes [1], since they are efficient, i.e. they provide very fast calculation of the function evaluation, and they are robust, which means that they can perform large time-steps without losing stability.…”

“…The hybrid method [1] shares the first stage with the topological method previously described, i.e. until the equations of motion are established in relative co-ordinates, dependent in general, for the open-loop version of the mechanism.…”

“…In a first work [1], the authors presented a new real-time formulation for the dynamics of multibody systems, which encompasses high ranks of efficiency, accuracy, robustness and easiness of implementation. The new method, called hybrid, was obtained as combination of a topological semi-recursive formulation based on velocity transformations [2], and a global penalty formulation for closed-loops consideration [3].…”

An Efficient Unified Method for the Combined Simulation of Multibody and Hydraulic Dynamics: Comparison with Simplified and Co-Integration Approaches

“…1. Pressure rates for the volumes on both sides of the cylinder piston are derived from fluid continuity and compressibility considerations [5] (2) where V A and V B are the volumes at each side of the cylinder andV A ,V B are their speeds of variation. Q PA , Q PB represent the flow incoming to chamber A or B from the pump, Q T A , Q T B are the flows to the tank from chamber A or B, while Q BA constitutes the leakage flow and is commonly neglected.…”