Design, construction, and control of curves and surfaces via deployable mechanisms

There has been an increasing interest in design and construction of deployable mechanisms (DMs) with multiple degrees of freedom (DOFs). This paper summarizes a family of deployable mechanisms that approximates a series of curves and surfaces using the polygonal approximation technique. These mechanisms are obtained by linking the two- and three-dimensional deployable units, which are constitutive of Sarrus and scissor linkages. Multiple unit mechanisms with varying sizes are assembled and alter their shape within a different family of parameterized curves and surfaces. A systematic methodology for polygonal approximation method is presented. Quadratic, semi-cubic, cubic, quartic and sextic curve boundaries, and quadric surfaces are approximated and controlled. Computer-aided design (CAD) models and kinematic simulations elucidate the mechanism's ability to approximate a set of curves and surfaces.