Minimum mass for haptic display simulations

This paper addresses the issue of providing stability guarantees during the implementation of multibody simulations for haptic display. Within the framework of the virtual coupling, we discuss the passivity of the haptic display. Previous work has established that, if the numerical methods used in the virtual environment are discrete time passive, it is possible to decouple the stability of the device from the virtual environment simulation. In the present work, we prove that discrete time passive operators must be implicit, making them unlikely candidates for real time implementation. Given restrictions on environment parameters, however, passivity can sometimes be preserved even when using explicit numerical methods. An important benchmark simulation is that of a point mass, and restrictions take the form of a minimum mass that can be simulated passively. This minimum mass is derived for several simple numerical integrator-virtual coupling pairs.