Finding Rigid Body Modes of Rigid-Foldable Origami Through the Simulation of Vertex Motion

2017 ◽  
Author(s):  
Luca Zimmermann ◽  
Tino Stanković ◽  
Kristina Shea
Keyword(s):  
Rigid Body ◽  
Engineering Applications ◽  
Computational Tools ◽  
Constraint Equations ◽  
Mountain Valley ◽  
Design Alternatives ◽  
Foldable Structures ◽  
Rigid Body Modes ◽  
Design Requirements ◽  
Origami Engineering

Designing structures through the means of origami brings many advantages for engineering applications. In current research, the underlying origami principle is often selected based on experience out of a range of known patterns and then manually altered to fit the design problem. This tedious and time-consuming procedure, if automated through computational tools, has the potential to facilitate the design of origami engineering applications. This however requires efficient kinematic simulation of origamis that is also able to accommodate to design requirements specific to foldable structures. In this paper, a simulator is implemented that is able to model the motion of origami vertices without the need for mountain-valley assignments and with a path of deployment as activation. The formulation of constraint equations through these vertex positions does not restrict the system to certain folding configurations, which is why the approach is able to detect different rigid body modes resulting from single activations. Finding rigid body modes can be beneficial for the search of design alternatives conforming to certain input requirements. The results of the simulation show promise for the incorporation of the simulator within an automated procedure for the design of origamis.

scholarly journals A Computational Design Synthesis Method for the Generation of Rigid Origami Crease Patterns

2021 ◽  
pp. 1-57
Author(s):  
Luca Zimmermann ◽  
Kristina Shea ◽  
Tino Stankovic
Keyword(s):  
Rigid Body ◽  
Synthesis Method ◽  
Computational Design ◽  
Graph Grammar ◽  
Generative Design ◽  
Engineering Applications ◽  
Design Synthesis ◽  
Design Alternatives ◽  
Rigid Body Modes ◽  
Computational Design Synthesis

Abstract Today most origami crease patterns employed in technical applications are selected from a handful of well-known origami principles. Computational algorithms capable of generating novel crease patterns either target artistic origami, focus on quadrilateral creased paper, or do not incorporate direct knowledge for the purposeful design of crease patterns tailored to engineering applications. The lack of computational methods for the generative design of crease patterns for engineering applications arises from a multitude of geometric complexities intrinsic to origami, such as rigid foldability and rigid body modes, many of which have been addressed by recent work of the authors. Based on these findings, in this paper we introduce a Computational Design Synthesis method for the generative design of novel crease patterns to develop origami concepts for engineering applications. The proposed method first generates crease pattern graphs through a graph grammar that automatically builds the kinematic model of the underlying origami and introduces constraints for rigid foldability. Then, the method enumerates all design alternatives that arise from the assignment of different rigid body modes to the internal vertices. These design alternatives are then automatically optimized and checked for intersection to satisfy the given design task. The proposed method is generic and applied here to two design tasks that are a rigidly foldable gripper and a rigidly foldable robotic arm.

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.

Generalized Modes in Time-Domain Seakeeping Calculations

2012 ◽  
Vol 56 (04) ◽  
pp. 215-233
Author(s):  
Johan T. Tuitman ◽  
Šime Malenica ◽  
Riaan van't Veer
Keyword(s):  
Rigid Body ◽  
Transient Response ◽  
Time Domain ◽  
Large Amplitude ◽  
Degrees Of Freedom ◽  
Mode Shapes ◽  
Nonlinear Load ◽  
Large Amplitude Motions ◽  
Rigid Body Modes ◽  
The Time Domain

The concept of "generalized modes" is to describe all degrees of freedom by mode shapes and not using any predefined shape, like rigid body modes. Generalized modes in seakeeping computations allow one to calculate the response of a single ship, springing, whipping, multibody interaction, etc., using a uniform approach. The generalized modes have already been used for frequency-domain seakeeping calculations by various authors. This article extents the generalized modes methodology to be used for time-domain seakeeping computations, which accounts for large-amplitude motions of the rigid-body modes. The time domain can be desirable for seakeeping computations because it is easy to include nonlinear load components and to compute transient response, like slamming and whipping. Results of multibody interaction, two barges connected by a hinge, whipping response of a ferry resulting from slamming loads, and the response of a flexible barge are presented to illustrate the theory.

BDS: A Knowledge-Based Bumper Design System

1997 ◽  
Author(s):  
Beverly J. Becker ◽  
Gregory A. Kaepp
Keyword(s):  
Software Design ◽  
Product Performance ◽  
Design System ◽  
Design Knowledge ◽  
Performance Requirement ◽  
Knowledge Based ◽  
Design Engineers ◽  
Design Alternatives ◽  
Design Requirements ◽  
Knowledge Based Engineering

Abstract A knowledge-based Bumper Design System (BDS) has been developed which automatically generates optimized conceptual bumper beams which meet manufacturing and product performance requirement. The BDS has captured and refined the corporate design knowledge of the product design engineer, the CAD designer, the CAE analyst and manufacturer. The BDS enables the bumper design engineers to evaluate multiple design alternatives quickly and early in the design process. It also automates repetitive bumper analysis tasks. The purpose of the paper is to describe the BDS. A description of the Knowledge Based Engineering (KBE) methodology used to create the BDS is given, as well as an overview of bumper designs and design requirements. An overview of the BDS software design, user interface, and a sample run are also presented.

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.

Receptance Series for Systems Possessing “Rigid Body” Modes

1962 ◽  
Vol 66 (618) ◽  
pp. 394-397 ◽  
Author(s):  
G. M. L. Gladwell ◽  
R. E. D. Bishop ◽  
D. C. Johnson
Keyword(s):  
Rigid Body ◽  
Natural Frequencies ◽  
Series Representation ◽  
Forced Vibrations ◽  
Rigid Bodies ◽  
Points Of Interest ◽  
Elastic Systems ◽  
Rigid Body Modes ◽  
Simple Systems

SummaryCertain elastic systems may not only vibrate freely at proper (non-zero) natural frequencies, but may also move as rigid bodies. Such systems have “rigid body” modes which behave like principal modes corresponding to zero natural frequencies. These modes may be disregarded in the series representation of static distortions of such systems but must be taken into account in the representation of forced vibrations.This note is concerned with the series representation of receptances of certain simple systems of this type, namely strings, bars, shafts and beams. These systems were discussed in reference 1, but there the rigid body modes were omitted. As the matter appears to raise some points of interest, a discussion of it seems to be called for. A similar analysis to that presented here may be applied to other unsupported, or partially supported systems, such as an unsupported plate.

Validation of Measured Dynamic Data Using Rigid Body Response

2012 ◽  
Vol 55 (1) ◽  
pp. 25-39
Author(s):  
David Smallwood
Keyword(s):  
Rigid Body ◽  
Low Frequency ◽  
Linear Combinations ◽  
Resonant Frequencies ◽  
Low Frequencies ◽  
Spectral Density Matrix ◽  
Rigid Body Modes ◽  
Linear Fit ◽  
Value Decomposition ◽  
Body Response

As multiple axis vibration testing has become more widespread, it has become increasingly important to ensure the instrumentation is accurately portrayed in the instrumentation table. However, errors do occur. The method used in this paper to help uncover these errors is based on the condition that at low frequencies (below any resonant frequencies of the object being studied) the response is essentially rigid body. The spectral density matrix (SDM) at a low frequency, of many more than six response measurements, is decomposed using singular value decomposition (SVD). Under the assumption of rigid body response, it is assumed that the first six singular vectors are linear combinations of the six rigid body modes. The best linear fit is then calculated for this fit. The measurements are then removed one at a time, and the reduction in the fit error is calculated. It is assumed that if the removal of a measurement reduces the error significantly, that measurement is likely in error.

Research on Mechanical Manufacturing with Creative Design and Combination of 3D Mechanical Manipulator Based on Fischertechnik

2014 ◽  
Vol 910 ◽  
pp. 366-369 ◽  
Author(s):  
Zhu Tao ◽  
Tao Wu ◽  
Chun Hua He
Keyword(s):  
Teaching Experiment ◽  
Creative Design ◽  
Engineering Applications ◽  
Design Intent ◽  
Combination Model ◽  
Production Practice ◽  
Design Requirements

This paper describes the design, composition and application of Fischer creative model. Combined with production practice, the Fischertechnik model is used to establish the structure of the 3D manipulator system. The results of model meet design requirements. Practice shows that the application of Fischer creative combination model is quickly and easily to build medium-sized machinery and equipment. It significantly reduces the build cycle and system debug, which could help designers quickly implement a variety of design intent and improvements. Fischer creative mix model plays an important role in teaching experiment and engineering applications.

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