In this thesis new closed-form equations for stability analysis of a linear haptic device are presented using two different methods of frequency and state-space analysis. The developed equations provide critical virtual damping and stiffness of the virtual environment versus mass and viscous friction of the haptic device, sampling time and time delay. Unlike prior work in this field, the developed equations are valid without any limitation on the values of the time delay and virtual damping. It is shown that they cover available well known equations in literature for special cases of small values of virtual damping and time delay. The resulting equations are of practical usefulness in many fields, such as surgery simulation for avoiding instability during virtual tool interaction with high-stiffness virtual environments. The proposed analytical derivation can also be used for studying the effect of operator, sensors, actuator dynamics, and velocity filtering. Simulation and experimental results on the KUKA Light Weight Robot (LWR) show that the proposed criterion can accurately predict the stability boundaries. Also describing function of Karnopp and LuGre friction models are determined for the first time. Using these describing functions, dynamic phenomenas such as Stribeck effect, sticksion, variable break-away force, Hysteresis and frictional lag are involved in stability of haptic devices. Simulations show that stability boundaries can be determined with good precision in this case. Keywords: Haptic devices; stability; time delay; describing function; Karnopp friction; LuGre friction; LMI.
