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Developable mechanism

Developable mechanisms are a special class of mechanisms that can be placed on developable surfaces.

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Examples

Some well-known examples of developable mechanisms include the door on the Apollo Command Module and the cargo doors on the Space Shuttle.  Both of these examples are single-hinge-line mechanisms. Note how in each case the joint axes are in line with the ruling lines of the surface. Images are shown on the right.

Origami uses developable surfaces because the paper can be assumed to not stretch.3 Action origami utilizes the movement of the origami.45

Ortho-planar mechanisms are a subset of developable mechanisms where the developable surface is a plane and the links emerge out of the plane.6 Lamina Emergent Mechanisms are ortho-planar mechanisms (and hence also developable mechanisms) where the joints are compliant mechanisms.7 The same joints used to create lamina emergent mechanisms can be used to approximate developable surfaces89

Advantages

Developable surfaces are easy to manufacture10 and are found in many applications. Developable mechanism can be embedded within these surfaces.11

Developable mechanisms are deployable.12

Developable mechanism stow compactly during one position of the mechanism's motion.13

Mathematical Modeling

The motion of developable mechanisms can be modeled using traditional kinematics formulas. In rigid-body linkages, the shape of the rigid links does not change the motion.14

References

  1. "Developable Mechanisms | About Developable Mechanisms". compliantmechanisms. Retrieved 2019-02-13. https://www.compliantmechanisms.byu.edu/about-developable-mechanisms ↩

  2. Nelson, Todd G.; Zimmerman, Trent K.; Magleby, Spencer P.; Lang, Robert J.; Howell, Larry L. (2019). "Developable mechanisms on developable surfaces". Science Robotics. 4 (27): eaau5171. doi:10.1126/scirobotics.aau5171. PMID 33137737. https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=3977&context=facpub ↩

  3. Callens, Sebastien J.P.; Zadpoor, Amir A. (2018). "From flat sheets to curved geometries: Origami and kirigami approaches". Materials Today. 21 (3): 241–264. doi:10.1016/j.mattod.2017.10.004. https://doi.org/10.1016%2Fj.mattod.2017.10.004 ↩

  4. Bowen, Landen (2013-07-02). A Study of Action Origami as Systems of Spherical Mechanisms (MS thesis). Brigham Young University. hdl:1877/etd6391. https://scholarsarchive.byu.edu/etd/3685 ↩

  5. Callens, Sebastien J.P.; Zadpoor, Amir A. (2018). "From flat sheets to curved geometries: Origami and kirigami approaches". Materials Today. 21 (3): 241–264. doi:10.1016/j.mattod.2017.10.004. https://doi.org/10.1016%2Fj.mattod.2017.10.004 ↩

  6. Parise, John J. (1999). Ortho-planar mechanisms (MS thesis). Brigham Young University. Retrieved 2019-02-13. https://www.researchgate.net/publication/34191699 ↩

  7. Jacobsen, Joseph (2008-02-22). Fundamental Components for Lamina Emergent Mechanisms (MS thesis). Brigham Young University. hdl:1877/etd2277. https://scholarsarchive.byu.edu/etd/1330 ↩

  8. Nelson, Todd (2018-06-01). Art to Engineering: Curved Folding and Developable Surfaces in Mechanism and Deployable Structure Design (PhD dissertation). Brigham Young University. hdl:1877/etd10068. https://scholarsarchive.byu.edu/etd/6865 ↩

  9. Nelson, Todd G.; Lang, Robert J.; Pehrson, Nathan A.; Magleby, Spencer P.; Howell, Larry L. (2016). "Facilitating Deployable Mechanisms and Structures Via Developable Lamina Emergent Arrays". Journal of Mechanisms and Robotics. 8 (3): 031006. doi:10.1115/1.4031901. /wiki/Doi_(identifier) ↩

  10. Chalfant, Julie S.; Maekawa, Takashi (September 1998). "Design for Manufacturing Using B-Spline Developable Surfaces". Journal of Ship Research. 42 (3): 207–215. doi:10.5957/jsr.1998.42.3.207. /wiki/Doi_(identifier) ↩

  11. Nelson, Todd G.; Zimmerman, Trent K.; Magleby, Spencer P.; Lang, Robert J.; Howell, Larry L. (2019). "Developable mechanisms on developable surfaces". Science Robotics. 4 (27): eaau5171. doi:10.1126/scirobotics.aau5171. PMID 33137737. https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=3977&context=facpub ↩

  12. Nelson, Todd (2018-06-01). Art to Engineering: Curved Folding and Developable Surfaces in Mechanism and Deployable Structure Design (PhD dissertation). Brigham Young University. hdl:1877/etd10068. https://scholarsarchive.byu.edu/etd/6865 ↩

  13. "Developable Mechanisms | About Developable Mechanisms". compliantmechanisms. Retrieved 2019-02-13. https://www.compliantmechanisms.byu.edu/about-developable-mechanisms ↩

  14. L., Norton, Robert (2007). Design of Machinery. McGraw-Hill College. ISBN 9780073290980. OCLC 150367304.{{cite book}}: CS1 maint: multiple names: authors list (link) 9780073290980 ↩