Rigid Foldability of Triangle-Twist Origami Pattern and its Derived 6R Linkage

2017 ◽  
Author(s):  
Rui Peng ◽  
Jiayao Ma ◽  
Yan Chen
Keyword(s):  
Theoretical Method ◽  
Geometric Parameters ◽  
Degree Of Freedom ◽  
Space Structures ◽  
Engineering Applications ◽  
Systematic Method ◽  
Mountain Valley ◽  
Folding Pattern ◽  
Spatial Linkages ◽  
Spherical Linkages

Rigid origami is an important subset of origami with broad engineering applications from space structures to metamaterials. The rigid foldability of an origami pattern is determined by both the geometric parameters and the mountain-valley crease assignment. In this paper, by using the equivalent relationships between origami vertices and spherical linkages, a systematic method was proposed to analyze the motion of the triangle-twist pattern with varying distribution of mountain and valley creases, and its rigid folding types were identified. Moreover, kirigami technology was applied to the rigid folding pattern without changing its degree of freedom, from which a new kind of overconstrained 6R linkage was developed. The theoretical method proposed in this paper can be readily extended to study other types of origami patterns, which will in turn help to design structures with large deployable ratio as well as some new spatial linkages.

scholarly journals Rigid Foldability of Generalized Triangle Twist Origami Pattern and Its Derived 6R Linkages

2018 ◽  
Vol 10 (5) ◽  
Author(s):  
Huijuan Feng ◽  
Rui Peng ◽  
Jiayao Ma ◽  
Yan Chen
Keyword(s):  
Degree Of Freedom ◽  
Geometrical Parameters ◽  
Engineering Applications ◽  
Systematic Method ◽  
Mountain Valley ◽  
Foldable Structures ◽  
New Type ◽  
Spherical Linkages ◽  
Kinematic Equivalence ◽  
Overconstrained Linkages

Rigid origami is a restrictive form of origami that permits continuous motion between folded and unfolded states along the predetermined creases without stretching or bending of the facets. It has great potential in engineering applications, such as foldable structures that consist of rigid materials. The rigid foldability is an important characteristic of an origami pattern, which is determined by both the geometrical parameters and the mountain-valley crease (M-V) assignments. In this paper, we present a systematic method to analyze the rigid foldability and motion of the generalized triangle twist origami pattern using the kinematic equivalence between the rigid origami and the spherical linkages. All schemes of M-V assignment are derived based on the flat-foldable conditions among which rigidly foldable ones are identified. Moreover, a new type of overconstrained 6R linkage and a variation of doubly collapsible octahedral Bricard are developed by applying kirigami technique to the rigidly foldable pattern without changing its degree-of-freedom. The proposed method opens up a new way to generate spatial overconstrained linkages from the network of spherical linkages. It can be readily extended to other types of origami patterns.

Branch Identification of Spherical Six-Bar Linkages

2016 ◽  
Author(s):  
Liangyi Nie ◽  
Jun Wang ◽  
Kwun-Lon Ting ◽  
Daxing Zhao ◽  
Quan Wang ◽  
...  
Keyword(s):  
Range Of Motion ◽  
Degree Of Freedom ◽  
Joint Rotation ◽  
Single Degree Of Freedom ◽  
Complex Issue ◽  
Single Degree ◽  
Identification Method ◽  
Spatial Linkages ◽  
Spherical Linkages

Branch (assembly mode or circuit) identification is a way to assure motion continuity among discrete linkage positions. Branch problem is the most fundamental, pivotal, and complex issue among the mobility problems that may also include sub-branch (singularity-free) identification, range of motion, and order of motion. Branch and mobility complexity increases greatly in spherical or spatial linkages. This paper presents the branch identification method suitable for automated motion continuity rectification of a single degree-of-freedom of spherical linkages. Using discriminant method and the concept of joint rotation space (JRS), the branch of a spherical linkage can be easily identified. The proposed method is general and conceptually straightforward. It can be applied for all linkage inversions. Examples are employed to illustrate the proposed method.

On the Rotatability of Spherical N-Bar Chains

1994 ◽  
Vol 116 (3) ◽  
pp. 920-923 ◽  
Author(s):  
Yung-Way Liu ◽  
Kwun-Lon Ting
Keyword(s):  
Degree Of Freedom ◽  
Spatial Linkages ◽  
Spherical Linkages ◽  
Planar Linkages

This paper established the spherical counterparts of Ting’s rotatability laws of planar linkages. Generally speaking, similar rotatability properties exist between a pair of adjoining links in planar and spherical linkages and the concept of invariant link rotatability is valid for spherical linkage only if it is referred to that between adjoining links. The established spherical rotatability criteria are also valid for single and multiple degree of freedom nR3C, nR2C1P, nR1C2P and nR3P spatial linkages.

Creating Rigid Foldability to Enable Mobility of Origami-Inspired Mechanisms

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Alden Yellowhorse ◽  
Larry L. Howell
Keyword(s):  
Design Guidelines ◽  
Degree Of Freedom ◽  
Engineering Applications

Rigidly foldable origami crease patterns can be translated into corresponding rigid mechanisms with at least one degree of freedom. However, origami crease patterns of interest for engineering applications are not always rigidly foldable, and designers trying to adapt a crease pattern may be confronted with the need to add more mobility to their design. This paper presents design guidelines for making alterations to a crease pattern to make it rigidly foldable. Adding creases, removing panels, and splitting creases are presented as potential alterations for increasing mobility, and approaches for determining the position and number of alterations are discussed. This paper also investigates means for reducing the number of changes necessary to achieve this condition. The approach is developed in general and illustrated through a demonstrative example.

Velocity, Acceleration, and Static-Force Analyses of Spatial Linkages

1965 ◽  
Vol 32 (4) ◽  
pp. 903-910 ◽  
Author(s):  
J. Denavit ◽  
R. S. Hartenberg ◽  
R. Razi ◽  
J. J. Uicker
Keyword(s):  
Virtual Work ◽  
Algebraic Method ◽  
Degree Of Freedom ◽  
Static Force ◽  
Virtual Displacement ◽  
Single Loop ◽  
Loop Equation ◽  
The Matrix ◽  
Spatial Linkages

The algebraic method using 4 × 4 matrices is extended to the analysis of velocities, accelerations, and static forces in one-degree-of-freedom, single-loop, spatial linkages consisting of revolute and prismatic pairs, either singly or in combination. The methods are well suited for machine calculations and have been tested on a number of examples, one of which is presented. Velocities and accelerations are obtained by differentiation of the matrix-loop or position equation. Static forces are found by combining the method of virtual work with the matrix-loop equation to relate the virtual displacement of the load to given virtual deformations of the links.

Geometric Simulation for Thick Origami

2019 ◽  
Author(s):  
Tsz-Ho Kwok
Keyword(s):  
Design Problem ◽  
Three Dimensional ◽  
Experimental Results ◽  
Engineering Applications ◽  
Research Attention ◽  
3D Shape ◽  
Mountain Valley ◽  
Geometry Design ◽  
Geometric Simulation ◽  
Geometric Formulation

Abstract Origami is an art that creates a three-dimensional (3D) shape only by folding. This capability has drawn much research attention recently, and its applied or inspired designs are utilized in various engineering applications. Most current designs are based on the existing origami patterns and their known deformation, but origami patterns are universally designed for zero-thickness like a paper. To extend the designs for engineering applications, simulation of origami is needed to help designers explore and understand the designs, and the simulation must take the material thickness into account. With the observation that origami is mainly a geometry design problem, this paper develops a geometric simulation for thick origami, similar to a pseudo-physics approach. The actuation, constraints, and mountain/valley assignments of origami are also incorporated in the geometric formulation. Experimental results show that the proposed method is efficient and accurate. It can simulate successfully the bistable property of a waterbomb base, two different action origami, and the elasticity of origami panels when they are not rigid.

Initial Estimates in the Design of Rack-and-Pinion Steering Linkages

2000 ◽  
Vol 122 (2) ◽  
pp. 194-200 ◽  
Author(s):  
P. A. Simionescu ◽  
M. R. Smith
Keyword(s):  
Synthesis Method ◽  
Geometric Parameters ◽  
Degree Of Freedom ◽  
Minimum Pressure ◽  
Pressure Angle ◽  
Early Stages ◽  
Design Charts

Based on recent results concerning the occurrence of function cognates in Watt II linkages, it is shown that only 3 geometric parameters are sufficient for defining the kinematic function of simplified planar rack-and-pinion steering linkages. The steering performances of the mechanisms are analytically expressed in terms of these parameters and, by employing an optimization-based synthesis method involving increasing the degree of freedom of the mechanism, the optimum domains are determined. The parameter sets corresponding to these minimum steering error domains are displayed in design charts. These charts aid the automotive engineer in the early stages of conceiving a new steering linkage by providing initial estimates of the basic geometry of the mechanism. They also provide information on two other characteristics of concern, i.e. the minimum pressure angle occurring in the joints and the rack stroke required for maximum turn of the wheels. [S1050-0472(00)00402-5]

Geometric Design of a Bio-Inspired Flapping Wing Mechanism Based on Bennett-Derived 6R Deployable Mechanisms

2014 ◽  
Author(s):  
Huang Hailin ◽  
Li Bing
Keyword(s):  
Flapping Wing ◽  
Geometric Design ◽  
Geometric Parameters ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Flapping Motion ◽  
Single Degree ◽  
Revolute Joints ◽  
Air Vehicle ◽  
Deployable Mechanism

In this paper, we present the concept of designing flapping wing air vehicle by using the deployable mechanisms. A novel deployable 6R mechanism, with the deploying/folding motion of which similar to the flapping motion of the vehicle, is first designed by adding two revolute joints in the adjacent two links of the deployable Bennett linkage. The mobility of this mechanism is analyzed based on a coplanar 2-twist screw system. An intuitive projective approach for the geometric design of the 6R deployable mechanism is proposed by projecting the joint axes on the deployed plane. Then the geometric parameters of the deployable mechanism can be determined. By using another 4R deployable Bennett connector, the two 6R deployable wing mechanisms can be connected together such that the whole flapping wing mechanism has a single degree of freedom (DOF).

scholarly journals Algebraic Formulation for Moderately Thick Elastic Frames, Beams, Trusses, and Grillages within Timoshenko Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Jan Pełczyński ◽  
Wojciech Gilewski
Keyword(s):  
Space Structures ◽  
Algebraic Equations ◽  
Timoshenko Theory ◽  
Engineering Applications ◽  
Constitutive Matrix ◽  
Algebraic Formulation

The paper is dedicated to the algebraic formulation of elastic frame equations. The obtained set of equations describe deformations of moderately thick frames made of both compressible and incompressible bars, grillages of rigid or pin-joined connections, and trusses. Plane as well as space structures are presented. The paper is an extension of the article of T. Lewiński written in 2001 related to thin bars. Algebraic equations with diagonal constitutive matrix are original and suitable for various engineering applications and for educational purposes.

On the Application of Kinematic Units to the Topological Analysis of Geared Mechanisms

2000 ◽  
Vol 123 (2) ◽  
pp. 240-246 ◽  
Author(s):  
Chia-Pin Liu ◽  
Dar-Zen Chen
Keyword(s):  
Topological Analysis ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Systematic Method ◽  
Input And Output

Based on the concept of kinematic fractionation, a systematic method for the topological analysis of geared mechanisms is presented in this paper. It is shown that a geared kinematic chain (GKC) can be regarded as a combination of kinematic unit(s). By identifying the embedded kinematic units, kinematic insight in the GKC can be exposed. The disclosed information leads to straightforward and promising rules to prevent redundant links. These rules form the basis of a by-inspection procedure to determine admissible assignments of the ground, input and output links in a GKC. Admissible assignments of the ground, input and output links of one degree-of-freedom 5 link GKCs are determined as an illustrative example.

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