Rounding Spatial G-Code Tool Paths Using Pythagorean Hodograph Curves

[+] Author and Article Information
Zbyněk Šír

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675 Prague, Czech Republic

Elmar Wings

 ProCom Systemhaus und Ingenieurunternehmen GmbH, Luisenstrasse 41, 52070 Aachen, Germany

Bert Jüttler

Institute of Applied Geometry, Johannes Kepler University, Altenberger Str. 69, 4040 Linz, Austria

J. Comput. Inf. Sci. Eng 7(3), 186-191 (Jun 08, 2007) (6 pages) doi:10.1115/1.2764488 History: Received October 02, 2006; Revised June 08, 2007

We describe and analyze a new algorithm for rounding standard G-code tool paths. The joints of circular/linear elements are replaced by small segments of Pythagorean hodograph (PH) curves so that the final curve is globally C2 continuous. The PH segments are produced via a second order Hermite interpolation. We discuss some implementation details and investigate the error introduced by replacing a part of G-code by a PH curve segment. We also report results of tests within an industrial environment that demonstrate an increase in path velocity while decreasing peak acceleration.

Copyright © 2007 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Leading coefficient F(β)

Grahic Jump Location
Figure 2

Example of the joint replacement by PH curves. The left figure shows two circular arcs (black) and the PH replacement (gray) for h=7.50×10−1.

Grahic Jump Location
Figure 3

Test data (top). A detail (bottom) before (left) and after (right) rounding with PH curves (gray). In addition, the top right corner of the curve was rounded without taking the error constraint into account.

Grahic Jump Location
Figure 4

Comparison of axes’ speed and accelerations and path speed using PH curve rounding (a) and traditional methods (b), (c)



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