scholarly journals Symmetric Free Form Building Structures Arranged Regularly on Smooth Surfaces with Polyhedral Nets

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 763
Author(s):  
Jacek Abramczyk
Keyword(s):  
Three Dimensional ◽  
Free Form ◽  
Dimensional Euclidean Space ◽  
Building Structures ◽  
Steel Sheets ◽  
Corrugated Shell ◽  
Original Insight ◽  
Parametric Algorithms ◽  
Symmetric Structures ◽  
Regular Networks

The article is an original insight into interdisciplinary challenges of shaping innovative unconventional complex free form buildings roofed with multi-segment shell structures arranged with using novel parametric regular networks. The roof structures are made up of nominally plane thin-walled folded steel sheets transformed elastically and rationally into spatial shapes. A method is presented for creating such symmetric structures based on the regular spatial polyhedral networks created as a result of a composition of many complete reference tetrahedrons by their common flat sides and straight side edges arranged regularly and symmetrically in the three-dimensional Euclidean space. The use of the regularity and symmetry in the process of shaping different forms of (a) single tetrahedral meshes and whole consistent polyhedral structures, (b) individual plane walls and complex elevations, (c) single transformed folds, entire corrugated shell roofs, and their structures allow a creative search for attractive rational parametric solutions using a few author’s parametric algorithms and their implementation as built-in commands of the AutoCAD visual editor or applications of the Rhino/Grasshopper program.

scholarly journals Transformed Shell Structures Determined by Regular Networks as a Complex Material for Roofing

Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3582
Author(s):  
Jacek Abramczyk
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Shell Structures ◽  
Complex Material ◽  
Corrugated Shell ◽  
Construction Morphology ◽  
Specific Complex ◽  
Interdisciplinary Problems ◽  
Orthotropic Properties ◽  
Regular Networks

The article presents a comprehensive extension of the proprietary basic method for shaping innovative systems of corrugated shell roof structures by means of a specific complex material that comprises regular transformable shell units limited by spatial quadrangles. The units are made up of nominally plane folded sheets transformed into shell shapes. The similar shell units are regularly and effectively arranged in the three-dimensional space in an orderly manner with a universal regular reference surface, polyhedral network, and polygonal network. The extended method leads to the increase in the variety of the designed complex shell roof forms and plane-walled elevation forms of buildings. For this purpose, the rules governing the creation of the continuous roof shell structures of many shells arranged in different unconventional visually attractive patterns and their discontinuous regular modifications are sought. To obtain several novel groups of similar unconventional parametric roof forms, single division coefficients and double division coefficients are used. The easy and intuitive modifications of the positions of the vertices belonging to the polygonal network on the side edges of the polyhedral network accomplished by means of a parametric algorithm allow one to adjust the geometry of the complete shell units to the geometric and material constraints related to the orthotropic properties of the transformed sheeting by means of these coefficients. The innovative approach to the shaping of the diverse unconventional roof structures requires the solving of many interdisciplinary problems in the field of mathematics, civil engineering, construction, morphology, architecture, mechanics, computer visualization, and programming.

scholarly journals Two view NURBS reconstruction based on GACO model

2021 ◽  
Author(s):  
Deepika Saini ◽  
Sanoj Kumar ◽  
Manoj K. Singh ◽  
Musrrat Ali
Keyword(s):  
Optimization Algorithms ◽  
Three Dimensional ◽  
Optimization Procedure ◽  
Least Square ◽  
Ant Colony ◽  
Free Form ◽  
Reconstruction Process ◽  
Nurbs Curve ◽  
Data Points ◽  
Ant Colony Optimization Algorithms

AbstractThe key job here in the presented work is to investigate the performance of Generalized Ant Colony Optimizer (GACO) model in order to evolve the shape of three dimensional free-form Non Uniform Rational B-Spline (NURBS) curve using stereo (two) views. GACO model is a blend of two well known meta-heuristic optimization algorithms known as Simple Ant Colony and Global Ant Colony Optimization algorithms. Basically, the work talks about the solution of NURBS-fitting based reconstruction process. Therefore, GACO model is used to optimize the NURBS parameters (control points and weights) by minimizing the weighted least-square errors between the data points and the fitted NURBS curve. The algorithm is applied by first assuming some pre-fixed values of NURBS parameters. The experiments clearly show that the optimization procedure is a better option in a case where good initial locations of parameters are selected. A detailed experimental analysis is given in support of our algorithm. The implemented error analysis shows that the proposed methodology perform better as compared to the conventional methods.

scholarly journals Deciphering the Role of Residues Involved in Disorder-To-Order Transition Regions in Archaeal tRNA Methyltransferase 5

Genes ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 399
Author(s):  
Ambuj Srivastava ◽  
Dhanusha Yesudhas ◽  
Shandar Ahmad ◽  
M. Michael Gromiha
Keyword(s):  
Three Dimensional ◽  
Md Simulations ◽  
Order Transition ◽  
Free Form ◽  
Wild Type ◽  
Intrinsically Disordered ◽  
Intrinsically Disordered Regions ◽  
Type Complex ◽  
In The Wild ◽  
Trna Methyltransferase

tRNA methyltransferase 5 (Trm5) enzyme is an S-adenosyl methionine (AdoMet)-dependent methyltransferase which methylates the G37 nucleotide at the N1 atom of the tRNA. The free form of Trm5 enzyme has three intrinsically disordered regions, which are highly flexible and lack stable three-dimensional structures. These regions gain ordered structures upon the complex formation with tRNA, also called disorder-to-order transition (DOT) regions. In this study, we performed molecular dynamics (MD) simulations of archaeal Trm5 in free and complex forms and observed that the DOT residues are highly flexible in free proteins and become stable in complex structures. The energetic contributions show that DOT residues are important for stabilising the complex. The DOT1 and DOT2 are mainly observed to be important for stabilising the complex, while DOT3 is present near the active site to coordinate the interactions between methyl-donating ligands and G37 nucleotides. In addition, mutational studies on the Trm5 complex showed that the wild type is more stable than the G37A tRNA mutant complex. The loss of productive interactions upon G37A mutation drives the AdoMet ligand away from the 37th nucleotide, and Arg145 in DOT3 plays a crucial role in stabilising the ligand, as well as the G37 nucleotide, in the wild-type complex. Further, the overall energetic contribution calculated using MMPBSA corroborates that the wild-type complex has a better affinity between Trm5 and tRNA. Overall, our study reveals that targeting DOT regions for binding could improve the inhibition of Trm5.

scholarly journals Numerical Analysis of the Perforated Steel Sheets Under Uni-Axial Tensile Force

Metals ◽  
2019 ◽  
Vol 9 (6) ◽  
pp. 632 ◽  
Author(s):  
Ahmed M. Sayed
Keyword(s):  
Load Capacity ◽  
Tensile Force ◽  
Three Dimensional ◽  
Tensile Load ◽  
Experimental Tests ◽  
Strain Engineering ◽  
Uniaxial Tensile ◽  
Fe Model ◽  
Stress Strain ◽  
Steel Sheets

The perforated steel sheets have many uses, so they should be studied under the influence of the uniaxial tensile load. The presence of these holes in the steel sheets certainly affects the mechanical properties. This paper aims at studying the behavior of the stress-strain engineering relationships of the perforated steel sheets. To achieve this, the three-dimensional finite element (FE) model is mainly designed to investigate the effect of this condition. Experimental tests were carried out on solid specimens to be used in the test of model accuracy of the FE simulation. Simulation testing shows that the FE modeling revealed the ability to calculate the stress-strain engineering relationships of perforated steel sheets. It can be concluded that the effect of a perforated rhombus shape is greater than the others, and perforated square shape has no effect on the stress-strain engineering relationships. The efficiency of the perforated staggered or linearly distribution shapes with the actual net area on the applied loads has the opposite effect, as it reduces the load capacity for all types of perforated shapes. Despite the decrease in load capacity, it improves the properties of the steel sheets.

scholarly journals On a Question of Bourgain about Geometric Incidences

2008 ◽  
Vol 17 (4) ◽  
pp. 619-625 ◽  
Author(s):  
JÓZSEF SOLYMOSI ◽  
CSABA D. TÓTH
Keyword(s):  
Euclidean Space ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Geometric Incidences

Given a set of s points and a set of n2 lines in three-dimensional Euclidean space such that each line is incident to n points but no n lines are coplanar, we show that s = Ω(n11/4). This is the first non-trivial answer to a question recently posed by Jean Bourgain.

scholarly journals Orthogonal Isomorphic Representations Of Free Groups

1956 ◽  
Vol 8 ◽  
pp. 256-262 ◽  
Author(s):  
J. De Groot
Keyword(s):  
Euclidean Space ◽  
Free Groups ◽  
Three Dimensional ◽  
Rotation Group ◽  
Dimensional Euclidean Space ◽  
Orthogonal Matrices ◽  
Abelian Subgroups ◽  
Proper Orthogonal

1. Introduction. We consider the group of proper orthogonal transformations (rotations) in three-dimensional Euclidean space, represented by real orthogonal matrices (aik) (i, k = 1,2,3) with determinant + 1 . It is known that this rotation group contains free (non-abelian) subgroups; in fact Hausdorff (5) showed how to find two rotations P and Q generating a group with only two non-trivial relationsP2 = Q3 = I.

An Equivalent-Plane Cross-Coupling Position Control for Contour-Accuracy Improvement in Three-Axis Free-Form Contour Following Tasks

2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Jian-Wei Ma ◽  
De-Ning Song ◽  
Zhen-Yuan Jia ◽  
Wen-Wen Jiang ◽  
Fu-Ji Wang ◽  
...  
Keyword(s):  
Error Control ◽  
Position Control ◽  
Three Dimensional ◽  
Cross Coupling ◽  
Experimental Tests ◽  
Numerical Control ◽  
Free Form ◽  
Contouring Error ◽  
Contour Following ◽  
Better Than

To reduce the contouring errors in computer-numerical-control (CNC) contour-following tasks, the cross-coupling controller (CCC) is widely researched and used. However, most existing CCCs are well-designed for two-axis contouring and can hardly be generalized to compensate three-axis curved contour following errors. This paper proposes an equivalent-plane CCC scheme so that most of the two-axis CCCs or flexibly designed algorithms can be utilized for equal control of the three-axis contouring errors. An initial-value regeneration-based Newton method is first proposed to compute the foot point from the actual motion position to the desired contour with a high accuracy, so as to establish the equivalent plane where the estimated three-dimensional contouring-error vector is included. After that, the signed contouring error is computed in the equivalent plane, thus a typical two-axis proportional-integral-differential (PID)-based CCC is utilized for its control. Finally, the two-axis control commands generated by the typical CCC are coupled to three-axis control commands according to the geometry of the established equivalent plane. Experimental tests are conducted to verify the effectiveness of the presented method. The testing results illustrate that the proposed equivalent-plane CCC performs much better than conventional method in both error estimation and error control.

Kinesthetically Augmented Mid-Air Sketching of Multi-Planar 3D Curve-Soups

2018 ◽  
Author(s):  
Ronak R. Mohanty ◽  
Umema H. Bohari ◽  
Vinayak ◽  
Eric Ragan
Keyword(s):  
Force Feedback ◽  
Three Dimensional ◽  
Free Form ◽  
Manual Labor ◽  
3D Design ◽  
Planar Curves ◽  
Kinesthetic Feedback ◽  
Curve Modeling

We present haptics-enabled mid-air interactions for sketching collections of three-dimensional planar curves — 3D curve-soups — as a means for 3D design conceptualization. Haptics-based mid-air interactions have been extensively studied for modeling of surfaces and solids. The same is not true for modeling curves; there is little work that explores spatiality, tangibility, and kinesthetics for curve modeling, as seen from the perspective of 3D sketching for conceptualization. We study pen-based mid air interactions for free-form curve input from the perspective of manual labor, controllability, and kinesthetic feedback. For this, we implemented a simple haptics-enabled workflow for users to draw and compose collections of planar curves on a force-enabled virtual canvas. We introduce a novel force-feedback metaphor for curve drawing, and investigate three novel rotation techniques within our workflow for both controlled and free-form sketching tasks.

Gröbner basis and resultant method for the forward displacement of 3-DoF planar parallel manipulators in seven-dimensional kinematic space

Robotica ◽  
2015 ◽  
Vol 34 (11) ◽  
pp. 2610-2628 ◽  
Author(s):  
Davood Naderi ◽  
Mehdi Tale-Masouleh ◽  
Payam Varshovi-Jaghargh
Keyword(s):  
Euclidean Space ◽  
Gröbner Basis ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Dimensional Euclidean Space ◽  
Grobner Basis ◽  
Kinematic Space ◽  
Forward Kinematic Problem ◽  
Forward Kinematic

SUMMARYIn this paper, the forward kinematic analysis of 3-degree-of-freedom planar parallel robots with identical limb structures is presented. The proposed algorithm is based on Study's kinematic mapping (E. Study, “von den Bewegungen und Umlegungen,” Math. Ann.39, 441–565 (1891)), resultant method, and the Gröbner basis in seven-dimensional kinematic space. The obtained solution in seven-dimensional kinematic space of the forward kinematic problem is mapped into three-dimensional Euclidean space. An alternative solution of the forward kinematic problem is obtained using resultant method in three-dimensional Euclidean space, and the result is compared with the obtained mapping result from seven-dimensional kinematic space. Both approaches lead to the same maximum number of solutions: 2, 6, 6, 6, 2, 2, 2, 6, 2, and 2 for the forward kinematic problem of planar parallel robots; 3-RPR, 3-RPR, 3-RRR, 3-RRR, 3-RRP, 3-RPP, 3-RPP, 3-PRR, 3-PRR, and 3-PRP, respectively.

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