SUMMARY
A formable surface is part of an effort to create a haptic device that allows for a three dimensional human-computer interface called digital clay. As with real clay, digital clay allows a user to physically manipulate the surface into some form or orientation that is sensed and directly represented in a computer model. Also, digital clay will allow a user to change the computer model by manipulating the inputs that are directly represented in the physical model. The digital clay device being researched involves a computer-interfaced array of vertically displacing actuators that is bound by a formable surface. The surface is composed of an array of unit cells that are constructed of compliant spherical joints and leaf-spring joints. The focus of this research was to create an accurate mathematical model that mimics the movement of the surface. This main focus was divided into three main goals. The first goal was to further develop unit cell designs that allow the surface to stretch in the horizontal direction. The second goal was to further develop formulations and algorithms to create a mathematical model that simulates how a stretchable planar surface reacts when points on the surface are actuated in a direction perpendicular to the planar surface. The third goal was to validate the mathematical model through different procedures that compared unit cell displacements of the mathematical model to that of a fabricated surface.