scholarly journals Modeling of Free-Form Complex Curves Using SG-Bézier Curves with Constraints of Geometric Continuities

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 545 ◽  
Author(s):  
Gang Hu ◽  
Cuicui Bo ◽  
Junli Wu ◽  
Guo Wei ◽  
Fei Hou
Keyword(s):  
Computer Aided Design ◽  
Sufficient Conditions ◽  
Free Form ◽  
Product Modeling ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Form Complex ◽  
Complex Curves ◽  
Computer Aided ◽  
Cad Cam

The modeling of free-form engineering complex curves is an important subject in product modeling, graphics, and computer aided design/computer aided manufacturing (CAD/CAM). In this paper, we propose a novel method to construct free-form complex curves using shape-adjustable generalized Bézier (or SG-Bézier, for short) curves with constraints of geometric continuities. In order to overcome the difficulty that most of the composite curves in engineering cannot often be constructed by using only a single curve, we propose the necessary and sufficient conditions for G1 and G2 continuity between two adjacent SG-Bézier curves. Furthermore, the detailed steps of smooth continuity for two SG-Bézier curves, and the influence rules of shape parameters on the composite curves, are studied. We also give some important applications of SG-Bézier curves. The modeling examples show that our methods in this paper are very effective, can easily be performed, and can provide an alternative powerful strategy for the design of complex curves.

Algorithmen-basierte Freiformflächenstrukturierung/Generation of NC programs for the micromilling structuring of free-form surfaces – Algorithm-based free-form surface structuring

2021 ◽  
Vol 111 (11-12) ◽  
pp. 797-802
Author(s):  
Leonhard Alexander Meijer ◽  
Torben Merhofe ◽  
Timo Platt ◽  
Dirk Biermann
Keyword(s):  
Computer Aided Design ◽  
Computational Effort ◽  
Free Form ◽  
Process Chain ◽  
Surface Structuring ◽  
Computer Aided ◽  
Cad Cam ◽  
Free Form Surface ◽  
Aided Design ◽  
Free Form Surfaces

In diesem Beitrag wird ein neuer Ansatz zum Erstellen von Maschinenprogrammen zur mikrofrästechnischen Oberflächenstrukturierung vorgestellt und die Anwendung der Prozesskette für ein komplexes, industrielles Verzahnungswerkzeug beschrieben. Durch die Reduzierung des Berechnungsaufwandes in der CAD/CAM (Computer-aided Design & Manufacturing)-Umgebung können die Limitierungen konventioneller Softwarelösungen umgangen und Bearbeitungsprogramme für komplexe Strukturierungsaufgaben effizient erstellt werden.   A new method for generating machine programs for micromilling surface structuring is presented, and the application of the process chain to a complex, industrial gearing die is described. By reducing the computational effort in the CAD/CAM (Computer-aided Design & Manufacturing) environment, the problems of conventional software solutions can be avoided and complex machining programs can be created.

scholarly journals Explicit Continuity Conditions for G1 Connection of S-λ Curves and Surfaces

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1359 ◽  
Author(s):  
Gang Hu ◽  
Huinan Li ◽  
Muhammad Abbas ◽  
Kenjiro T. Miura ◽  
Guoling Wei
Keyword(s):  
Computer Aided Design ◽  
Linear Independence ◽  
Basis Functions ◽  
Geometric Continuity ◽  
Complex Curves ◽  
Curves And Surfaces ◽  
Computer Aided ◽  
Cad Cam ◽  
Geometric Representations ◽  
Aided Design

The S-λ model is one of the most useful tools for shape designs and geometric representations in computer-aided geometric design (CAGD), which is due to its good geometric properties such as symmetry, shape adjustable property. With the aim to solve the problem that complex S-λ curves and surfaces cannot be constructed by a single curve and surface, the explicit continuity conditions for G1 connection of S-λ curves and surfaces are investigated in this paper. On the basis of linear independence and terminal properties of S-λ basis functions, the conditions of G1 geometric continuity between two adjacent S-λ curves and surfaces are proposed, respectively. Modeling examples imply that the continuity conditions proposed in this paper are easy and effective, which indicate that the S-λ curves and surfaces can be used as a powerful supplement of complex curves and surfaces design in computer aided design/computer aided manufacturing (CAD/CAM) system.

Morphological Offset Computing for Contour Pocketing

2006 ◽  
Vol 129 (2) ◽  
pp. 400-406 ◽  
Author(s):  
R. Molina-Carmona ◽  
A. Jimeno ◽  
R. Rizo-Aldeguer
Keyword(s):  
Computer Aided Design ◽  
Tool Path ◽  
Free Form ◽  
Computer Aided Manufacturing ◽  
Theoretical Formulation ◽  
Topological System ◽  
Computer Aided ◽  
Cad Cam ◽  
Tool Shape ◽  
Aided Design

Background. Tool path generation problem is one of the most complexes in computer aided manufacturing. Although some efficient algorithms have been developed to solve it, their technological dependency makes them efficient in only a limited number of cases. Method of Approach. Our aim is to propose a model that will set apart the geometrical issues involved in the manufacturing process from the purely technology-dependent physical issues by means of a topological system. This system applies methods and concepts used in mathematical morphology paradigms. Thus, we will obtain a geometrical abstraction which will not only provide solutions to typically complex problems but also the possibility of applying these solutions to any machining environment regardless of the technology. Presented in the paper is a method for offsetting any kind of curve. Specifically, we use parametric cubic curves, which is one of the most general and popular models in computer aided design (CAD)/computer aided manufacturing (CAM) applications. Results. The resulting method avoids any constraint in object or tool shape and obtains valid and optimal trajectories, with a low temporal cost of O(n∙m), which is corroborated by the experiments. It also avoids some precision errors that are present in the most popular commercial CAD/CAM libraries. Conclusions. The use of morphology as the base of the formulation avoids self-intersections and discontinuities and allows the system to machine free-form shapes using any tool without constraints. Most numerical and geometrical problems are also avoided. Obtaining a practical algorithm from the theoretical formulation is straightforward. The resulting procedure is simple and efficient.

Regularity of Bézier Curves

2011 ◽  
Vol 48-49 ◽  
pp. 877-880
Author(s):  
Qing Xian Meng ◽  
Hui Li Liu
Keyword(s):  
Computer Aided Design ◽  
Practical Method ◽  
Singular Points ◽  
Algebraic Equations ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Computer Aided ◽  
Aided Design ◽  
Zero Points ◽  
Isolation Theorem

Regularity is one of important properties of curves in computer aided design. In this paper, we convert the problem of determining regularity of Bézier curves to that of detecting existence of zero points of polynomials. Based on the properties of algebraic equations and isolation theorem of roots, a simple and practical method is presented. Regularity of Bézier curves and number of singular points can be determined by easier computation.

scholarly journals Curve and surface construction based on the generalized toric-Bernstein basis functions

2020 ◽  
Vol 18 (1) ◽  
pp. 36-56 ◽  
Author(s):  
Jing-Gai Li ◽  
Chun-Gang Zhu
Keyword(s):  
Computer Aided Design ◽  
Geometric Modeling ◽  
Basis Functions ◽  
Bernstein Basis ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Parametric Curve ◽  
Curves And Surfaces ◽  
Computer Aided ◽  
Bernstein Basis Functions

Abstract The construction of parametric curve and surface plays an important role in computer aided geometric design (CAGD), computer aided design (CAD), and geometric modeling. In this paper, we define a new kind of blending functions associated with a real points set, called generalized toric-Bernstein (GT-Bernstein) basis functions. Then, the generalized toric-Bézier (GT-Bézier) curves and surfaces are constructed based on the GT-Bernstein basis functions, which are the projections of the (irrational) toric varieties in fact and the generalizations of the classical rational Bézier curves/surfaces and toric surface patches. Furthermore, we also study the properties of the presented curves and surfaces, including the limiting properties of weights and knots. Some representative examples verify the properties and results.

scholarly journals Parametric Model for Kitchen Product Based on Cubic T-Bézier Curves with Symmetry

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 505
Author(s):  
Xin Sun ◽  
Xiaomin Ji
Keyword(s):  
Computer Aided Design ◽  
Parametric Method ◽  
Design Stage ◽  
Shape Parameters ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Cad Cam ◽  
G2 Continuity ◽  
Kitchen Cabinet ◽  
Aided Design

The parametric method of product design is a pivotal and practical technique in computer-aided design and manufacturing (CAD/CAM) and used in many manufacturing sectors. In this paper, we presented a novel parametric method to design a kitchen product in the residential environment, a kitchen cabinet, by using cubic T-Bézier curves with constraints of geometric continuities. First, we introduced a class of cubic T-Bézier curves with two shape parameters and derived the G1 and G2 continuity conditions of the cubic T-Bézier curves. Then, we constructed shape-controlled complex contour curves of the kitchen cabinet by using closed composite cubic T-Bézier curves. The shapes of the contour curves can be adjusted intuitively and predictably by altering the values of the shape parameters. Finally, we studied shape optimization and representation of ellipses for the contour curves of the kitchen cabinet by finding optimal shape parameters and applicable control points respectively. The provided modeling examples showed that our method in this paper can improve the design and scheme adjustment effectively in the conceptual design stage of kitchen products.

Structural Analysis of Product and Computer-Aided Assembly Planning in AssemBL Software Package

2018 ◽  
pp. 11-33
Author(s):  
A. N. Bozhko
Keyword(s):  
Computer Aided Design ◽  
State Of The Art ◽  
Graph Model ◽  
Design System ◽  
Assembly Planning ◽  
Complex Products ◽  
Assembly Sequences ◽  
Computer Aided ◽  
Cad Cam ◽  
Aided Design

Computer-aided design of assembly processes (Computer aided assembly planning, CAAP) of complex products is an important and urgent problem of state-of-the-art information technologies. Intensive research on CAAP has been underway since the 1980s. Meanwhile, specialized design systems were created to provide synthesis of assembly plans and product decompositions into assembly units. Such systems as ASPE, RAPID, XAP / 1, FLAPS, Archimedes, PRELEIDES, HAP, etc. can be given, as an example. These experimental developments did not get widespread use in industry, since they are based on the models of products with limited adequacy and require an expert’s active involvement in preparing initial information. The design tools for the state-of-the-art full-featured CAD/CAM systems (Siemens NX, Dassault CATIA and PTC Creo Elements / Pro), which are designed to provide CAAP, mainly take into account the geometric constraints that the design imposes on design solutions. These systems often synthesize technologically incorrect assembly sequences in which known technological heuristics are violated, for example orderliness in accuracy, consistency with the system of dimension chains, etc.An AssemBL software application package has been developed for a structured analysis of products and a synthesis of assembly plans and decompositions. The AssemBL uses a hyper-graph model of a product that correctly describes coherent and sequential assembly operations and processes. In terms of the hyper-graph model, an assembly operation is described as shrinkage of edge, an assembly plan is a sequence of shrinkages that converts a hyper-graph into the point, and a decomposition of product into assembly units is a hyper-graph partition into sub-graphs.The AssemBL solves the problem of minimizing the number of direct checks for geometric solvability when assembling complex products. This task is posed as a plus-sum two-person game of bicoloured brushing of an ordered set. In the paradigm of this model, the brushing operation is to check a certain structured fragment for solvability by collision detection methods. A rational brushing strategy minimizes the number of such checks.The package is integrated into the Siemens NX 10.0 computer-aided design system. This solution allowed us to combine specialized AssemBL tools with a developed toolkit of one of the most powerful and popular integrated CAD/CAM /CAE systems.

scholarly journals Fracture Load of Metal, Zirconia and Polyetheretherketone Posterior CAD-CAM Milled Fixed Partial Denture Frameworks

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 959
Author(s):  
Verónica Rodríguez ◽  
Celia Tobar ◽  
Carlos López-Suárez ◽  
Jesús Peláez ◽  
María J. Suárez
Keyword(s):  
Computer Aided Design ◽  
Testing Machine ◽  
Fracture Load ◽  
Fracture Pattern ◽  
Bending Test ◽  
Weibull Statistics ◽  
Promising Alternative ◽  
Computer Aided ◽  
Cad Cam ◽  
Group 2

The aim of this study was to investigate the load to fracture and fracture pattern of prosthetic frameworks for tooth-supported fixed partial dentures (FPDs) fabricated with different subtractive computer-aided design and computer-aided manufacturing (CAD-CAM) materials. Materials and Methods: Thirty standardized specimens with two abutments were fabricated to receive three-unit posterior FDP frameworks with an intermediate pontic. Specimens were randomly divided into three groups (n = 10 each) according to the material: group 1 (MM)—milled metal; group 2 (L)—zirconia; and group 3 (P)—Polyetheretherketone (PEEK). The specimens were thermo-cycled and subjected to a three-point bending test until fracture using a universal testing machine (cross-head speed: 1 mm/min). Axial compressive loads were applied at the central fossa of the pontics. Data analysis was made using one-way analysis of variance, Tamhane post hoc test, and Weibull statistics (α = 0.05). Results: Significant differences were observed among the groups for the fracture load (p < 0.0001). MM frameworks showed the highest fracture load values. The PEEK group registered higher fracture load values than zirconia samples. The Weibull statistics corroborated these results. The fracture pattern was different among the groups. Conclusions: Milled metal provided the highest fracture load values, followed by PEEK, and zirconia. However, all tested groups demonstrated clinically acceptable fracture load values higher than 1000 N. PEEK might be considered a promising alternative for posterior FPDs.

scholarly journals Evaluation of the Feasibility of NaCaPO4-Blended Zirconia as a New CAD/CAM Material for Dental Restoration

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3819
Author(s):  
Ting-Hsun Lan ◽  
Yu-Feng Chen ◽  
Yen-Yun Wang ◽  
Mitch M. C. Chou
Keyword(s):  
Computer Aided Design ◽  
Optical Microscope ◽  
Dental Restoration ◽  
Numerical Control ◽  
Test Results ◽  
Cnc Machine ◽  
Computer Aided ◽  
Cad Cam ◽  
Aided Design ◽  
Better Than

The computer-aided design/computer-aided manufacturing (CAD/CAM) fabrication technique has become one of the hottest topics in the dental field. This technology can be applied to fixed partial dentures, removable dentures, and implant prostheses. This study aimed to evaluate the feasibility of NaCaPO4-blended zirconia as a new CAD/CAM material. Eleven different proportional samples of zirconia and NaCaPO4 (xZyN) were prepared and characterized by X-ray diffractometry (XRD) and Vickers microhardness, and the milling property of these new samples was tested via a digital optical microscope. After calcination at 950 °C for 4 h, XRD results showed that the intensity of tetragonal ZrO2 gradually decreased with an increase in the content of NaCaPO4. Furthermore, with the increase in NaCaPO4 content, the sintering became more obvious, which improved the densification of the sintered body and reduced its porosity. Specimens went through milling by a computer numerical control (CNC) machine, and the marginal integrity revealed that being sintered at 1350 °C was better than being sintered at 950 °C. Moreover, 7Z3N showed better marginal fit than that of 6Z4N among thirty-six samples when sintered at 1350 °C (p < 0.05). The milling test results revealed that 7Z3N could be a new CAD/CAM material for dental restoration use in the future.

scholarly journals Characterisation of the Filler Fraction in CAD/CAM Resin-Based Composites

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 1986
Author(s):  
Andreas Koenig ◽  
Julius Schmidtke ◽  
Leonie Schmohl ◽  
Sibylle Schneider-Feyrer ◽  
Martin Rosentritt ◽  
...  
Keyword(s):  
Computer Aided Design ◽  
Point Of View ◽  
Specific Information ◽  
Dental Resin ◽  
X Ray ◽  
Computer Aided ◽  
Cad Cam ◽  
Filler Fraction ◽  
The Individual ◽  
Aided Design

The performance of dental resin-based composites (RBCs) heavily depends on the characteristic properties of the individual filler fraction. As specific information regarding the properties of the filler fraction is often missing, the current study aims to characterize the filler fractions of several contemporary computer-aided design/computer-aided manufacturing (CAD/CAM) RBCs from a material science point of view. The filler fractions of seven commercially available CAD/CAM RBCs featuring different translucency variants were analysed using Scanning Electron Microscopy (SEM) with Energy Dispersive X-ray Spectroscopy (EDS), Micro-X-ray Computed Tomography (µXCT), Thermogravimetric Analysis (TG) and X-ray Diffractometry (XRD). All CAD/CAM RBCs investigated included midifill hybrid type filler fractions, and the size of the individual particles was clearly larger than the individual specifications of the manufacturer. The fillers in Shofu Block HC featured a sphericity of ≈0.8, while it was <0.7 in all other RBCs. All RBCs featured only X-ray amorphous phases. However, in Lava Ultimate, zircon crystals with low crystallinity were detected. In some CAD/CAM RBCs, inhomogeneities (X-ray opaque fillers or pores) with a size <80 µm were identified, but the effects were minor in relation to the total volume (<0.01 vol.%). The characteristic parameters of the filler fraction in RBCs are essential for the interpretation of the individual material’s mechanical and optical properties.

Sign in / Sign up

Export Citation Format

Share Document