Bistable collapsible compliant mechanisms and shape-changing structures that comprise them

A bistable collapsible compliant mechanism unitarily formed from a single piece of material, the mechanism comprising:

• a first sub-mechanism comprising opposed first and second quaternary links, a first binary link that connects to a top inner corner of the first quaternary link and to an top inner corner of the second quaternary link, a second binary link that connects to a bottom inner corner of the first quaternary link and to a bottom inner corner of the second quaternary link, and third and fourth binary links, the third binary link being connected to a bottom outer corner of the second quaternary link and a bottom end of the fourth binary link and the fourth binary link being connected to a bottom outer corner of the first quaternary link, each link being connected to the other links in the first sub-mechanism with a living hinge;
• a second sub-mechanism connected to the first sub-mechanism, the second sub-mechanism comprising opposed first and second quaternary links, a first binary link that connects to a top inner corner of the first quaternary link and to an top inner corner of the second quaternary link, and a second binary link that connects to a bottom inner corner of the first quaternary link and to a bottom inner corner of the second quaternary link, each link being connected to the other links in second the sub-mechanism with a living hinge, the second sub-mechanism being smaller than the first sub-mechanism;
• a third sub-mechanism connected to the second sub-mechanism, the third sub-mechanism comprising opposed first and second quaternary links, a first binary link that connects to a top inner corner of the first quaternary link and to an top inner corner of the second quaternary link, a second binary link that connects to a bottom inner corner of the first quaternary link and to a bottom inner corner of the second quaternary link, and third and fourth binary links, the third binary link being connected to a top outer corner of the first quaternary link and a top end of the fourth binary link, and the fourth binary link being connected to a top outer corner of the second quaternary link, each link being connected to the other links in the third sub-mechanism with a living hinge, the third sub-mechanism being smaller than the second sub-mechanism;
• and
• a bistability link that alternatively maintains the bistable collapsible compliant mechanism in a stable extended orientation in which the bistable collapsible compliant mechanism has a trapezoidal shape and in a stable contracted orientation in which the bistable collapsible compliant mechanism has a polygonal spiral shape.

A shape-changing structure comprising:

• multiple bistable collapsible compliant mechanisms, each mechanism comprising:
• a first sub-mechanism comprising opposed first and second quaternary links and multiple binary links, each link being connected to at least two other links in the first sub-mechanism, and
• a second sub-mechanism connected to the first sub-mechanism, the second sub-mechanism also comprising opposed first and second quaternary links and multiple binary links, each link being connected to at least two other links in the second sub-mechanism,
• wherein the bistable collapsible compliant mechanism can be alternatively be placed in a stable extended orientation in which the bistable collapsible compliant mechanism has a trapezoidal shape and in a stable contracted orientation in which the bistable collapsible compliant mechanism has a polygonal spiral shape;
• wherein the shape-changing structure can be alternatively placed in a stable extended orientation in which the structure has a frustoconical shape and in a stable contracted orientation in which the structure has a planar shape.