This paper addresses the issue of providing stability guarantees during the implementation of multibody simulations for haptic display. It introduces the concept of a virtual coupling between the multibody simulation and haptic display hardware. This coupling separates the simulation design process from the sampled-data stability issues that arise during its implementation with a haptic display. Necessary conditions for passivity of a 1-DOF haptic display with a discrete-time passive simulation and an arbitrary virtual coupling are given. The implications of discrete-time passivity on numerical integration and collision response algorithms are also addressed.

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