A method is presented utilizing networks of lamina emergent joints, known as lamina emergent arrays, to accommodate large-curvature developable structures suited to deployable applications. By exploiting the ruling lines in developable surfaces, this method enables developable structures and mechanisms that can be manufactured with two-dimensional geometry and yet have a greater range of elastic motion than is possible with a solid sheet of material. Aligning the joints to the ruling lines also biases the structure to a specific deployment path. A mathematical model is developed to describe the resulting stiffness of the structure employing the lamina emergent arrays and equations are derived to facilitate stress analysis of the structure. Finite element results show the sensitivity of alignment of the elements in the array to the stress present in the developed structure. A specific technique for creating an array pattern for conical developable surfaces is described. Examples of developable structures and mechanisms, including curved-fold origami models transitioned to thick materials and two origami-inspired mechanisms, are examined.
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June 2016
Research-Article
Facilitating Deployable Mechanisms and Structures Via Developable Lamina Emergent Arrays
Robert J. Lang,
Robert J. Lang
Lang Origami,
Alamo, CA 94507
Alamo, CA 94507
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Nathan A. Pehrson,
Nathan A. Pehrson
Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
Brigham Young University,
Provo, UT 84602
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Spencer P. Magleby,
Spencer P. Magleby
Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
Brigham Young University,
Provo, UT 84602
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Larry L. Howell
Larry L. Howell
Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
Brigham Young University,
Provo, UT 84602
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Todd G. Nelson
Robert J. Lang
Lang Origami,
Alamo, CA 94507
Alamo, CA 94507
Nathan A. Pehrson
Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
Brigham Young University,
Provo, UT 84602
Spencer P. Magleby
Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
Brigham Young University,
Provo, UT 84602
Larry L. Howell
Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
Brigham Young University,
Provo, UT 84602
1Corresponding author.
Manuscript received June 30, 2015; final manuscript received October 14, 2015; published online March 7, 2016. Assoc. Editor: Mary Frecker.
J. Mechanisms Robotics. Jun 2016, 8(3): 031006 (10 pages)
Published Online: March 7, 2016
Article history
Received:
June 30, 2015
Revised:
October 14, 2015
Citation
Nelson, T. G., Lang, R. J., Pehrson, N. A., Magleby, S. P., and Howell, L. L. (March 7, 2016). "Facilitating Deployable Mechanisms and Structures Via Developable Lamina Emergent Arrays." ASME. J. Mechanisms Robotics. June 2016; 8(3): 031006. https://doi.org/10.1115/1.4031901
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