Digital Clay represents a new type of 3-D human-computer interface device that enables tactile and haptic interactions. The Digital Clay kinematics structure is computer controlled and can be commanded to acquire a wide variety of desired shapes (shape display), or be deformed by the user in a manner similar to that of real clay (shape editing). The design of the structure went through various modifications where we finally settled on a crust matrix of spherical joint unit cells. After designing the kinematics structure, the next step is predicting the deformation of the crust matrix based upon a handful of inputs. One possible solution for predicting the shape outcome is considering minimizing the potential energy of the system. In this thesis two methods will be introduced. The first method will be an abstract model of the crust where the energy is calculated from a simplified model with one type of angular springs. The second method is the actual manufacturable crust model with two types of angular springs. From the implementation of these two methods, the output will be center-points of the unit cells. From the center-points, one can also calculate the joint angles within each unit cell.

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. Furthermore, 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 translational joints. As part of this thesis, a series of unit cells were developed and planar surfaces were fabricated utilizing the additive manufacturing process of stereolithography. The process of computing the resultant shape of a manipulated surface was modeled mathematically through energy minimization algorithms that utilized least squares analysis to compute the positions of the unit cells of the surface. Simulation results were computed and analyzed against the movement of a fabricated planar surface. Once the mathematical models were validated against the manufactured surface, a method for attaching the surface to an array of actuators was recommended.