scholarly journals Approximation of Generalized Ovals and Lemniscates towards Geometric Modeling

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3325
Author(s):  
Valery Ochkov ◽  
Inna Vasileva ◽  
Ekaterina Borovinskaya ◽  
Wladimir Reschetilowski
Keyword(s):  
Computer Aided Design ◽  
Geometric Modeling ◽  
Three Dimensional ◽  
Numerical Data ◽  
Closed Curves ◽  
B Splines ◽  
Three Dimensional Modeling ◽  
Dimensional Modeling ◽  
High Smoothness ◽  
Aided Design

This paper considers an approach towards the building of new classes of symmetric closed curves with two or more focal points, which can be obtained by generalizing classical definitions of the ellipse, Cassini, and Cayley ovals. A universal numerical method for creating such curves in mathematical packages is introduced. Specific aspects of the provided numerical data in computer-aided design systems with B-splines for three-dimensional modeling are considered. The applicability of the method is demonstrated, as well as the possibility to provide high smoothness of the curvature profile at the specified accuracy of modeling.

Engineering and Art

2017 ◽  
pp. 277-291
Author(s):  
Sara B. Smith
Keyword(s):  
Computer Aided Design ◽  
Engineering Students ◽  
Three Dimensional ◽  
First Year ◽  
Student Work ◽  
Three Dimensional Modeling ◽  
Dimensional Modeling ◽  
Engineering Design Process ◽  
Principles Of Design ◽  
Aided Design

This chapter per the author discusses challenges faced by first year pre-engineering students. Also discussed are several topics taught within the curriculum including: the engineering design process, sketching, measurement, the elements and principles of design, and three-dimensional modeling. The chapter proposes a design project for engineering students that would tie all of these concepts together to provide an additional learning opportunity for students and more relevant practice of skills like isometric sketching, creating three-dimensional computer-aided design models, and measurement. Samples of student work from the project are included.

Engineering and Art

2020 ◽  
pp. 258-273
Author(s):  
Sara B. Smith
Keyword(s):  
Computer Aided Design ◽  
Engineering Students ◽  
Three Dimensional ◽  
First Year ◽  
Student Work ◽  
Three Dimensional Modeling ◽  
Dimensional Modeling ◽  
Engineering Design Process ◽  
Principles Of Design ◽  
Aided Design

This chapter discusses challenges faced by first year pre-engineering students. Also discussed are several topics taught within the curriculum including: the engineering design process, sketching, measurement, the elements and principles of design, and three-dimensional modeling. The chapter proposes a design project for engineering students that would tie all of these concepts together to provide an additional learning opportunity for students and more relevant practice of skills like isometric sketching, creating three-dimensional computer-aided design models, and measurement. Samples of student work from the project are included.

scholarly journals Agustín de Betancourt’s Optical Telegraph: Geometric Modeling and Virtual Reconstruction

2020 ◽  
Vol 10 (5) ◽  
pp. 1857 ◽  
Author(s):  
José Ignacio Rojas-Sola ◽  
Eduardo De la Morena-De la Fuente
Keyword(s):  
3D Modeling ◽  
Geometric Modeling ◽  
3D Model ◽  
18Th Century ◽  
Three Dimensional ◽  
Assembly System ◽  
Three Dimensional Modeling ◽  
Dimensional Modeling ◽  
Virtual Reconstruction ◽  
History Of

This article shows the geometric modeling and virtual reconstruction of the optical telegraph by Agustín de Betancourt and Abraham Louis Breguet developed at the end of the 18th century. Autodesk Inventor Professional software has been used to obtain the three-dimensional (3D) model of this historical invention and its geometric documentation. The material for the research is available on the website of the Betancourt Project of the Canary Orotava Foundation for the History of Science. Thanks to the three-dimensional modeling performed, it has been possible to explain in detail both its operation and the assembly system of this invention in a coherent way. After carrying out its 3D modeling and functional analysis, it was discovered that the transmissions in the telegraph were not performed by hemp ropes but rather by metal chains with flat links, considerably reducing possible error. Similarly, it has also been found that the use of the gimbal joint facilitated the adaptability of the invention to geographical areas where there was a physical impediment to the alignment of telegraph stations. In addition, it was not now necessary for the telescope frames to be located parallel to the mast frame (frame of the indicator arrow) and therefore they could work in different planes.

Modeling in OpenSCAD: examples

2019 ◽  
Author(s):  
Alexander Bashkatov
Keyword(s):  
3D Printing ◽  
Science Teachers ◽  
Geometric Modeling ◽  
Three Dimensional ◽  
Federal State ◽  
Introductory Course ◽  
Three Dimensional Modeling ◽  
Dimensional Modeling ◽  
Graphical Data ◽  
State Educational

The tutorial is an introductory course to the study of the basics of geometric modeling for 3D printing using the programming language OpenSCAD and is built on the basis of descriptions of instructions for creating primitives, determining their properties, carrying out transformations and other service operations. It contains a large number of examples with detailed comments and description of the performed actions, which allows you to get basic skills in creating three-dimensional and flat models, exporting and importing graphical data. Meets the requirements of the Federal state educational standards of higher education of the last generation. It can be useful for computer science teachers, students, students and anyone who is interested in three-dimensional modeling and preparation of products for 3D printing.

Three-dimensional modeling and simulation of deformation behavior of fancy weft knitted stitch fabric

2016 ◽  
Vol 87 (14) ◽  
pp. 1742-1751 ◽  
Author(s):  
Sha Sha ◽  
Pibo Ma ◽  
Lisa Parrillo Chapman ◽  
Gaoming Jiang ◽  
Aijun Zhang
Keyword(s):  
Deformation Behavior ◽  
Scale Up ◽  
Three Dimensional ◽  
B Splines ◽  
Three Dimensional Modeling ◽  
Dimensional Modeling ◽  
Nurbs Curves ◽  
Weft Knitted Fabric ◽  
Spatial Coordinates ◽  
Pass Through

In order to obtain deformation behavior and volumetric characteristic of fancy weft knitted fabric, loop models are built on improved particle systems in this article. The problem of the non-uniform rational B-splines (NURBS) curves, which cannot pass through all control points, is solved by using an interpolation algorithm which can generate new auxiliary points. To simulate the twist of folded yarns, the NURBS curves are regarded as the geometric center, which is rotated with cylinders whose three relative Euler angles are calculated by the spatial coordinates of adjacent points. By analyzing the relationship between the deformation of the loop and the displacement of the particles, the deformation behavior of fancy weft knitted stitches is simulated. Velocity-Verlet, a numerical integration, is introduced to simulate fancy weft knitted stitches, and stable results are obtained. The results show that these models and algorithm accurately display the deformation behavior of fancy weft knitted stitches, as demonstrated by qualitative comparisons to measure the deformations of actual samples, and the simulator can scale up to animations with complex dynamic motion.

Computer-Aided Modeling and Manufacturing of Spherical Mechanisms via a Novel Web Tool

2007 ◽  
Vol 7 (4) ◽  
pp. 339-346 ◽  
Author(s):  
J. Schuler ◽  
J. Ketchel ◽  
P. Larochelle
Keyword(s):  
Dynamic Simulation ◽  
Computer Aided Design ◽  
Geometric Modeling ◽  
Three Dimensional ◽  
Software Tool ◽  
Web Based ◽  
Spherical Mechanisms ◽  
Computer Aided ◽  
Manufacturing Software ◽  
Aided Design

In this paper, we present a novel web-based computer-aided modeling and manufacturing software tool for spherical mechanisms. Our purpose is to facilitate the analysis, dynamic simulation, and manufacture of one degree of freedom spherical four-bar mechanisms. First, a brief review of some of the current computer-aided design software for spherical four-bar mechanisms is presented. These software packages provide the three-dimensional visualization and computational capabilities necessary to synthesize and analyze spherical four-bar mechanisms. However, to date, no readily available and effective tools exist to aid in the modeling and manufacture of spherical mechanisms. Next, the kinematics of spherical four-bar mechanisms are reviewed as they pertain to their geometric modeling and manufacture. Finally, we present our web-based implementation of a computer-aided modeling, simulation, and manufacturing methodology for spherical four-bar mechanisms called SFBDESIGNER (for spherical four-bar designer). SFBDESIGNER facilitates the design, dynamic simulation, prototyping, and manufacture of spherical four-bar mechanisms.

Dynamic Modelling of Blades Based on a Novel Curved Thin Walled Beam Theory

2018 ◽  
Author(s):  
Juan C. Jauregui ◽  
Diego Cardenas ◽  
Hugo Elizalde ◽  
Oliver Probst
Keyword(s):  
Computer Aided Design ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Dynamic Modelling ◽  
Beam Theory ◽  
General Description ◽  
B Splines ◽  
Out Of Plane ◽  
Thin Walled ◽  
Aided Design

There are several Thin-Walled Beam models for straight beams, but few TWB models consider beams with arbitrary curvatures. Although, a curved beam can be modelled using finite elements, the number of degrees of freedom is too large and a nonlinear dynamic solution is very cumbersome, if not impossible. In this work, a general description of arbitrary three-dimensional curves, based on the Frenet-Serret field frame, is applied to determine the dynamic stresses in wing turbines blades. The dynamic model is developed using the Isogeometric Analysis (IGA) and the in plane and out-of-plane curvature’s gradients are found in an Euler-type formulation, allowing the treatment of cases with highly-curved geometry. An Isogeometrical (IGA) formulation relies on a linear combination of Non-Uniform Rational B-Splines (NURBS) to represent not just the model’s geometry, a standard practice in most Computer-Aided Design (CAD) platforms, but also the unknown solution field of each sought variable. For the unified model hitherto described, these variables are represented by a NURBS curve.

Right ventricular function and three-dimensional modeling using computer-aided design

1990 ◽  
Vol 68 (4) ◽  
pp. 1707-1716 ◽  
Author(s):  
F. G. Spinale ◽  
B. A. Carabello ◽  
F. A. Crawford
Keyword(s):  
Right Ventricular ◽  
Computer Aided Design ◽  
Three Dimensional ◽  
Three Dimensional Modeling ◽  
Computer Aided ◽  
Dimensional Reconstruction ◽  
Three Dimensional Models ◽  
New Perspective ◽  
Highly Correlated ◽  
Aided Design

Right ventricular (RV) volumetric and morphological analysis is complicated by the trabeculations and geometric configuration of the RV chamber. To improve RV analysis, custom computer-aided design programs were employed to obtain RV volumes and three-dimensional models from biplane ventriculograms. Biplane RV ventriculograms were analyzed from 14 anesthetized dogs and 22 RV casts. Computed volumes were highly correlated with reference RV volumes (r = 0.98, n = 36, P less than 0.01) with a range of 5-73 ml. Three-dimensional wire-frame and solid models constructed from the ventriculographic images provided excellent detail and a new perspective in chamber shape. This modeling technique was then used to examine RV volumes, geometric conformation, and regional shortening in 10 pigs during inotropic stimulation and preload reduction. Changes in RV volumes, ejection fraction, and regional motion were detected as well as alterations in chamber conformation. In summary 1) computer-aided design offers an accurate and simplified means to compute RV volumes using basic microcomputer equipment, and 2) three-dimensional reconstruction provided a unique view of RV geometry and a means to examine regional RV function.

SphinxCAM-Pro|E: Computer-Aided Modeling and Manufacturing of Spherical Mechanisms Via the Web

2006 ◽  
Author(s):  
Pierre M. Larochelle ◽  
Jason M. Schuler ◽  
John S. Ketchel
Keyword(s):  
Dynamic Simulation ◽  
Computer Aided Design ◽  
Geometric Modeling ◽  
Three Dimensional ◽  
Web Based ◽  
Modeling Simulation ◽  
Spherical Mechanisms ◽  
Software Packages ◽  
Computer Aided ◽  
Aided Design

In this paper we present a web-based computer-aided design modeling and manufacturing methodology for spherical mechanisms. Our purpose is to facilitate the analysis, dynamic simulation, and manufacture of one degree of freedom spherical four-bar mechanisms. First, a brief review of some of the current computer-aided design (CAD) software for spherical four-bar mechanisms, e.g. SPHINX, SPHINXPC, ISIS, and OSIRIS is presented. These software packages provide the three-dimensional visualization and computational capabilities necessary to design spherical four-bar mechanisms. However, to date no readily available and effective tools exist to aid in the modeling and manufacture of spherical mechanisms. Next, the kinematics of spherical four-bar mechanisms are reviewed as they pertain to their geometric modeling and manufacture. Finally, we present our web-based implementation of a computer-aided modeling, simulation, and manufacturing methodology for spherical four-bar mechanisms called SPHINXCAM-Pro|E. SPHINXCAM-Pro|E, when used with the CAD tools mentioned above, facilitates the design, dynamic simulation, prototyping, and manufacture of spherical four-bar mechanisms.

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