The convergence surface method for the design of deployable updates scissor structures

In this paper, the operability of the most recent method to design bistable and non-bistable deployable scissors structures (the method of the convergence surface) is extended and this operability will be divided into two types of formulas: The exact formula and the approximate formulas. The exact formula involves the obtaining of the convergence surface using its own equations and this paper will prove that this surface is a triaxial two-leaf hyperboloid (for translational units) and a non-standard surface (for polar units). On the other hand, the approximate formulas are designed due to the need to obtain the convergence surface when the exact formula cannot be used. Finally, this research will demonstrate the potential of these approximate strategies to compete against the exact formulas and to boost an improvement in the mathematical results in terms of precision in the scissor design and speed in the calculation process.