Rounding Spatial G-Code Tool Paths Using Pythagorean Hodograph Curves

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 C 2 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.

[1]  Bahram Ravani,et al.  Computer aided geometric design of motion interpolants , 1994 .

[2]  Moshe Shpitalni,et al.  Realtime curve interpolators , 1994, Comput. Aided Des..

[3]  Rida T. Farouki,et al.  Real-time CNC interpolators for Pythagorean-hodograph curves , 1996, Comput. Aided Geom. Des..

[4]  Josef Hoschek,et al.  Fundamentals of computer aided geometric design , 1996 .

[5]  Yoram Koren.  Interpolator for a Computer Numerical Control System , 1976, IEEE Transactions on Computers.

[6]  Bert Jüttler,et al.  An algebraic approach to curves and surfaces on the sphere and on other quadrics , 1993, Comput. Aided Geom. Des..

[7]  Rida T. Farouki,et al.  Performance analysis of CNC interpolators for time-dependent feedrates along PH curves , 2001, Comput. Aided Geom. Des..

[8]  Hans F. de Groote,et al.  On the Complexity of Quaternion Multiplication , 1975, Inf. Process. Lett..

[9]  Daniel C. H. Yang,et al.  Parametric interpolator versus linear interpolator for precision CNC machining , 1994, Comput. Aided Des..

[10]  Rida T. Farouki,et al.  Variable-feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves , 1998, Comput. Aided Des..

[11]  B. Jüttler,et al.  Constructing acceleration continuous tool paths using Pythagorean Hodograph curves , 2005 .

[12]  J. Kuipers.  Quaternions and Rotation Sequences , 1998 .

[13]  Bert Jüttler,et al.  C HERMITE INTERPOLATION BY PYTHAGOREAN HODOGRAPH SPACE CURVES , 2007 .

[14]  Bert Jüttler,et al.  Generating tool paths on surfaces for a numerically controlled calotte cutting system , 2004, Comput. Aided Des..