In this paper we investigate the stability properties of a single degree of freedom (DoF) haptic display while a virtual viscoelastic object is touched where the viscoelastic object is modeled using the standard linear solid model (also called the Kelvin model). We will demonstrate that this model leads to a discrete-time PID control-like representation of the virtual environment. A detailed dynamic analysis and simulations are presented in this paper with a particular attention to determine stability charts in the space of the parameters given by the virtual viscoelastic model.

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