A novel three-dimensional robotic surface is devised and implemented using triangular modules. Each module is connected by a passive sixbar mechanism that mimics the constraints of a spherical joint at each triangle intersection. The finite element method (FEM) is applied to the static loading of this device using linear three dimensional (6 degrees of freedom) beam elements to calculate the cartesian displacement and force and the angular displacement and torque at each joint. In this way, the traditional methods of finding joint forces and torques are completely bypassed. An effiecient algorithm is developed to linearly combine local stiffness matrices into a full structural stiffness matrix for the easy application of loads. This is then decomposed back into the local matrices to easily obtain joint variables used in the design and open-loop control of the surface.

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