Lamina Emergent Torsional Research Articles

Laser Forming of Compliant Mechanisms

AbstractSmall-scale flexible (or compliant) mechanisms are valuable in replacing rigid components while retaining comparable motion and behavior. However, fabricating such mechanisms on this scale (from 0.01 to 10 cm) proves difficult, especially with thin sheet metals. The manufacturing method of laser forming, which uses a laser to cut and bend metal into desired shapes, could facilitate this fabrication. However, specific methods for designing mechanisms formed by lasers need to be developed. This work presents laser forming as a means for creating compliant mechanisms on this scale with thin sheet metal. The unique challenges for designing mechanisms to be laser formed are explored, and new adaptations of existing designs are fabricated and discussed. The design of basic “building-block” features is developed for several mechanisms: a parallel-guided mechanism, a cross-axis flexural pivot, a lamina emergent torsional (LET) joint array, a split-tube flexure, and a bi-stable switch. These mechanisms are shown to perform repeatable behavior and motion comparable to existing nonlaser-formed versions. The further possibilities for fabricating compliant mechanisms with laser forming are explored, as advanced applications can benefit from using lasers to create compliant mechanisms from thin sheet metal.

Design of mmWave Foldable Vertically Stacked Yagi–Uda Antenna Inspired by Origami and Kirigami Theories

This letter presents a foldable vertically stacked Yagi–Uda antenna at millimeter-wave (mmWave) frequency band. The proposed antenna is built on a FR4 substrate. The antenna consists of a balun, feed dipole element, stacked folded dipole, and inside lamina emergent torsional (LET) joint array. The LET joint array is introduced to reduce and distribute the mechanical stress generated in folding the rigid FR4 substrate. In the planar mode, the antenna results in a measured gain value of 4.9 dBi at the design frequency 24 GHz with a cross-polarization suppression level of less than 12 dB. In the folded mode, the antenna has a measured gain value of 3.9 dB at the target frequency 24 GHz with a cross-polarization suppression level of less than 10 dB. Both operation modes of the proposed antenna cover the broad bandwidth from 23 to 28 GHz (about 20 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> ).

Design and Performance Analysis of Lamina Emergent Torsional Joints Based on Double-Laminated Material Structure

Flexibility and accuracy are two key aspects of the performances of compliant joints. In order to obtain high flexibility while maintain high accuracy, this paper proposes a design method to improve the tensile stiffness of Lamina Emergent Torsional (LET) joint by utilizing double-laminated material structure. The joint is made of a LET joint and a layer of flexible H18 aluminum foil fixing on it (called double-laminated LET, DL-LET). The kinetostatic model for the joint is given, and the equations needed to calculate the equivalent spring constant are derived. The model is verified using finite element analysis (FEA). The results obtained through two different ways coincide with each other very well. The results show that DL-LET and LET joints have similar bending stiffness, while the tensile stiffness of the DL-LET joint is much larger than that of the LET joint. The results are validated by tensile tests. Finally, to further demonstrate the extension of this idea, a DL-Triple-LET joint is presented and compared to the Triple-LET joint.

종이접기와 키리가미 이론에 기반한 3차원 T-자형 다이폴 안테나 설계

In this study, the design of a 3D foldable T-shaped dipole antenna inspired by origami and kirigami theory is presented. The origami- and kirigami-inspired techniques map 2D to 3D space. Moreover, the lamina emergent torsional (LET) joint is designed to fold the planar structure. The proposed antenna, including the LET joint, is printed on a planar 0.5 mm thick FR4 substrate. The proposed antenna is fed by a capacitively coupled microstrip line to achieve a 20 % fractional bandwidth (2.7~3.3 GHz), with a measured antenna gain value of 6.5 dBi.

Hinges and Curved Lamina Emergent Torsional Joints in Cylindrical Developable Mechanisms

Abstract Cylindrical developable mechanisms are devices that conform to and emerge from a cylindrical surface. These mechanisms can be formed or cut from the cylinder wall itself. This paper presents a study on adapting traditional hinge options to achieve revolute motion in these mechanisms. A brief overview of options is given, including classical pin hinges, small-length flexural pivots, initially curved beams, and an adaptation of the membrane thickness-accommodation technique. Curved lamina emergent torsional (LET) joints are then evaluated in detail, and a thin-walled modeling assumption is checked analytically and empirically. A small-scale cylindrical developable mechanism is then evaluated with Nitinol curved LET joints.

Design and analysis of Lamina Emergent Joint (LEJ) based on origami technology and mortise-tenon structure

Lamina Emergent Mechanisms (LEMs) are an important part of compliant mechanisms, and origami technology can fold simple two-dimensional planes into complex three-dimensional geometries. This paper introduces a design method to achieve large deformation of Lamina Emergent torsional (LET) joints in multiple directions through origami technology. A Foldable mortise-tenon structure (FMTS) is proposed to make permanent creases in origami-based mechanisms. The influence of structural parameters of the FMTS on its maximum deformation and maximum stress under tension is studied. Based on the proposed method and structure, a two degree of freedom Lamina Emergent Joint (2DOF-LEJ) is designed. The structural design, equivalent stiffness analysis, and finite element analysis (FEA) of the 2DOF-LEJ are carried out. Experimental tests verify the effectiveness of the proposed method and FMTS on the prototype. Finally, some applications of the proposed method and FMTS in origami-based mechanisms are discussed.

A Foldable and Reconfigurable Monolithic Reflectarray for Space Applications

An origami-based foldable and reconfigurable Reflectarray Antenna (RA) with multiple apertures is proposed for CubeSat applications. The proposed configuration consists of a central RA embedded in folding panels using Lamina Emergent Torsional (LET) joints based on compliant mechanisms. Depending on the folding direction of these panels (forward or backward), a new RA aperture is formed. The proposed RA along with its folding panels and hinges is fabricated using only a single PCB. A prototype of such an RA with two foldable panels is fabricated and measured. This RA operates in the Ku-band at 16 GHz and provides two pencil beams pointing at ( $\theta = 30^{\circ }$ , $\varphi = 0^{\circ }$ ) and ( $\theta = -30^{\circ }$ , $\varphi = 0^{\circ }$ ), and a dual-beam pointing at ( $\theta = +27^{\circ }$ , $\varphi = 0^{\circ }$ ) and ( $\theta = -29^{\circ }$ , $\varphi = 0^{\circ }$ ). The proposed RA provides a gain of 25 dB and 19 dB in its single- and dual-beam operations, respectively. For CubeSat applications, the key advantages of this RA are its small stowed volume, reconfigurable EM performance, beamsteering capabilities, monolithic construction, low fabrication cost, and reduced complexity.

Regional Stiffness Reduction Using Lamina Emergent Torsional Joints for Flexible Printed Circuit Board Design

Flexible printed circuit boards (PCBs) make it possible for engineers to design devices that use space efficiently and can undergo changes in shape and configuration. However, they also suffer from tradeoffs due to nonideal material properties. Here, a method is presented that allows engineers to introduce regions of flexibility in otherwise rigid PCB substrates. This method employs geometric features to reduce local stiffness in the PCB, rather than reducing the global stiffness by material selection. Analytical and finite element models are presented to calculate the maximum stresses caused by deflection. An example device is produced and tested to verify the models.

Membrane-Enhanced Lamina Emergent Torsional Joints for Surrogate Folds

Lamina emergent compliant mechanisms (including origami-adapted compliant mechanisms) are mechanical devices that can be fabricated from a planar material (a lamina) and have motion that emerges out of the fabrication plane. Lamina emergent compliant mechanisms often exhibit undesirable parasitic motions due to the planar fabrication constraint. This work introduces a type of lamina emergent torsion (LET) joint that reduces parasitic motions of lamina emergent mechanisms, and presents equations for modeling parasitic motion of LET joints. The membrane joint also makes possible one-way joints that can ensure origami-based mechanisms emerge from their flat state (a change point) into the desired configuration. Membrane-enhanced LET (M-LET) joints, including one-way surrogate folds, are described here and show promise for use in a wide range of compliant mechanisms and origami-based compliant mechanisms. They are demonstrated as individual joints and in mechanisms such as a kaleidocycle (a 6R Bricard linkage), degree-4 origami vertices (spherical mechanisms), and waterbomb base mechanisms (an 8R multi-degrees-of-freedom origami-based mechanism).

Design and analysis of Outside-Deployed Lamina Emergent Joint (OD-LEJ)

Lamina emergent mechanisms (LEMs) can be fabricated in plane, while achieve motion that emerges out of fabrication plane. This paper presents a new flexure hinge called Outside-Deployed Lamina Emergent Joint (OD-LEJ) with a small equivalent spring constant and a large angular displacement. The closed-form model is given and a finite element analysis (FEA) model is created. The FEA results show that this joint can achieve nearly 170.17˚ of rotation without plastic deformation. Stress analysis is done and the results gotten from theoretical calculation and FEA coincide with each other very well. Safety analysis and fatigue analysis are done as well. An Inside-Deployed Lamina Emergent Joint (ID-LEJ) is also proposed. The joint is analyzed through FEA and theoretical calculation. The joint shows a similar bending property as OD-LEJ. Comparisons between these two joints and Lamina Emergent Torsional (LET) joint are made. OD-LEJ and ID-LEJ do better than LET joint in large angular displacement and have a smaller equivalent spring constant. Finally, the movement of the center of rotation and some other problems are discussed.

Failure analysis and performance comparison of Triple-LET and LET flexure hinges

Abstract A new type of flexure hinge named the Triple Lamina Emergent Torsional (Triple-LET) was proposed in this paper. Its 3D structure was designed, and its equivalent bending stiffness was also derived. Based on the equivalent formula and the finite element simulation analysis, the equivalent bending stiffness of the Triple-LET and the LET flexure hinge with the same overall dimensions were analyzed and compared. It was concluded that under the same torque, the Triple-LET flexure hinge can realize larger deformation than the LET flexure hinge. Thus, the proposed new flexure hinge is presented as a compliant joint suitable for applications where large angular rotation is desired. Failure analyses of the Triple-LET and the LET flexure hinges were also carried out, respectively. The analysis results show that the Triple-LET flexure hinge made of polypropylene can reach 180° with no plastic deformation, while the LET flexure hinge with the same overall dimensions will plastically deform once the bending angle is greater than 161.4°. The results also indicate that the range of bending angles of the Triple-LET flexure hinge made of beryllium bronze is from 0° to 128.2°, which is two times larger than that of the LET flexure hinge.

Introduction of planar compliant joints designed for combined bending and axial loading conditions in lamina emergent mechanisms

This work introduces three joints to allow motion in lamina emergent mechanisms (LEMs) that were designed to have minimal parasitic motion under tension, compression, and a combination of tension and compression loadings. Closed-form models of the joints were developed and combined with optimization algorithms for maximum flexibility in bending and then modeled using finite element analysis (FEA). The FEA results were used to predict the stiffnesses of the joints in bending, tension, and compression. As a baseline, Lamina Emergent Torsional (LET) joints were designed to match the bending stiffness of each of the joints, so that the tensile-compressive performance could be compared. The joints demonstrate improved off-axis stiffness in tensile and/or compressive stiffness, at the cost of limited bending flexibility compared to the LET joint and requiring more material area. The resulting joints provide a broad set of capabilities that can be used by designers in lamina emergent mechanism design.

Lamina Emergent Torsional (LET) Joint

Part of the challenge in designing compliant mechanisms is finding suitable joints that provide the needed motion and force–deflection characteristics. The Lamina Emergent Torsional (LET) Joint is presented as a compliant joint suited for applications where large angular rotation is desired, but high off-axis stiffness is not as critical. The joint is introduced and the equations necessary for determining the force–deflection characteristics are presented. Since the LET Joint can be fabricated from a single planar layer, it is well suited for macro and micro applications. Illustrative examples are provided with devices fabricated from materials as diverse as steel, polypropylene, and polycrystalline silicon.