Two problems are addressed in this paper. First, the mathematical model to perform the static analysis of an antiprism tensegrity structure subjected to a wide variety of external loads is presented. The virtual work approach is used to deduce the equilibrium equations and a method based on Newton’s Third Law is used to verify the numerical results. Two numerical examples are provided to demonstrate the use of the mathematical model, as well as the verification method. The second problem deals with the development of a mathematical model to perform the static analysis of a prestressed antiprism tensegrity structure subjected to an arbitrary length reduction of its connecting ties. Again, a virtual work approach is used to deduce the equilibrium equations and the numerical results are verified using a Newtonian approach. One example is provided to illustrate the mathematical model.

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Tensegrity systems have been used in several disciplines such as architecture, biology, aerospace, mechanics, and robotics during the last 50 years. However, just a few references in literature have stated the possibility of using such systems in ocean or energy-related applications. This work addresses the kinematic and dynamic analyses of a planar tensegrity mechanism for ocean wave energy harvesting. Ocean wave mechanics and the most important concepts related to fluid–structure interaction are presented. Then, a planar 3 degrees of freedom (3-dof) tensegrity mechanism, based on a morphology defined by Kenneth Snelson in 1960 which is known as “X-frame,” is proposed as connecting linkage to transmit wave-generated forces. A geometric approach is used to solve the forward and reverse displacement problems. The theory of screws is used to perform the forward and reverse velocity analyses of the device. The Lagrangian approach is used to deduce the equations of motion considering the interaction between the mechanism and ocean waves. The tensegrity-based mechanism is analyzed using a linear model of ocean waves and its energy harvesting capabilities are compared to a purely heaving device. Results show that the proposed tensegrity configuration allows to harvest 10% more energy than the traditional heaving mechanism used in several wave energy harvesting applications. Therefore, tensegrity systems could play an important role in the expansion of clean energy technologies that help the world's sustainable development.

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In this paper the kinematic and the dynamic analysis, and a nonlinear control strategy for a planar three-degree-of-freedom tensegrity robot manipulator are addressed. A geometric method is used to obtain the set of equations that describe the position analysis. Initially, solutions to the problems concerning forward and reverse kinematic analysis are presented; then, the forward velocity coefficients matrix is obtained analytically. The Lagrangian approach is used to deduce the dynamic equation of motion and its main properties are described using the nonlinear control system theory. Finally, a feedback-linearization-based nonlinear control scheme is applied to the mechanism to follow a prescribed path in the Cartesian coordinate system. The obtained results show that lightweight mechanisms which incorporate tensegrity systems could be used in a positioning problem.