A robust model for 3D tracking in object-oriented multibody systems based on singularity-free Frenet framing

Abstract

The article presents an object-oriented representation of Frenet frame motion along spatial curves in multibody systems. In this setting, the spatial track is regarded as a kinetostatic transmission element transmitting motion and forces as in a generic joint. It is shown that for the Frenet frame parameterization it is possible to avoid singularities at the points of inflection by a special exponential blending technique. The combination of the simple Frenet frame formulas with singularity treatment leads to robust and efficient code for dynamic multibody simulation. All concepts have been tested within an industrial application of roller coaster design.