Deployable Prismatic Structures With Origami Patterns

2014 ◽  
Author(s):  
Sicong Liu ◽  
Weilin Lv ◽  
Yan Chen ◽  
Guoxing Lu
Keyword(s):  
Design Method ◽  
Kinematic Model ◽  
The Other ◽  
Dihedral Angles ◽  
Geometric Condition ◽  
Compatibility Conditions ◽  
Deployable Structures ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Geometric Compatibility

In order to find the general condition of the rigid origami pattern for the deployable prismatic structures, the kinematic model is proposed based on the mobile assemblies of spherical 4R linkages. The kinematic and geometric compatibility conditions of the mobile assemblies are derived. Two groups of 2n-side deployable prismatic structures are obtained. When n=2, one of them is with kite-shape intersection, while the other is with parallelgram. The variations of the unit are discussed. The straight and curvy multilayer prisms are built by changing the dihedral angles between the intersecting planes. The general design method for the 2n-side multilayer deployable prismatic structures is proposed with the geometric condition of the origami patterns. All the deployable structures constructed with this method can be deployed and folded along the central axis of the prisms with single degree of freedom, which makes the structures have wide engineering applications.

Deployable Prismatic Structures With Rigid Origami Patterns

2016 ◽  
Vol 8 (3) ◽  
Author(s):  
Sicong Liu ◽  
Weilin Lv ◽  
Yan Chen ◽  
Guoxing Lu
Keyword(s):  
Closed Loop ◽  
Design Method ◽  
Kinematic Model ◽  
Deployable Structures ◽  
Engineering Applications ◽  
Single Degree Of Freedom ◽  
General Design ◽  
Plane Symmetric ◽  
Single Degree ◽  
Spherical Linkages

Rigid origami inspires new design technology in deployable structures with large deployable ratio due to the property of flat foldability. In this paper, we present a general kinematic model of rigid origami pattern and obtain a family of deployable prismatic structures. Basically, a four-crease vertex rigid origami pattern can be presented as a spherical 4R linkage, and the multivertex patterns are the assemblies of spherical linkages. Thus, this prismatic origami structure is modeled as a closed loop of spherical 4R linkages, which includes all the possible prismatic deployable structures consisting of quadrilateral facets and four-crease vertices. By solving the compatibility of the kinematic model, a new group of 2n-sided deployable prismatic structures with plane symmetric intersections is derived with multilayer, straight and curvy variations. The general design method for the 2n-sided multilayer deployable prismatic structures is proposed. All the deployable structures constructed with this method have single degree-of-freedom (DOF), can be deployed and folded without stretching or twisting the facets, and have the compactly flat-folded configuration, which makes it to have great potential in engineering applications.

scholarly journals Symmetric waterbomb origami

2016 ◽  
Vol 472 (2190) ◽  
pp. 20150846 ◽  
Author(s):  
Yan Chen ◽  
Huijuan Feng ◽  
Jiayao Ma ◽  
Rui Peng ◽  
Zhong You
Keyword(s):  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Solar Panels ◽  
Deployable Structures ◽  
Single Degree Of Freedom ◽  
Folding Process ◽  
Multiple Degrees Of Freedom ◽  
Single Degree ◽  
Flat Roofs ◽  
Additional Constraints

The traditional waterbomb origami, produced from a pattern consisting of a series of vertices where six creases meet, is one of the most widely used origami patterns. From a rigid origami viewpoint, it generally has multiple degrees of freedom, but when the pattern is folded symmetrically, the mobility reduces to one. This paper presents a thorough kinematic investigation on symmetric folding of the waterbomb pattern. It has been found that the pattern can have two folding paths under certain circumstance. Moreover, the pattern can be used to fold thick panels. Not only do the additional constraints imposed to fold the thick panels lead to single degree of freedom folding, but the folding process is also kinematically equivalent to the origami of zero-thickness sheets. The findings pave the way for the pattern being readily used to fold deployable structures ranging from flat roofs to large solar panels.

Conditions for Rigid and Flat Foldability of Degree-n Vertices in Origami

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
Luca Zimmermann ◽  
Kristina Shea ◽  
Tino Stanković
Keyword(s):  
Engineering Design ◽  
Kinematic Model ◽  
Spherical Triangle ◽  
Simple Rule ◽  
Dihedral Angles ◽  
Single Vertex ◽  
Efficient Approach ◽  
Single Degree ◽  
Revolute Joints ◽  
Intrinsic Condition

Abstract In rigid origami, the complex folding motion arises from the rotation of strictly rigid faces around crease lines that represent perfect revolute joints. The rigid folding motion of an origami crease pattern is collectively determined by the kinematics of its individual vertices. Establishing a kinematic model and determining the conditions for the rigid foldability of a single vertex is thus important to exploit rigid origami in engineering design tasks. Today, there exists neither an efficient kinematic model to determine the unknown dihedral angles nor an intrinsic condition for the rigid foldability of arbitrarily complex vertices of degree n. In this paper, we present the principle of three units (PTU) that provides an efficient approach to modeling the kinematics of single degree-n vertices. The PTU is based on the notion that the kinematics of a vertex is determined by the behavior of a single underlying spherical triangle. The condition for the existence of this triangle leads to the condition for the rigid and flat foldability of degree-n vertices. These findings are transferred from single vertices to crease patterns, resulting in a simple rule to generate kinematically determinate crease patterns that can be designed to fold rigidly. Finally, we discuss the limitations of the PTU with respect to the global rigid foldability of a crease pattern.

Robust Control Design of a Single Degree-of-Freedom Magnetic Levitation System by Quantitative Feedback Theory

2012 ◽  
Author(s):  
Feng Tian ◽  
Mark Nagurka
Keyword(s):  
Robust Control ◽  
Magnetic Levitation ◽  
Design Method ◽  
Control Design ◽  
Open Loop ◽  
Quantitative Feedback Theory ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Maglev System ◽  
Robust Control Design

A magnetic levitation (maglev) system is inherently nonlinear and open-loop unstable because of the nature of magnetic force. Most controllers for maglev systems are designed based on a nominal linearized model. System variations and uncertainties are not accommodated. The controllers are generally designed to satisfy gain and phase margin specifications, which may not guarantee a bound on the sensitivity. To address these issues, this paper proposes a robust control design method based on Quantitative Feedback Theory (QFT) applied to a single degree-of-freedom (DOF) maglev system. The controller is designed to successfully meet the stability requirement, robustness specifications, and bounds on the sensitivity. Experiments verify that the controller maintains stable levitation even with 100% load variation. Experiments prove that it guarantees the transient response design requirements even with 100% load change and 39% model uncertainties. The QFT control design method discussed in this paper can be applied to other open-loop unstable systems as well as systems with large uncertainties and variations to improve system robustness.

The Rigid Origami Patterns for Flat Surface

2013 ◽  
Author(s):  
Sicong Liu ◽  
Yan Chen ◽  
Guoxing Lu
Keyword(s):  
Flat Surface ◽  
Kinematic Model ◽  
Simulation Models ◽  
Compatibility Conditions ◽  
Engineering Applications ◽  
Internal Mobility ◽  
Mobile Processes ◽  
Geometric Compatibility

Because of the internal mobility, rigid origami structures have great potential in engineering applications. In this research, a kinematic model of the rigid origami pattern is proposed based on the assembly of spherical 4R linkages. To ensure the rigid origami pattern with mobility one, the kinematic and geometric compatibility conditions of the kinematic model are derived. Four types of flat rigid origami patterns are obtained, including three existing types as well as a novel one called the supplementary type. To testify and display the mobile processes of the patterns, their simulation models are built accordingly.

Single-Degree-of-Freedom Rigidly Foldable Origami Flashers

2015 ◽  
Author(s):  
Robert J. Lang ◽  
Spencer Magleby ◽  
Larry Howell
Keyword(s):  
Degree Of Freedom ◽  
Deployable Structures ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Revolute Joints

We present the design for a family of deployable structures based on the origami flasher that are rigidly foldable, i.e., foldable with revolute joints at the hinges and planar rigid faces, and that exhibit a single degree of freedom in their motion. These structures may be used to realize highly compact deployable mechanisms.

Effect of Third Harmonic Vibratory Force on a Linear Spring-Mass System

1963 ◽  
Vol 67 (636) ◽  
pp. 799-803
Author(s):  
C. L. Kirk
Keyword(s):  
Resonant Frequency ◽  
Elastic System ◽  
Rate Of Change ◽  
Degree Of Freedom ◽  
The Other ◽  
Mass System ◽  
Single Degree Of Freedom ◽  
Third Harmonic ◽  
Single Degree ◽  
Linear Spring

SummaryThe response of an elastic system having a single degree of freedom, to a vibratory force whose waveform can be varied, is examined. The variable waveform is produced by a system of two pairs of unbalanced rotors in which one pair rotates at three times the speed of the other pair. The waveform depends on the frequency of excitation, the phasing of the rotors and the ratio of their amounts of unbalance. If the rotors are run at a speed at which the faster pair rotates above resonance while the slower pair rotates below resonance, a frequency is found at which the rate of change of amplitude with respect to frequency is zero. At this point, however, the waveform is quite sensitive to small changes in the frequency of excitation. If the rotor speeds cannot be maintained constant, and if stable vibration waveforms are required, it is necessary to run the slowest rotor well above the resonant frequency where both the amplitude and waveform will be virtually independent of frequency.

Single Degree-of-Freedom Rigidly Foldable Cut Origami Flashers

2016 ◽  
Vol 8 (3) ◽  
Author(s):  
Robert J. Lang ◽  
Spencer Magleby ◽  
Larry Howell
Keyword(s):  
Degree Of Freedom ◽  
Deployable Structures ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Revolute Joints

We present the design for a family of deployable structures based on the origami flasher, which are rigidly foldable, i.e., foldable with revolute joints at the creases and planar rigid faces. By appropriate choice of sector angles and introduction of a cut, a single degree-of-freedom (DOF) mechanism is obtained. These structures may be used to realize highly compact deployable mechanisms.

Suppression of Machine Tool Chatter Using a Viscoelastic Dynamic Damper

1987 ◽  
Vol 109 (1) ◽  
pp. 58-65 ◽  
Author(s):  
K. J. Kim ◽  
J. Y. Ha
Keyword(s):  
Loss Factor ◽  
The Other ◽  
Primary System ◽  
Single Degree Of Freedom ◽  
Dynamic Damper ◽  
Single Degree ◽  
Machine Tool Chatter ◽  
Chatter Vibrations ◽  
Resonance Frequencies ◽  
Viscoelastic Element

Optimization procedures to install a viscoelastic dynamic damper into a single degree of freedom primary system is briefly reviewed. Excitation methods are shown to identify elastic modulus and loss factor of a viscoelastic material at given prestrain, which are needed in the optimum design of the damper. An optimum-designed damper is attached on the toolpost of a lathe and its excellent chatter-suppressing effects are observed under six cutting conditions in terms of integrated power of the accelerations around the chatter frequency. Because one of the resonance frequencies responsible for the chatter varies depending upon the location of the carriage on the sliding surface, the prestrain of the viscoelastic element, which is initially optimum-tuned and damped at a location of the carriage, is readjusted for optimum tuning at the other locations. The effects of the readjustment are discussed in terms of the reduction of structural compliances and magnitudes of chatter vibrations.

Model-free vibration control based on a virtual controlled object considering actuator uncertainty

2020 ◽  
pp. 107754632094092
Author(s):  
Ansei Yonezawa ◽  
Itsuro Kajiwara ◽  
Heisei Yonezawa
Keyword(s):  
Parameter Uncertainty ◽  
Controller Design ◽  
Design Method ◽  
Order System ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Model Free ◽  
Simulation And Experiment ◽  
Model Free Controller ◽  
Controlled Object

The purpose of this research is to construct a simple and practical controller design method, considering the actuator’s parameter uncertainty, without using a model of controlled objects. In this method, a controller is designed with an actuator model including a single-degree-of-freedom virtual structure inserted between actuator and controlled object, resulting in a model-free controller design. Furthermore, an [Formula: see text] control problem is defined so that the actuator’s parameter uncertainty is compensated by satisfying a robust stability condition. Because the actuator model including the virtual controlled object is a simple low-order system, and the actuator’s parameter uncertainty is considered, a controller with high robustness to the actuator’s parameter uncertainty can be designed based on traditional model-based control theory. The effectiveness of the proposed method is verified by both simulation and experiment.

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