Numerical control programming in APT
Numerical control programming in APT
Real-time shaded NC milling display
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Sweeping of three-dimensional objects
Computer-Aided Design
Geometric representation of swept volumes with application to polyhedral objects
International Journal of Robotics Research
NC milling error assessment and tool path correction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Bridging the gap between CSG and Brep via a triple ray representation
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Generating swept solids for NC verification using the SEDE method
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Generation of swept volumes of toroidal endmills in five-axis motion using space curves
Proceedings of the fifth ACM symposium on Solid modeling and applications
The Handbook of Mathematics and Computational Science
The Handbook of Mathematics and Computational Science
Collision prediction for polyhedra under screw motions
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Fast swept volume approximation of complex polyhedral models
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Online sculpting and visualization of multi-dexel volumes
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Boundary of the volume swept by a free-form solid in screw motion
Computer-Aided Design
Geometric Modeling for Swept Volume of Moving Solids
IEEE Computer Graphics and Applications
The implicit equation of a canal surface
Journal of Symbolic Computation
Chinese-Japanese cross language information retrieval: a Han character based approach
WWSM '00 Proceedings of the ACL-2000 workshop on Word senses and multi-linguality - Volume 8
Review: 5-axis flank milling: A state-of-the-art review
Computer-Aided Design
A mathematical model for simulating and manufacturing ball end mill
Computer-Aided Design
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In this paper, we present a methodology to generate swept volume of prevailing cutting tools undergoing multi-axis motion and it is proved to be robust and amenable for practical purposes with the help of a series of tests. The exact and complete SV, which is closed from the tool bottom to the top of the shaft, is generated by stitching up envelope profiles calculated by Gauss map. The novel approach finds the swept volume boundary for five-axis milling by extending the basic idea behind Gauss map. It takes piecewise C^1-continuous tool shape into account. At first, the tool shape is transformed from Euclidean space into Tool map (T-Map) on the unit sphere and the velocity vector of a cutter is transformed into Contact map (C-Map) using Gauss map. Then, closed intersection curve is found between T-Map and C-Map on the Gaussian sphere. At last, the inverse Gauss map is exploited to get envelope profile in Euclidean space from the closed curve in the range. To demonstrate its validity, a cutting simulation kernel for five-axis machining has been implemented and applied to mold and die machining.