This paper describes a novel type synthesis methodology for creating planar shape-morphing mechanism chains of any length with specified mobility (degree-of-freedom). It is expected that this will be of use in designing complex shape-morphing objects. The methodology is based on using graph theory in conjunction with symmetry theory for borders (Frieze groups). It is shown that the methodology can produce chains of a variety of lengths and mobility, and these chains have symmetric topologies and that symmetric kinematics may be possible for some of the chains, which simplifies their analysis. Techniques for decreasing and increasing the mobility of the chains are discussed. Finally, a gallery of shape morphing chains is given to provide concrete illustrations of the diversity of designs generated using this methodology.

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