A Novel Three Dimensional Aircraft Wing Design Method Using High Order Bezier Curves

2016 ◽  
Author(s):  
Cheolmin Im
Keyword(s):  
Design Method ◽  
Three Dimensional ◽  
High Order ◽  
Wing Design ◽  
Aircraft Wing ◽  
Bezier Curves ◽  
Bézier Curves

scholarly journals Quaternionic Bézier curves, surfaces and volume

2013 ◽  
Vol 54 ◽  
Author(s):  
Severinas Zube
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Dimensional Subspace ◽  
Bezier Curves ◽  
Bézier Curves ◽  
The Real

We extended the rational Bézier construction for linear, bi-linear and threelinear map, by allowing quaternion weights. These objects are Möbius invariant and have halved degree with respect to the real parametrization. In general, these parametrizations are in four dimensional space. We analyse when a special the three-linear parametrized volume is in usual three dimensional subspace and gives three orthogonal family of Dupine cyclides.

scholarly journals Turbine blade profile design method using Bezier curves

2017 ◽  
Author(s):  
Vladimir Gribin ◽  
Aleksandr Tishchenko ◽  
Ilya Gavrilov ◽  
Victor Tishchenko ◽  
Ivan Sorokin ◽  
...  
Keyword(s):  
Turbine Blade ◽  
Design Method ◽  
Blade Profile ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Profile Design

Designing Three-Dimensional Directional Well Trajectories Using Bézier Curves

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
Jorge H. B. Sampaio
Keyword(s):  
Three Dimensional ◽  
Automated System ◽  
Hole Drilling ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Smooth Change ◽  
End Conditions ◽  
Planning Cycle ◽  
Three Space ◽  
End Set

A relatively simple, general, and very flexible method to design complex, three-dimensional hole trajectories can be obtained by using a 3D extension for Bézier curves. This approach offers superior results in terms of coding, use, and flexibility compared to other methods using double-arc, cubic functions, spline-in-tension functions, or constant curvature. The mathematics is surprisingly simple, and the method can be used to obtain trajectories for any of the four typical end conditions in terms of inclination and azimuth, namely: free-end, set-end, set-inclination/free azimuth, and free-inclination/set-azimuth. The resulting trajectories are smooth, with continuous and smooth change of curvature and toolface, better exploiting the expected delivery of modern rotary steerable deviation tools, particularly the point-the-bit and the push-the-bit systems. With the relevant parameters at any point of the trajectory (curvature and toolface angle) an automated system can steer the hole toward the defined targets in a smooth fashion. The beauty of the method is that the description of the trajectory is obtained with one single expression that handles the three space coordinates, instead of working with three separate coordinate functions. It uses a generalization of the well-known 2D Bézier curve. The concept is easy to understand, and implementation even using spreadsheets is straightforward. Besides, the conditions at both ends (coordinates and inclination/azimuth for set ends) the trajectory curve has up to two independent parameters. By playing suitably with these parameters, one can obtain a curve that favors the reduction of drag and torque during drilling, tripping, and casing running. In addition to the formulation for trajectory calculation, the paper presents the expressions to calculate the inclination, azimuth, curvature, and toolface at any point along the trajectory. Proper numerical examples illustrate the various end-conditions. The method can be used during the hole planning cycle as well as during the hole drilling for automatic and manual steerage.

scholarly journals Interpolation method for quaternionic-Bezier curves

2018 ◽  
Vol 59 ◽  
pp. 13-18
Author(s):  
Severinas Zube
Keyword(s):  
Interpolation Method ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Three Dimensional Space ◽  
Tangent Vectors

We study rational quaternionic-Bézier curves in three dimensional space. We construct the quadratic quaternionic-Bézier curve which interpolates five points, or three points and two tangent vectors.

scholarly journals Quaternion rational Bézier curves

2011 ◽  
Vol 52 ◽  
Author(s):  
Severinas Zube
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Dimensional Subspace ◽  
Space Curve ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Rational Bézier Curves

We extended the rational Bézier model for space curve, by allowing quaternion weights. These curves are Möbius invariant and have halved degree with respect to real Bézier curves. This simplify the analysis of curves. In general, these curves are in four dimensional space. We analyze when the quadratically parameterized quaternion curve is in usual three dimensional subspace.  

scholarly journals Off-line path programming for three-dimensional robotic friction stir welding based on Bézier curves

2018 ◽  
Vol 45 (5) ◽  
pp. 669-678 ◽  
Author(s):  
Komlan Kolegain ◽  
François Leonard ◽  
Sandra Chevret ◽  
Amarilys Ben Attar ◽  
Gabriel Abba
Keyword(s):  
Friction Stir Welding ◽  
Three Dimensional ◽  
Control Force ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Content Type ◽  
Friction Stir ◽  
Computer Aided ◽  
Position And Orientation ◽  
Robotic Friction Stir Welding

Purpose Robotic friction stir welding (RFSW) is an innovative process which enables solid-state welding of aluminum parts using robots. A major drawback of this process is that the robot joints undergo elastic deformation during the welding, because of the high forces induced by the process. This leads to tool deviation and incorrect orientation. There is currently no computer-aided manufacturing/computer-aided design (CAD) software for generating off-line paths which integrates robot deflections, and the main purpose of this study is to propose an off-line methodology to plan a path for RFSW with the integration of the deflections. Design/methodology/approach The approach is divided into two steps. The first step consists of extracting position and orientation data from CAD models of the workpieces and adding the deflections calculated with a deflection model to generate a suitable path for performing RFSW. The second step consists of the smooth fitting of the suitable path using Bézier curves. Findings The method is experimentally validated by welding a curved workpiece using a Kuka KR500-2MT robot. A suitable tool position and orientation were calculated to perform this welding, an experimental procedure was set up, a defect-free weld was performed and a high accuracy was achieved in terms of position and orientation. Practical implications This method can help manufacturers to easily perform RFSW for three-dimensional workpieces regardless of the lateral tool deviation, loss of the right orientation and control force stability. Originality/value The originality of this method lies in compensating for robot deflections without using expensive sensors, which is the most commonly used method for compensating for robot deflection. This off-line method can lead to a reduction in programming time in comparison with teach programming method and leads to reduced investment costs in comparison with commercial off-line programming packages.

scholarly journals Exploiting lattice structures in shape grammar implementations

2018 ◽  
Vol 32 (2) ◽  
pp. 147-161 ◽  
Author(s):  
Hau Hing Chau ◽  
Alison McKay ◽  
Christopher F. Earl ◽  
Amar Kumar Behera ◽  
Alan de Pennington
Keyword(s):  
Three Dimensional ◽  
Real Life ◽  
General Purpose ◽  
Three Dimensions ◽  
Shape Grammar ◽  
Shape Grammars ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Computation Process ◽  
Shape Computation

AbstractThe ability to work with ambiguity and compute new designs based on both defined and emergent shapes are unique advantages of shape grammars. Realizing these benefits in design practice requires the implementation of general purpose shape grammar interpreters that support: (a) the detection of arbitrary subshapes in arbitrary shapes and (b) the application of shape rules that use these subshapes to create new shapes. The complexity of currently available interpreters results from their combination of shape computation (for subshape detection and the application of rules) with computational geometry (for the geometric operations need to generate new shapes). This paper proposes a shape grammar implementation method for three-dimensional circular arcs represented as rational quadratic Bézier curves based on lattice theory that reduces this complexity by separating steps in a shape computation process from the geometrical operations associated with specific grammars and shapes. The method is demonstrated through application to two well-known shape grammars: Stiny's triangles grammar and Jowers and Earl's trefoil grammar. A prototype computer implementation of an interpreter kernel has been built and its application to both grammars is presented. The use of Bézier curves in three dimensions opens the possibility to extend shape grammar implementations to cover the wider range of applications that are needed before practical implementations for use in real life product design and development processes become feasible.

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