Applications of deployable mechanisms can be found in aeronautic and civil engineering, often in the creation of unfolding large-scale structures with curved surfaces. This paper proposes novel mechanical networks, which are used to approximate three-dimensional surfaces, such as cuboids, ellipsoids, or hyperboloids. Each such deployable structure is assembled from unit Sarrus and scissor linkages of different sizes, has several decoupled degrees of freedom, and can take any shape within a different family of parameterized surfaces. Each degree of freedom controls a separate parameter in the equation describing the physical boundary of the linkage network. The size and placement of the unit linkages and their elements are analyzed and selected for obtaining the expected families of surfaces. CAD models and kinematic simulations demonstrate the abilities of the mechanisms to perform dynamically the desired approximation.

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