Movimientos simétrico lineales esféricos segmentados para interpolación de orientaciones en planificación de trayectorias de herramienta en CNC de 5 Ejes

RESUMEN: Este artículo emplea biarcos cuaterniónicos para interpolar un conjunto de orientaciones con restricciones de velocidad angular. La curva cuaterniónica resultante representa un movimiento simétrico lineal esférico segmentado con continuidad C1 . El propósito de este esfuerzo es poner en uso los movimientos simétrico lineales desde el punto de vista de aproximación e interpolación de movimiento y presentar su potencial aplicación en la simulación de mecanizado por Control Numérico Computarizado (CNC) y planeación de trayectorias de herramienta. Los biarcos cuaterniónicos pueden ser usados para aproximar curvas B-spline cuaterniónicas que representan movimientos esféricos racionales, los cuales tienen aplicaciones en planeación de trayectorias de robots, en CAD/CAM y en gráficas por computador.ABSTRACT: This paper employs quaternion biarcs to interpolate a set of orientations with angular velocity constraints. The resulting quaternion curve represents a piecewise line-symmetric spherical motion with C1 continuity. The purpose of this effort is to put line-symmetric motions into use from the viewpoint of motion approximation and interpolation, and to present their potential applications in Computerized Numerical Control (CNC) machining simulation and tool path planning. Quaternion biarcs may be used to approximate B-spline quaternion curves that represent rational spherical motions that have applications in robot path planning, CAD/CAM and computer graphics

Reliability-based G1 Continuous Arc Spline Approximation

In this paper, we present an algorithm to approximate a set of data points with G1 continuous arcs, using points' covariance data. To the best of our knowledge, previous arc spline approximation approaches assumed that all data points contribute equally (i.e. have the same weights) during the approximation process. However, this assumption may cause serious instability in the algorithm, if the collected data contains outliers. To resolve this issue, a robust method for arc spline approximation is suggested in this work, assuming that the 2D covariance for each data point is given. Starting with the definition of models and parameters for single arc approximation, the framework is extended to multiple-arc approximation for general usage. Then the proposed algorithm is verified using generated noisy data and real-world collected data via vehicle experiment in Sejong City, South Korea.Comment: 42 pages, 19 figures, Submitted to Computer Aided Geometric Desig

Control of Curvature Extrema in Curve Modeling

We present a method for constructing almost-everywhere curvature-continuous curves that interpolate a list of control points and have local maxima of curvature only at the control points. Our premise is that salient features of the curve should occur only at control points to avoid the creation of features unintended by the artist. While many artists prefer to use interpolated control points, the creation of artifacts, such as loops and cusps, away from control points has limited the use of these types of curves. By enforcing the maximum curvature property, loops and cusps cannot be created unless the artist intends to create such features. To create these curves, we analyze the curvature monotonicity of quadratic, rational quadratic and cubic curves and develop a framework to connect such curve primitives with curvature continuity. We formulate an energy to encode the desired properties in a boxed constrained optimization and provide a fast method of estimating the solution through a numerical optimization. The optimized curve can serve as a real-time curve modeling tool in art design applications

Toolpath Smoothing using Clothoids for High Speed CNC Machines

As a result of this research, new methods for CNC toolpath smoothing were developed. Utilising these methods can increase the speed, decrease vibrations and improve the cut quality of a CNC machine. In the developed techniques, Euler spirals have been used to smooth the corners