A polygon-scaling mechanism is a single DOF (degree-of-freedom) mechanism for scaling a polygon. This paper presents a tetragon-elements based synthesis method of polygon-scaling mechanisms. According to movable conditions of radial scaling elements, four basic tetragon elements (rhombus element, parallelogram element, kite element and general tetragon element) are proposed. For a given polygon, these four types of elements can be selected based on the characteristics of target polygons to construct polygon-scaling mechanisms in a straightforward manner. Using this synthesis method, some planar 1-DOF scaling mechanisms are obtained with the characteristics of retracting and deploying. Their 3D models are also presented to proof the validity of the proposed method. Finally, a table of tetragon elements with the characteristics of their associated polygon-scaling mechanisms is summarized using which polygon-scaling mechanisms can be easily constructed.

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