scholarly journals Characterisation of Frenet–Serret and Bishop motions with applications to needle steering

Robotica ◽  
2013 ◽  
Vol 31 (6) ◽  
pp. 981-992 ◽  
Author(s):  
J. M. Selig
Keyword(s):  
Constant Curvature ◽  
Computer Aided Design ◽  
Kinematic Model ◽  
Tangent Vector ◽  
Moving Frame ◽  
Needle Steering ◽  
Potential Applications ◽  
Rigid Body Motions ◽  
Frame Motion ◽  
Aided Design

SUMMARYFrenet–Serret and Bishop rigid-body motions have many potential applications in robotics, graphics and computer-aided design. In order to study these motions, new characterisations in terms of their velocity twists are derived. This is extended to general motions based on any moving frame to a space curve. Furthermore, it is shown that any such general moving frame motion is the product of a Frenet–Serret motion with a rotation about the tangent vector.These ideas are applied to a simple model of needle steering. A simple kinematic model of the path of the needle is derived. It is then shown that this leads to Frenet–Serret motions of the needle tip but with constant curvature. Finally, some remarks about curves with constant curvature are made.

scholarly journals Monitoring Alveolar Ridge Remodelling Post-Extraction Using Sequential Intraoral Scanning over a Period of Four Months

2020 ◽  
Vol 17 (18) ◽  
pp. 6638
Author(s):  
Khaled E. Ahmed
Keyword(s):  
Computer Aided Design ◽  
Three Dimensional ◽  
Dimensional Changes ◽  
Intraoral Scanning ◽  
Computer Aided ◽  
Potential Applications ◽  
Cad Cam ◽  
Aided Design ◽  
2D And 3D

The potential applications of computer-aided design/computer-aided manufacturing (CAD/CAM) and intraoral scanning exceed the delivery of standard prosthodontic interventions. The aim of this study was to clinically present a developed assessment technique, that relies on the use of sequential intraoral scanning, three-dimensional superimposition, and 2D and 3D deviation analyses based on a standardised protocol, as an auxiliary tool in monitoring dimensional changes of residual ridge post-extraction with a follow-up period of four months.

A Method of Determining the Direction of Two Dimensional Curves

2014 ◽  
Vol 980 ◽  
pp. 159-164
Author(s):  
F. Wang ◽  
R.K.F. Abdelmaguid ◽  
H.M.A. Hussein
Keyword(s):  
Computer Aided Design ◽  
Tangent Vector ◽  
Two Dimensional ◽  
Linear Algorithm ◽  
Complete Cycle ◽  
Angular Change ◽  
Computer Aided ◽  
Aided Design ◽  
Relationship Of

Two-dimensional curves are represented by a list of vertices and other parameters that control the shape or curvature of the segments. In computer programming to deal with closed two-dimensional curves, it is often required to know the direction of the curve, which is reflected by the sequence of the vertex data. It can be anticlockwise or clockwise. This paper presents a robust, linear algorithm to determine the direction of a closed two-dimensional curve, by computing the total angular change of a tangent vector travelling along the curve for a complete cycle. A new, robust linear algorithm is proposed for the determination of the positional relationship of a point to a two-dimensional curve. For curves that consist of line and arc segments, which are most commonly used in engineering applications in computer aided design, the paper presents algorithms and procedures for solving the above problems.

Single-Vertex Multicrease Rigid Origami With Nonzero Thickness and Its Transformation Into Deployable Mechanisms

2017 ◽  
Vol 10 (1) ◽  
Author(s):  
Chenhan Guang ◽  
Yang Yang
Keyword(s):  
Computer Aided Design ◽  
Screw Theory ◽  
Kinematic Model ◽  
Degree Of Freedom ◽  
Single Vertex ◽  
Geometrical Characteristics ◽  
Computer Aided ◽  
Deployable Mechanism ◽  
Aided Design ◽  
Basic Configuration

The radial folding ratio of single-vertex multicrease rigid origami, from the folded configuration to the unfolded configuration, is satisfactory. In this study, we apply two approaches to add nonzero thickness for this kind of origami and identify different geometrical characteristics. Then, the model of the secondary folding origami, which can help to further decrease the folding ratio, is constructed. We apply the method of constraining the edges of the panels on prescribed planes to geometrically obtain the kinematic model. Based on the kinematic model and the screw theory, the nonzero thickness origami is transformed into the deployable mechanism with one degree-of-freedom (1DOF). Other similar mechanisms can be derived based on this basic configuration. The computer-aided design examples are presented to indicate the feasibility.

scholarly journals An advanced GCode analyser for predicting the build time for additive manufacturing components

ACTA IMEKO ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 30
Author(s):  
Luca Di Angelo ◽  
Paolo Di Stefano ◽  
Emanuele Guardiani
Keyword(s):  
Additive Manufacturing ◽  
Computer Aided Design ◽  
Object Oriented ◽  
Accurate Method ◽  
Physical Models ◽  
Production Costs ◽  
Design Data ◽  
Build Time ◽  
Potential Applications ◽  
Aided Design

<p class="Abstract">Additive manufacturing is a technology for quickly fabricating physical models, functional prototypes, and small batches of parts by stacking two-dimensional layered features directly from computer-aided design data. One of the most important challenges in this sector relates to the capability to predict the build time in advance, since this is crucial to evaluating the production costs. In this paper, an accurate method for obtaining build-time is proposed. This method is based on an advanced GCode analyzer written in Python following an object-oriented paradigm for scalability and maintainability. Various examples are used to demonstrate the reliability of the algorithm, while its potential applications are also illustrated.</p>

Local Least Squares Fitting for Surface Mesh Fairing in Automobile Panel Design

2002 ◽  
Author(s):  
Miguel Vieira ◽  
Kenji Shimada ◽  
Tomotake Furuhata
Keyword(s):  
Least Squares ◽  
Constant Curvature ◽  
Computer Aided Design ◽  
Laser Scanning ◽  
Linear Time ◽  
Local Coordinate System ◽  
Three Dimensional ◽  
Laser Scanners ◽  
Automobile Panel ◽  
Aided Design

Three-dimensional laser scanning equipment is being used more frequently to convert clay model automobile designs to large, detailed meshes for computer-aided design of outer-body panels. The panels are generally composed of large, constant curvature patches with small local features, called character lines, superposed to give the car a distinctive look. Although modern laser scanners are very accurate and precise, their tolerances nevertheless admit meshes with geometric flaws that destroy the constant curvature of patches and make character lines nearly invisible in a reflection simulation. Thus, we require an algorithm to fair the mesh by restoring the intended curvature while minimizing the vertex displacemtents. Existing approaches such as Laplacian and curvature flow operators are not suitable because they tend to shrink the mesh and introduce a bias toward planar geometries. Our approach aims to solve both of these problems by fitting a least squares surface to a set of vertices adjacent to the target vertex and moving the target vertex vertically onto the least squares surface in a local coordinate system. This algorithm has linear time complexity in the number of vertices and makes convergence likely while eliminating the planar bias of other operators. We show the effectiveness of our operator with both geometric and real-world mesh examples.

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