Describing function of the Gaussian friction model and its effect on stability of a haptic device

Friction exists in any moving body, such as manipulator joints. Haptic devices (HDs) are manipulators that can simulate virtual objects for their operators and have different applications in education, medical, and entertainment areas. The existence of friction and inertia in HDs is unavoidable. The friction and effective mass of the HDs decrease the transparency of simulating virtual objects. The Gaussian friction model includes nonlinear phenomena like stiction and the Stribeck effect. In this research, a describing function (DF) for the Gaussian friction model is obtained. Afterward, as an application, this determined DF is used in the stability analysis of a HD to consider the effect of nonlinear friction on its stability boundary. This yields the derivation of a closed-form equation to predict the stability boundary without any limitations on time delay and virtual damping, including nonlinear phenomena such as stiction and the Stribeck effect. Afterward, the determined stability equations were verified by simulations with different time delays and virtual damping with good precision. Also, performing experiments on a HD shows that by using the new DF, the experimental results are predicting approximately %80\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%80$$\end{document} better, compared with the case of not using this DF.