In the physical world, impedances vary widely. For example, while holding a pencil, the perceived impedance is that of a low mass rigid body, but when pressing the same pencil against a writing surface, the perceived impedance is that of a stiff viscoelastic body. In one case, the pencil provides almost no resistance to motion, in the other case almost complete resistance to motion (at least in the direction normal to the surface). This type of interaction is called a unilateral constraint, and prevents the interpenetration of bodies without holding them together. Unilateral constraints are ubiquitous in tool use, as they occur whenever rigid bodies collide. These two characteristics, a wide impedance range and the ability to enforce unilateral constraints, are features we would like to retain in our implementation of haptic virtual environments.
Unfortunately, this type of interaction can be extremely challenging to implement, as it requires a single device to exhibit a wide range of mechanical behaviors in a robust fashion. Furthermore, the device needs to be able to switch between these extremes seamlessly. The situation is further complicated when the virtual environment involves complex geometric interactions between multiple rigid bodies (e.g. hand tool simulation). As a result, any given haptic display has a finite range of impedances that it can successfully emulate, and that outside that range, the interactions typically become unstable. We have found that the challenge of designing a haptic interface is to build a single programmable device which can exhibit a comparably broad dynamic range of impedances.
This thesis does not address the psychophysics of what makes a virtual wall feel good, except to say that one important factor seems to be dynamic range. Excellent articles on this topic have been written recently by Rosenberg and Adelstein [26] and Lawrence and Chapel [21]. These papers begin to put limits on the types and range of impedances which a device must be capable of implementing in order to successfully simulate rigid contact. Preliminary results indicate that indeed the necessary range of impedances is quite wide. To achieve this range, we must put careful consideration into the design of the haptic display.