Research Papers

Computing Axes of Rotation for Setup Planning Using Visibility of Polyhedral Computer-Aided Design Models

[+] Author and Article Information
Ye Li

Department of Industrial and Manufacturing Engineering and Technology,  Bradley University, Peoria, IL 61625yli@bradley.edu

Matthew C. Frank

Department of Industrial and Manufacturing Systems Engineering,  Iowa State University, Ames, IA 50011mfrank@iastate.edu

J. Manuf. Sci. Eng 134(4), 041005 (Jul 18, 2012) (10 pages) doi:10.1115/1.4006969 History: Received September 19, 2011; Accepted May 13, 2012; Published July 18, 2012; Online July 18, 2012

This paper presents a method for determining feasible axes of rotation for setup planning, based on the visibility of a polyhedral model. The intent of this work was to develop a feature-free approach to setup planning, with the specific focus on multi-axis machine setups. Visibility mapping can provide a quantitative evaluation of a surface, a feature or an entire part model; however, the next step is to use this information for process planning. In this paper, we present an approach of using a visibility map to evaluate axes of rotation that could be used in an indexer-type setup on a machine tool. Instead of using expensive and complicated multi-axis machining, it may be feasible to machine using multiple three-axis toolpaths if a single axis of rotation can be used to rotate the part through the minimum set of orientations. An algorithm is presented that is capable of processing visibility information from a polyhedral model; hence, the method is generic and does not require feature detection. As such, the work is applicable to a variety of applications; in particular for subtractive rapid prototyping where complex geometry may not contain recognizable features.

Copyright © 2012 by American Society of Mechanical Engineers
Topics: Rotation , Machining
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Figure 1

Axis of rotation and accessibility to a simple feature on a cube; (a) poorly chosen axis with no accessibility to hemispherical pocket and (b) proper choice with pocket accessible

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Figure 2

SRP machined human bone, illustrating feature-free geometric information via cadaveric laser scanning before process planning

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Figure 3

Four-axis milling setup; (a) axis of rotation for four-axis milling setup and (b) a great circle intersecting visibility polygons on a unit sphere

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Figure 4

Illustration of nonvisibility by boundary tracing [23]; (a)–(e), tracing the boundary of an obstacle polygon with respect to another polygon, and (f) coinciding swept arcs of the nonvisibility map on a unit sphere

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Figure 5

Point visibility and axes of rotation; (a), (b), (c), and (d) are four instances of feasible axes of rotation on the corresponding great circle of the point visibility

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Figure 6

Arc of visibility and shaded region between two great circles representing feasible axes of rotation

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Figure 7

Visibility cone discretized to visibility arcs; (a) visibility cone, (b) corresponding visibility arcs used to approximate surface on the unit sphere

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Figure 8

Half great circle corresponds to a unit sphere for axes of rotation

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Figure 9

A visibility arc intersecting with a visibility cone

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Figure 10

Half circles pivoting along a common axis

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Figure 11

Great half circle angle γ

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Figure 12

Discretization of a unit sphere; (a) circular point array on a great half circle, (b) sphere represented by a grid of points

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Figure 13

Rasterization process with α = 0.5 deg and β = 0.5 deg

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Figure 14

Flow chart of implementation of the algorithm

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Figure 15

Example one: Orthogonal square pockets on a prismatic part; (a) three orthogonal square pockets, with no axis of rotation and (b) two orthogonal square pockets, with corresponding axis of rotation

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Figure 16

Example part (a) square cube with thru-hole, (b) feature-based approach to axes yield the equator on a unit sphere, and (c) feature-free approach expands to a band about the equator

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Figure 17

Setup orientations on a four-axis indexed machine; (a) a single feature-based solution, (b) one of several feature-free solution results

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Figure 18

Example industrial component; (a) STL model of the part, (b) axes of rotation results in clusters of axes illustrated on the hemisphere, with respect to the part model




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