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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

## Abstract

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.

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## Figures

Figure 1

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

Figure 10

Ranges used for segment visibility calculation

Figure 11

Visibility range [RV(uv¯),LV(uv¯)]

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

Figure 13

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

Figure 14

Algorithm 1: Determining values for LV and RV

Figure 15

Midpoint addition yields visibility to new segments

Figure 16

“Spiral” pocket

Figure 17

Algorithm 2: Detecting spiral pockets

Figure 18

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

Figure 19

Visibility blocked to uv¯

Figure 20

Locations of blocker chains with respect to uv¯

Figure 21

“Horseshoe” obstacle envelopes the segment

Figure 22

Algorithm 3: Determining values for RBu and LBv

Figure 23

Mapping of visible segments to orientations

Figure 24

STL model and sample cross section

Figure 25

Orientations required for machining

Figure 26

Sample models and visibility map results

Figure 27

Example prototype: “The jack”

Figure 28

Example prototype: Femur bone

Figure 2

Comparison of visibility

Figure 3

Sample model with cross section for visibility mapping

Figure 4

Visible ranges for segment of polygonal chain

Figure 5

Visibility to a set of polygons from one orientation

Figure 6

Midpoint yields visibility to newly formed segment

Figure 7

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

Figure 8

A point Pi and its adjacent convex hull points

Figure 9

Visibility of a point with respect to its chain

## Errata

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