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1. Deployable Convex Generalized Cylindrical Surfaces Using Torsional Joints

   https://doi.org/10.1115/1.4049951  

   Nelson, Todd G.; Baldelomar Pinto, Luis M.; Bruton, Jared T.; Deng, Zhicheng; Nelson, Curtis G.; Howell, Larry L. (June 2021, Journal of Mechanisms and Robotics)

   null (Ed.)

   Abstract The ability to deploy a planar surface to a desired convex profile with a simple actuation can enhance foldable or morphing airfoils, deployable antennae and reflectors, and other applications where a specific profile geometry is desired from a planar sheet. A model using a system of rigid links joined by torsional springs of tailorable stiffness is employed to create an approximate curved surface when two opposing tip loads are applied. A system of equations describing the shape of the surface during deployment is developed. The physical implementation of the model uses compliant torsion bars as the torsion springs. A multidimensional optimization algorithm is presented to place joints to minimize the error from the rigid-link approximation and account for additional manufacturing and stress considerations in the torsion bars. A proof is presented to show that equal torsion spring spacing along the horizontal axis of deployed parabolic profiles will result in minimizing the area between the model’s rigid-link approximation and smooth curve. The model is demonstrated through the physical construction of a deployable airfoil surface and a metallic deployable parabolic reflector. 

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2. Rapid Design of Fully Soft Deployable Structures Via Kirigami Cuts and Active Learning

   https://doi.org/10.1002/admt.202301305  

   Ma, Leixin; Mungekar, Mrunmayi; Roychowdhury, Vwani; Jawed, MK (January 2024, Advanced Materials Technologies)

   Abstract Soft deployable structures – unlike conventional piecewise rigid deployables based on hinges and springs – can assume intricate 3‐D shapes, thereby enabling transformative soft robotic and manufacturing technologies. Their virtually infinite degrees of freedom allow precise control over the final shape. The same enabling high dimensionality, however, poses a challenge for solving the inverse problem: fabrication of desired 3D structures requires manufacturing technologies with extensive local actuation and control, and a trial‐and‐error search over a large design space. Both of these shortcomings are addressed by first developing a simplified planar fabrication approach that combines two ingredients: strain mismatch between two layers of a composite shell and kirigami cuts that relieves localized stress. In principle, it is possible to generate targeted 3‐D shapes by designing the appropriate kirigami cuts and the amount of prestretch (without any local control). Second, a data‐driven physics‐guided framework is formulated that reduces the dimensionality of the inverse design problem using autoencoders and efficiently searches through the “latent” parameter space in an active learning approach. The rapid design procedure is demonstrated via a range of target shapes, such as peanuts, pringles, flowers, and pyramids. Experiments and our numerical predictions are found to be in good agreement. 

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3. Kirigami-Based Deployable Transcrease Hard Stop Models Usable in Origami Patterns

   https://doi.org/10.1115/DETC2019-98056  

   Andrews, David W.; Avila, Alex; Butler, Jared; Magleby, Spencer P.; Howell, Larry L. (January 2019, Proceedings of the 2019 International Design Engineering Conference)

   Abstract Stopping origami in arbitrary fold states can present a challenge for origami-based design. In this paper two categories of kirigami-based models are presented for stopping the fold motion of individual creases using deployable hard stops. These models are transcrease (across a crease) and deploy from a flat sheet. The first category is planar and has behavior similar to a four-bar linkage. The second category is spherical and behaves like a degree-4 origami vertex. These models are based on the zero-thickness assumption of paper and can be applied to origami patterns made from thin materials, limiting the motion of the base origami pattern through self-interference within the original facets. Model parameters are based on a desired fold or dihedral angle, as well as facet dimensions. Examples show model benefits and limitations. 

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4. Designing Developable Mechanisms From Flat Patterns

   https://doi.org/10.1115/DETC2020-22445  

   Hyatt, Lance P.; Lytle, Amanda; Magleby, Spencer P.; Howell, Larry L. (January 2020, Proceedings of the 2020 International Design Engineering Conferences)

   null (Ed.)

   Abstract This paper presents tools and methods to design cylindrical and conical developable mechanisms from flat, planar patterns. Equations are presented that relate the link lengths and link angles of planar and spherical mechanisms to the dimensions in a flat configuration. These flat patterns can then be formed into curved, developable mechanisms. Guidelines are established to determine if a mechanism described by a flat pattern can exhibit intramobile or extramobile behavior. A developable mechanism can only potentially exhibit intramobile or extramobile behavior if none of the links extend beyond half of the flat pattern. The behavior of a mechanism can change depending on the location of the cut of the flat pattern. Different joint designs are discussed including lamina emergent torsional (LET) joints. Physical examples are presented. 

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5. An Exceptional Spherical Five-bar Used as a Deployable Control Surface

   https://doi.org/10.1115/1.4070181  

   O’Connor, Sam; Plecnik, Mark; Wampler, Charles (February 2026, Journal of Mechanisms and Robotics)

   A spherical five-bar linkage generally has two degrees-of-freedom. However, some configurations arise where the mechanism is able to move with an additional degree-of-freedom, even with both input angles fixed. These configurations are termed exceptional. They appear in a configuration surface as embedded straight lines in the direction of its outputs. Without prior knowledge, these lines can be discovered by structured slicing of the configuration surface using the tools of polynomial homotopy continuation. This search procedure is conducted for spherical five-bars of equal-link-length. Cases for adjacent and nonadjacent input angles are analyzed. An equal-link-length spherical five-bar with 90 deg links is used for the design of a deployable control surface for an aircraft. Taking advantage of the exceptional sets in the mechanism, one motor is able to lock, deploy, and articulate the control surface. 

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