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.

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.

scholarly journals Modeling in ADAMS of a 6R industrial robot

2018 ◽  
Vol 184 ◽  
pp. 02006
Author(s):  
Mariana Ratiu ◽  
Alexandru Rus ◽  
Monica Loredana Balas
Keyword(s):  
Dynamic Analysis ◽  
Industrial Robot ◽  
Kinematic Model ◽  
Future Research ◽  
Robot Motion ◽  
Cad Model ◽  
3D Cad ◽  
Revolute Joints ◽  
Real Model ◽  
Articulated Robot

In this paper, we present the first steps in the process of the modeling in ADAMS MBS of MSC software of the mechanical system of an articulated robot, with six revolute joints. The geometric 3D CAD model of the robot, identical to the real model, in the PARASOLID format, is imported into ADAMS/View and then are presented the necessary steps for building the kinematic model of the robot. We conducted this work, in order to help us in our future research, which will consist of kinematic and dynamic analysis and optimization of the robot motion.

A New Family of Bricard-Derived Deployable Mechanisms

2016 ◽  
Vol 8 (3) ◽  
Author(s):  
Hailin Huang ◽  
Bing Li ◽  
Jianyang Zhu ◽  
Xiaozhi Qi
Keyword(s):  
Large Volume ◽  
Computer Aided Design ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
New Family ◽  
Revolute Joints ◽  
Computer Aided ◽  
Cad Models ◽  
Aided Design

This paper proposes a new family of single degree of freedom (DOF) deployable mechanisms derived from the threefold-symmetric deployable Bricard mechanism. The mobility and geometry of original threefold-symmetric deployable Bricard mechanism is first described, from the mobility characterstic of this mechanism, we show that three alternate revolute joints can be replaced by a class of single DOF deployable mechanisms without changing the single mobility characteristic of the resultant mechanisms, therefore leading to a new family of Bricard-derived deployable mechanisms. The computer-aided design (CAD) models are used to demonstrate these derived novel mechanisms. All these mechanisms can be used as the basic modules for constructing large volume deployable mechanisms.

Kinematics and Dynamics of Nanostructured Origami™

2005 ◽  
Author(s):  
P. Stellman ◽  
W. Arora ◽  
S. Takahashi ◽  
E. D. Demaine ◽  
G. Barbastathis
Keyword(s):  
Dynamic Modeling ◽  
Periodic Structures ◽  
Metal Layer ◽  
Three Dimensional ◽  
Spatial Dimension ◽  
Index Of Refraction ◽  
Coulomb Energy ◽  
Single Vertex ◽  
Revolute Joints ◽  
Final Design

Two-dimensional (2D) nanofabrication processes such as lithography are the primary tools for building functional nanostructures. The third spatial dimension enables completely new devices to be realized, such as photonic crystals with arbitrary defect structures and materials with negative index of refraction [1]. Presently, available methods for three-dimensional (3D) nanopatterning tend to be either cost inefficient or limited to periodic structures. The Nanostructured Origami method fabricates 3D devices by first patterning nanostructures (electronic, optical, mechanical, etc) onto a 2D substrate and subsequently folding segments along predefined creases until the final design is obtained [2]. This approach allows almost arbitrary 3D nanostructured systems to be fabricated using exclusively 2D nanopatterning tools. In this paper, we present two approaches to the kinematic and dynamic modeling of folding origami structures. The first approach deals with the kinematics of unfolding single-vertex origami. This work is based on research conducted in the origami mathematics community, which is making rapid progress in understanding the geometry of origami and folding in general [3]. First, a unit positive “charge” is assigned to the creases of the structure in its folded state. Thus, each configuration of the structure as it unfolds can be assigned a value of electrostatic (Coulomb) energy. Because of repulsion between the positive charges, the structure will unfold if allowed to decrease its energy. If the energy minimization can be carried out all the way to the completely unfolded state, we are simultaneously guaranteed of the absence of collisions for the determined path. The second method deals with dynamic modeling of folding multi-segment (accordion style) origamis. The actuation method for folding the segments uses a thin, stressed metal layer that is deposited as a hinge on a relatively stress free structural layer. Through the use of robotics routines, the hinges are modeled as revolute joints, and the system dynamics are calculated.

scholarly journals Control of a 3-RRR Planar Parallel Robot Using Fractional Order PID Controller

2020 ◽  
Vol 17 (6) ◽  
pp. 822-836
Author(s):  
Auday Al-Mayyahi ◽  
Ammar A. Aldair ◽  
Chris Chatwin
Keyword(s):  
Fractional Order ◽  
Material Handling ◽  
State Of The Art ◽  
Kinematic Model ◽  
Parallel Robot ◽  
Inverse Kinematic ◽  
Open Loop ◽  
Parallel Robots ◽  
The State ◽  
Revolute Joints

Abstract3-RRR planar parallel robots are utilized for solving precise material-handling problems in industrial automation applications. Thus, robust and stable control is required to deliver high accuracy in comparison to the state of the art. The operation of the mechanism is achieved based on three revolute (3-RRR) joints which are geometrically designed using an open-loop spatial robotic platform. The inverse kinematic model of the system is derived and analyzed by using the geometric structure with three revolute joints. The main variables in our design are the platform base positions, the geometry of the joint angles, and links of the 3-RRR planar parallel robot. These variables are calculated based on Cayley-Menger determinants and bilateration to determine the final position of the platform when moving and placing objects. Additionally, a proposed fractional order proportional integral derivative (FOPID) is optimized using the bat optimization algorithm to control the path tracking of the center of the 3-RRR planar parallel robot. The design is compared with the state of the art and simulated using the Matlab environment to validate the effectiveness of the proposed controller. Furthermore, real-time implementation has been tested to prove that the design performance is practical.

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).

Constructing Scissor-Like Structures and Parallelogram Linkages With 4-Crease Single-Vertex Flat-Foldable Rigid Origami and Their Thick-Panel Versions

2019 ◽  
Author(s):  
David Xing ◽  
Zhong You
Keyword(s):  
Dihedral Angle ◽  
Composite Structure ◽  
Dihedral Angles ◽  
Single Vertex ◽  
Rotation Matrices ◽  
Similar Construction ◽  
Complex Approach ◽  
Intuitive Method ◽  
Point Of Intersection ◽  
Rigid Supports

Abstract Scissor-like structures are commonly composed of two straight rigid supports in a crisscross pattern connected by a pivot at its point of intersection [1]. Opposite angles formed by the supports are equal regardless of the structure’s folded state. Parallelogram linkages have a similar property. Rigid origami can be used to create these structures by combining two identical copies of a 4-crease single-vertex flat-foldable rigid origami, a single 4C, to form a flat-foldable composite structure, a double 4C. In this paper, we prove mathematically that regardless of the folded state of a single-4C, its even dihedral angles are equal, and odd dihedral angles are equal. As a result, the double 4C consists of 2 scissor-like structures. A past method to prove these dihedral angle equalities requires a more complex approach involving rotation matrices using Denavit and Hartenberg parameters [2,3]. This paper will provide a more intuitive method that proves the same equalities. We will also show that a similar construction of the double 4C using thick-panel versions of the single 4C satisfies the same dihedral angle equalities necessary for the formation of parallelogram linkages. The construction of the double 4C can help design self-folding mechanisms and useful metamaterials.

Axis Motion Based System Calibration of an Automated Disassembly Work Cell

2000 ◽  
Author(s):  
Michael M. Bailey-Van Kuren
Keyword(s):  
Vision System ◽  
Kinematic Model ◽  
Image Data ◽  
Simple Relationship ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Homogeneous Transformation Matrix ◽  
Position And Orientation ◽  
A Chain ◽  
User Friendly

Abstract This paper presents an approach to calibrate a robotic cell consisting of a robot, a positioning table and a stereo vision system in an autonomous manner. The approach is designed to simplify the error relationships and parameter updates and thus eliminating the need for a large nonlinear search. The accumulation of error in the kinematic model is avoided by calibrating one joint at a time from the manipulator hand to the manipulator base. The error in the manipulator and sensor models are identified by using least squares estimates. The manipulator kinematic model is parameterized by the joint axes position and orientation instead of the Denavit-Hartenberg parameters. This approach leads to a more “user-friendly” interface to the calibration results. The model is derived using screw geometry, resulting in a simple relationship between the joint axis parameters and the path produced by moving a particular joint. The robot model provides an example of a chain of revolute joints while the positioning table provides an example of prismatic joints. Model simplifications result from each of these simplified motions. As with other methods, this formulation produces a four by four homogeneous transformation matrix which defines the motion of any point on the hand of the manipulator in terms of the sensed joint angles. It is shown that each camera can independently estimate the manipulators’ paths using the image data and distances along the path from the manipulator model. Error in position and orientation between the resulting two path estimates identify the relative error between the camera models. It is shown that a solution exists for any set of three or more points generated from one axis.

Single-Vertex Multicrease Rigid Origami With Nonzero Thickness and Its Transformation Into Deployable Mechanisms

2017 ◽  
Vol 10 (1) ◽  
Author(s):  
Chenhan Guang ◽  
Yang Yang
Keyword(s):  
Computer Aided Design ◽  
Screw Theory ◽  
Kinematic Model ◽  
Degree Of Freedom ◽  
Single Vertex ◽  
Geometrical Characteristics ◽  
Computer Aided ◽  
Deployable Mechanism ◽  
Aided Design ◽  
Basic Configuration

The radial folding ratio of single-vertex multicrease rigid origami, from the folded configuration to the unfolded configuration, is satisfactory. In this study, we apply two approaches to add nonzero thickness for this kind of origami and identify different geometrical characteristics. Then, the model of the secondary folding origami, which can help to further decrease the folding ratio, is constructed. We apply the method of constraining the edges of the panels on prescribed planes to geometrically obtain the kinematic model. Based on the kinematic model and the screw theory, the nonzero thickness origami is transformed into the deployable mechanism with one degree-of-freedom (1DOF). Other similar mechanisms can be derived based on this basic configuration. The computer-aided design examples are presented to indicate the feasibility.

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.

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