Kinematic and dynamic analysis of a spatial one-DOF foldable tensegrity mechanism

This paper presents a mechanical analysis of a spatial 1-DOF tensegrity mechanism created by connecting three planar tensegrity mechanisms to form a triangular prism. The subsequent investigation produced kinematic and dynamic models that allow the workspace-boundary singularities and minimum energy configuration to be determined. Singularities were found to occur when the mechanism is folded in the vertical X, Y plane or in the horizontal X, Z plane. The minimum energy configuration, formed by the angle between the horizontal plane and the actuated strut, was found to be θ= π/4. However, when the system was linearized to determine the analytic solution for the dynamics, the minimum energy configuration become θ = 1 due to the inherent error produced by the system linearization. The dynamic response of the mechanism to an initial small displacement was determined for each case of critically damped, overdamped, and underdamped systems