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TECHNICAL PAPERS

Determining Setup Orientations From the Visibility of Slice Geometry for Rapid Computer Numerically Controlled Machining

[+] Author and Article Information
Matthew C. Frank

Department of Industrial and Manufacturing Systems Engineering, Iowa State University, Ames, IA 50011

Richard A. Wysk, Sanjay B. Joshi

Department of Industrial and Manufacturing Engineering, Penn State University, University Park, PA 16802

J. Manuf. Sci. Eng 128(1), 228-238 (Mar 15, 2005) (11 pages) doi:10.1115/1.2039100 History: Received April 09, 2004; Revised March 15, 2005

A method for rapid computer numerically controlled (CNC) machining is being developed in an effort to automatically create functional prototypes and parts in a wide array of materials. The method uses a plurality of simple two-and-a-half-dimensional (212-D) toolpaths from various orientations about an axis of rotation in order to machine the entire surface of a part without refixturing. It is our goal to automatically create these toolpaths for machining and eliminate the complex planning traditionally associated with CNC machining. In this paper, we consider a problem that arises in automating this process—visibility to the surface of a model that is rotated about a fourth axis. Our approach involves slicing the computer-aided design (CAD) model orthogonal to the axis of rotation. The slice geometry is used to calculate two-dimensional visibility maps for the set of polygons on each slice plane. The visibility data provides critical information for determining the minimum number and orientation of 212-D toolpaths required to machine the entire surface of a part.

Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Rapid machining: (a) setup and (b) process steps

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Figure 2

Comparison of visibility

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Figure 3

Sample model with cross section for visibility mapping

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Figure 4

Visible ranges for segment of polygonal chain

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Figure 5

Visibility to a set of polygons from one orientation

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Figure 6

Midpoint yields visibility to newly formed segment

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Figure 7

Lines (L1,L2) from Pi through points in P

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Figure 8

A point Pi and its adjacent convex hull points

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Figure 9

Visibility of a point with respect to its chain

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Figure 10

Ranges used for segment visibility calculation

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Figure 11

Visibility range [RV(uv¯),LV(uv¯)]

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Figure 12

Problem geometries (a) RV is outside the 180deg range, (b) both RV and LV are outside the 180deg range, (c) no visibility due to overlapping, and (d) visibility to entire segment not possible since RV>LV

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Figure 13

Intersections in S1(I1) and S2(I2) to calculate RV and LV

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Algorithm 1: Determining values for LV and RV

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Figure 15

Midpoint addition yields visibility to new segments

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“Spiral” pocket

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Algorithm 2: Detecting spiral pockets

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Figure 18

Cases where at least one point of segment uv¯ is a convex hull point

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Figure 19

Visibility blocked to uv¯

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Figure 20

Locations of blocker chains with respect to uv¯

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Figure 21

“Horseshoe” obstacle envelopes the segment

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Figure 22

Algorithm 3: Determining values for RBu and LBv

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Figure 23

Mapping of visible segments to orientations

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Figure 24

STL model and sample cross section

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Figure 25

Orientations required for machining

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Figure 26

Sample models and visibility map results

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Figure 27

Example prototype: “The jack”

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Figure 28

Example prototype: Femur bone

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