Design of Single Degree-of-Freedom Triangular Resch Patterns with Thick-panel Origami

Yang, Fufu; Zhang, Miao; Zhang, You; Yu, Ying; Yan, Changjie; Paulino, Gláucio H.

doi:10.1016/j.mechmachtheory.2021.104650

Cited by 16 publications

(6 citation statements)

References 18 publications

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“…As an example of how the equations we have seen thus far can be applied to a larger crease pattern, we consider the triangle twist tessellation shown in figure 11. This was designed by Ron Resch in the 1960s [20,21] and has been studied extensively for rigid folding and metamaterial purposes [22][23][24].…”

Section: Example 45 (Resch Triangle Twist Tessellation)mentioning

confidence: 99%

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Rigid folding equations of degree-6 origami vertices

2022

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Rigid origami, with applications ranging from nano-robots to unfolding solar sails in space, describes when a material is folded along straight crease line segments while keeping the regions between the creases planar. Prior work has found explicit equations for the folding angles of a flat-foldable degree-4 origami vertex and some cases of degree-6 vertices. We extend this work to generalized symmetries of the degree-6 vertex where all sector angles equal 60 ∘ . We enumerate the different viable rigid folding modes of these degree-6 crease patterns and then use second-order Taylor expansions and prior rigid folding techniques to find algebraic folding angle relationships between the creases. This allows us to explicitly compute the configuration space of these degree-6 vertices, and in the process we uncover new explanations for the effectiveness of Weierstrass substitutions in modelling rigid origami. These results expand the toolbox of rigid origami mechanisms that engineers and materials scientists may use in origami-inspired designs.

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Section: Example 45 (Resch Triangle Twist Tessellation)mentioning

confidence: 99%

“…As a rigid folding, the Resch pattern has many degrees of freedom [24]. But if we insist on folding it with 120∘ rotational symmetry about the centre vertex r1, then it becomes 1-d.f.…”

Section: Equations For Symmetric Modesmentioning

confidence: 99%

Rigid folding equations of degree-6 origami vertices

2022

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“…Large-scale DMs are usually constructed by assembling similar modules with specific connecting approaches. Typical modules include scissor mechanisms (Bai et al, 2013;Sun et al, 2014) and singleloop mechanisms such as Bennett mechanisms (Chen and You, 2008;Song et al, 2017), Mycard mechanisms (Liu and Chen, 2009), Bricard mechanisms (Lee, 1996), Sarrus-like mechanisms (Chen et al, 2013;Lu et al, 2016), and also include origami patterns such as the Miura-ori pattern (Gattas et al, 2013), the waterbomb pattern (Lee et al, 2021), the Resch pattern (Yang et al, 2022), and the cuboid-twist pattern (Hull, 2014). These modules are usually connected by sharing links or kinematic pairs (Soykasap et al, 2004;Huang et al, 2021a;Zhao et al, 2009;Tian et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

“…Kiper (2009) proposed several new linkages based on the Fulleroid, which can be applied to the construction of deployable polyhedral mechanisms. Yang and Chen (2018) proposed a convertible DM by appropriately configuring the movable joint, which can realize the 1-DOF transformation between a tetrahedron and a truncated tetrahedron. In addition, Chen et al (2018) proposed a 1-DOF shape transformation between two paired polyhedrons by introducing 6R spatial links.…”

Section: Introductionmentioning

confidence: 99%

Design of an origami-based cylindrical deployable mechanism

et al. 2022

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Abstract. In this paper, an innovative cylindrical deployable mechanism (DM) based on rigid origami is presented, which is used to design a parabolic cylindrical deployable antenna. The mechanism can be deployed from the cuboid folded configuration to the cylindrical unfolded configuration with only one actuator. First, an innovative deployable string is proposed based on different types of four-vertices origami unit cells and kirigami techniques. By considering the units as 6R single-loop mechanisms, the kinematics of the origami unit cells are analyzed. Through the connection of identical deployable strings, the cylindrical DM is constructed, and its mobility is analyzed utilizing the screw theory. Then the proposed DM is used to design a parabolic cylindrical deployable antenna. A number of pillars are installed on the panels of the DM, and their lengths are determined to fit the required parabolic cylindrical surface. To verify the feasibility of the design, a scaled prototype of the deployable antenna is constructed.

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“…This chapter will introduce some origami tessellations with more complexity and provide qualitative analyses of multiple boundary cases in order to further display the applicability of this boundary analysis approach. There are an infinite number of novel origami patterns that can be created by this approach, but this discussion will be rather brief and primarily limited to the Resch pattern [38] and its derivative tessellations. For simplicity, these patterns will use symmetrical side lengths and angles.…”

Section: Analysis Of Origami Tessellation Unit-cell Combinationsmentioning

confidence: 99%

Design and analysis of origami-inspired structures

Muench¹

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This work focuses on creating novel structures by combining elements of common origami patterns. Multiple different types of physical and computer models are implemented to represent and analyze the structures. These structures have a broad range of potential applications, such as architecture, soft robotics, and aerospace. A combined Miura and EggBox pattern is presented. The combined unit cell for the sheet is parameterized, the Poisson ratio is calculated, and the sheets are 3D modeled using Solid Edge. Tubes constructed from the combined pattern are computer modeled and a static analysis is performed using the MERLIN2 software package in GNU Octave. These tubes can then be woven into cellular structures, some examples of which are 3D modeled and discussed. Also presented are many different combinations of the Miura and Resch unit cells. Crease patterns were drawn in Inkscape and computer folded using Origami Simulator. Some of these tessellations were found in literature but others were not. In addition to traditional origami paper folding, other fabrication methods for folded structures are presented, such as selective laser sintering (SLS) 3D printing and laser cutting of plastic sheets. Some software tools were developed and implemented to aid design.

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Design of Single Degree-of-Freedom Triangular Resch Patterns with Thick-panel Origami

Cited by 16 publications

References 18 publications

Rigid folding equations of degree-6 origami vertices

Rigid folding equations of degree-6 origami vertices

Design of an origami-based cylindrical deployable mechanism

Design and analysis of origami-inspired structures

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