Rigidly Foldable Thick Origami Using Designed-Offset Linkages

2020 ◽  
Vol 12 (2) ◽  
Author(s):  
Robert J. Lang ◽  
Nathan Brown ◽  
Brian Ignaut ◽  
Spencer Magleby ◽  
Larry Howell
Keyword(s):  
Plate Thickness ◽  
Degree Of Freedom ◽  
Unique Combination ◽  
Single Degree Of Freedom ◽  
Spatial Mechanism ◽  
Single Degree ◽  
Unfolded State ◽  
The Individual ◽  
Kinematic Motion

Abstract We present new families of thick origami mechanisms that achieve rigid foldability and parallel stacking of panels in the flat-folded state using linkages for some or all of the hinges between panels. A degree-four vertex results in a multiloop eight-bar spatial mechanism that can be analyzed as separate linkages. The individual linkages are designed so that they introduce offsets perpendicular to the panels that are mutually compatible around each vertex. This family of mechanisms offers the unique combination of planar unfolded state, parallel-stacked panels in the flat-folded state and kinematic single-degree-of-freedom motion from the flat-unfolded to the flat-folded state. The paper develops the mathematics defining the necessary offsets, beginning with a symmetric bird’s-foot vertex, and then shows that the joints can be developed for asymmetric flat-foldable systems. Although in the general case there is no guarantee of achieving perfect kinematic motion, we show that for many cases of interest, the deviation is a tiny fraction of the plate thickness. Mechanical realizations of several examples are presented.

Rigidly Foldable Thick Origami Using Designed-Offset Linkages

2019 ◽  
Author(s):  
Robert J. Lang ◽  
Nathan Brown ◽  
Brian Ignaut ◽  
Spencer Magleby ◽  
Larry Howell
Keyword(s):  
Degree Of Freedom ◽  
Unique Combination ◽  
Single Degree Of Freedom ◽  
Spatial Mechanism ◽  
Single Degree ◽  
Unfolded State ◽  
The Individual

Abstract We present new families of thick origami mechanisms that achieve rigid foldability and parallel stacking of panels in the flat-folded state using linkages for some or all of the hinges between panels. A degree-four vertex results in a multi-loop eight-bar spatial mechanism that can be analyzed as separate linkages. The individual linkages are designed so that they introduce offsets perpendicular to the panels that are mutually compatible around each vertex. This family of mechanisms offers the unique combination of a planar unfolded state, parallel-stacked panels in the flat folded state, and kinematic single-degree-of-freedom motion from the flat-unfolded to the flat-folded state.

Split-Vertex Technique for Thickness-Accommodation in Origami-Based Mechanisms

2017 ◽  
Author(s):  
Kyler A. Tolman ◽  
Robert J. Lang ◽  
Spencer P. Magleby ◽  
Larry L. Howell
Keyword(s):  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Unfolded State ◽  
Potential Applications ◽  
Split Vertex

A novel thickness-accommodation technique for origami based mechanisms is introduced. This technique modifies a zero-thickness pattern by splitting each vertex along the minor folds into a system of two vertices. The modified fold pattern then has thickness applied to it and the resulting mechanism is kinematically equivalent to the modified fold pattern. Origami patterns that are rigid-foldable and only have two panels that stack between folds are utilized in the technique. The technique produces thick origami mechanisms where all panels lie in a plane in the unfolded state without any holes or protrusions and maintain a single degree of freedom. Steps for synthesizing split-vertex mechanisms are presented and examples of split-vertex mechanisms are shown. Advantages and potential applications of the technique are discussed.

scholarly journals The origin of the mass of the Nambu–Goldstone bosons

2018 ◽  
Vol 33 (07) ◽  
pp. 1850041 ◽  
Author(s):  
Ivan Arraut
Keyword(s):  
Effective Mass ◽  
Chemical Potential ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Goldstone Bosons ◽  
Single Degree ◽  
The Individual

We explain the origin of the mass for the Nambu–Goldstone bosons when there is a chemical potential in the action which explicitly breaks the symmetry. The method is based on the number of independent histories for the interaction of the pair of Nambu–Goldstone bosons with the degenerate vacuum (triangle relations). The analysis suggests that under some circumstances, pairs of massive Nambu–Goldstone bosons can become a single degree of freedom with an effective mass defined by the superposition of the individual masses of each boson. Possible mass oscillations for the Nambu–Goldstone bosons are discussed.

Some Shock Spectra Characteristics and Uses

1958 ◽  
Vol 25 (3) ◽  
pp. 365-372
Author(s):  
Y. C. Fung ◽  
M. V. Barton
Keyword(s):  
Shock Wave ◽  
High Frequency ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Close Approximation ◽  
Single Degree Of Freedom ◽  
Peak Response ◽  
Single Degree ◽  
Frequency Oscillator ◽  
The Individual

Abstract A shock spectrum is a plot showing the peak response of a linear variable-frequency oscillator (of single degree of freedom) to a specific shock wave, as a function of the frequency of the oscillator. Such a spectrum may be measured, for example, by multifrequency reed gages and is sometimes used as a basis either for specifying the shock wave or for computing the response of a multi-degree-of-freedom structure to such a shock. In this paper these applications of the shock spectrum are discussed. In particular, it is shown that, if the fundamental frequency (f1, cps) of the structure is sufficiently high, a close approximation of the peak response of a multi-degree-of-freedom system can be obtained by the algebraic sum (not the sum of absolute values) of the peak responses of the individual degrees of freedom. Numerical results for a uniform cantilever beam subjected to a shock load uniformly distributed over its span show that the high-frequency requirement is satisfied if 2f1tm ≥ 1, where tm(sec) is the rise time of the pulse.

Synthesis of Spatial Mechanism UR-2SS for Path Generation

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Wen-Yeuan Chung
Keyword(s):  
Three Dimensional ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Path Generation ◽  
Single Degree Of Freedom ◽  
Numerical Examples ◽  
Spatial Mechanism ◽  
Single Degree ◽  
Three Stages ◽  
Moving Platform

This article presents a new spatial mechanism with single degree of freedom (DOF) for three-dimensional path generation. The path can be defined by prescribing at most seven precision points. The moving platform of the mechanism is supported by a U-R (universal-revolute) leg and two S–S (spherical–spherical) legs. The driving unit is the first axis of the universal pair. The U-R leg is synthesized first with the problem of order defects being considered. Precision points then lead to prescribed poses of the moving platform. Two S–S legs are then synthesized to meet these poses. This spatial mechanism with a given input is analogous to a planar kinematic chain so that all possible configurations of the spatial mechanism can be constructed. A strategy consisting of three stages for evaluating branch defects is developed with the aid of the characteristic of double configurations and the technique of coding three constituent four-bar linkages. Two numerical examples are presented to illustrate the design, the evaluation of defects, and the performance of the mechanism.

Cylindrical Single-Degree-of-Freedom Spatial Mechanisms for Cell Restraint

2012 ◽  
Vol 4 (2) ◽  
Author(s):  
Gregory H. Teichert ◽  
Quentin T. Aten ◽  
Sandra H. Burnett ◽  
Larry L. Howell ◽  
Brian D. Jensen
Keyword(s):  
Transgenic Animal ◽  
Degree Of Freedom ◽  
Surface Micromachining ◽  
Electromechanical Systems ◽  
Single Degree Of Freedom ◽  
Spatial Mechanism ◽  
Single Degree ◽  
Spatial Mechanisms ◽  
Production Techniques ◽  
Cell Support

Many transgenic animal production techniques require egg cells to be held in place during injection of the transgene. This paper presents a micro-electromechanical systems (MEMS) mechanism that provides cell support, self-centers the cell, and requires a single linear input for actuation. This restraint device uses an innovative spatial mechanism, termed a cylindrical mechanism. The kinematics and design of the restraint are discussed. The MEMS cell restraints were fabricated using a surface micromachining process, after which the mechanism’s cell support, self-centering of the cell, and motion were verified.

Sign in / Sign up

Export Citation Format

Share Document