Bistable collapsible compliant mechanisms and shape-changing structures that comprise them
A bistable collapsible compliant mechanism including 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 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 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.
1. A bistable collapsible compliant 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 with hinges; 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 second the sub-mechanism with hinges;
wherein the bistable collapsible compliant mechanism is unitarily formed from a single piece of material and the hinges comprise flexible living hinges;
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.
2. The bistable collapsible compliant mechanism of claim 1 , wherein the quaternary links of the first and second sub-mechanisms each comprise a quadrilateral link having four non-parallel sides and four corners.
3. The bistable collapsible compliant mechanism of claim 2 , wherein the first and second sub-mechanisms each comprise 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.
4. The bistable collapsible compliant mechanism of claim 3 , wherein the first and second sub-mechanisms each comprise 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.
5. The bistable collapsible compliant mechanism of claim 4 , wherein the first sub-mechanism further comprises 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.
6. The bistable collapsible compliant mechanism of claim 5 , further comprising a bistability link that alternatively maintains the bistable collapsible compliant mechanism in the extended or retracted orientations.
7. The bistable collapsible compliant mechanism of claim 6 , wherein the bistability link is connected to the third binary link and the first quaternary link.
8. The bistable collapsible compliant mechanism of claim 7 , wherein the bistability link connects to the third binary link at a point between its ends and connects to the first quaternary link between its bottom outer corner and its bottom inner corner.
9. The bistable collapsible compliant mechanism of claim 1 , further comprising a third sub-mechanism connected to the second sub-mechanism, the third 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 third sub-mechanism.
10. The bistable collapsible compliant mechanism of claim 9 , wherein the second sub-mechanism is smaller than the first sub-mechanism and the third sub-mechanism is smaller than the second sub-mechanism.
11. 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.
12. The bistable collapsible compliant mechanism of claim 11 , wherein the bistability link connects to the third binary link at a point between its ends and connects to the first quaternary link between its bottom outer corner and its bottom inner corner.
13. 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.
14. The structure of claim 13 , wherein each bistable collapsible compliant mechanism further comprises a third sub-mechanism connected to the second sub-mechanism, the third 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 third sub-mechanism.
15. The structure of claim 13 , wherein each bistable collapsible compliant mechanism is unitarily formed from a single piece of material and wherein the links of each bistable collapsible compliant mechanism connect to each other with flexible living hinges.
16. The structure of claim 13 , wherein each bistable collapsible compliant mechanism comprises a bistability link that alternatively maintains the bistable collapsible compliant mechanism in the extended or retracted orientations.
17. The structure of claim 13 , further comprising a base to which each bistable collapsible compliant mechanism is attached.
18. The structure of claim 17 , further comprising a top to which each bistable collapsible compliant mechanism is attached.