Authors:
Evgenia Selinger
1
and
Lars Linsen
2
Affiliations:
1
Jacobs University, Germany
;
2
Westfälische Wilhelms-Universität Münster and Jacobs University, Germany
Keyword(s):
NURBS Curves, 5-axis Machining, G2-continuity.
Related
Ontology
Subjects/Areas/Topics:
CAGD/CAD/CAM Systems
;
Computer Vision, Visualization and Computer Graphics
;
Geometry and Modeling
Abstract:
Automated machining with 5-axis robots require the generation of tool paths in form of positions of the tool
tip and orientations of the tool at each position. Such a tool path can be described in form of two curves, one
for the positional information and one for the orientational information, where the orientation is given by the
vector that points from a point on the orientation curve to the respective point on the position curve. As the
robots need to slow down for sharp turns, i.e., high curvatures in the tool path lead to slow processing, our goal
is to generate tool paths with minimized curvatures and a guaranteed error bound. Starting from an initial tool
path, which is given in form of polygonal representations of the position and orientation curves, we generate
optimized versions of the curves in form of B-spline curves that lie within some error bounds of the input path.
Our approach first computes an optimized version of the position curve within a tolerance band o
f the input
curve. Based on this first step, the orientation curve needs to be updated to again fit the position curve. Then,
the orientation curve is optimized using a similar approach as for the position curve, but the error bounds are
given in form of tolerance frustums that define the tolerance in lead and tilt. For an efficient optimization
procedure, our approach analyzes the input path and splits it into small (partially overlapping) groups before
optimizing the position curve. The groups are categorized according to their geometric complexity and handled
accordingly using two different optimization procedures. The simpler, but faster algorithm uses a local spline
approximation, while the slower, but better algorithm uses a local sleeve approach. These algorithms are
adapted to both the position and orientation curve optimization. Subsequently, the groups are combined into a
5-axis tool path in form of two G2-continuous B-spline curves over the same knot vector.
(More)