The topic of representing the offset of a 2-D B-spline curve in the same form has been under research for a long time, and it has many industrial applications, especially, in NC tool path generation for pocketing. For B-spline tool paths, it is often required that the tool paths have fewer control points, lower base function degree, and higher geometric accuracy. However, the existing methods often generate the offsets of 2-D free-form curves in the form of B-spline curves with high function degree and many control points. Although these offsets are useful in computer-aided design, they are inappropriate for the use of CNC machining. To address the problems in order to generate high quality B-spline tool paths, this original work formulates an error function of the offset approximation and then constructs a NURBS curve to globally bound the errors. By checking the maximum coefficient of the bounding curve, the upper bound of all the approximated offset errors is found and the errors can be reduced by adding more offset points at the appropriate locations. The proposed new approach is more efficient, and the resulting offsets in B-spline are more accurate with fewer control points and lower function degree. It is useful to generate B-spline tool paths for CNC pocketing, and has potential for other applications in industry.
- Design Engineering Division and Computers in Engineering Division
An Effective Approach to Approximating 2-D Free-Form Curve Offsets for B-Spline NC Tool Paths With Offset Error Globally Bounded
- Views Icon Views
- Share Icon Share
- Search Site
Khan, MA, & Chen, ZC. "An Effective Approach to Approximating 2-D Free-Form Curve Offsets for B-Spline NC Tool Paths With Offset Error Globally Bounded." Proceedings of the ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 3: 30th Computers and Information in Engineering Conference, Parts A and B. Montreal, Quebec, Canada. August 15–18, 2010. pp. 415-422. ASME. https://doi.org/10.1115/DETC2010-29150
Download citation file: