This thesis addresses current haptic display technology where the user interacts with a virtual environment by means of specialized interface devices. The user manipulates computer generated virtual objects and is able to feel the sense of touch through haptic feedback. The objective of this work is to design high performance haptic interactions by developing multi-purpose virtual tools and new control schemes to implement a PUMA 560 robotic manipulator as the haptic interface device. The interactions are modeled by coupling the motions of the virtual tool with those of the PUMA 560 robotic manipulator;The work presented in this dissertation uses both kinematic and dynamic based virtual manipulators as virtual simulators to address problems associated in both free and constrained motions. Both implementations are general enough to allow researchers with any six degree-of-freedom robot to apply the approaches and continue in this area of research. The results are expected to improve on the current haptic display technology by a new type of optimal position controller and better algorithms to handle both holonomic and nonholonomic constraints;Kane's method is introduced to model dynamics of multibody systems. Multibody dynamics of a virtual simulator, a dumbbell, is developed and the advantages of the Kane's method in handling the non-holonomic constraints are presented. The resulting model is used to develop an approach to dynamic simulation for use in interacting haptic display, including switching constraints. Experimental data is collected to show various contact configurations;A two-degree of freedom virtual manipulator is modeled to feel the surface of a taurus shape. An optimal position controller is designed to achieve kinematic coupling between the virtual manipulator and the haptic display device to impose motion constraints and the virtual interactions. Stability of the haptic interface is studied and proved using Lyapunov's direct method. Experimental data in various positions of the robotic manipulator is obtained to justify theoretical results. A shift mechanism is then implemented on the taurus shape, thus the motions of the robotic manipulator is further constrained. The difficulties in handling the motion constraints are discussed and an alternative approach is presented.