A framework for geometric reasoning about tools in assembly Page: 2 of 8
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vice plans.
Let a given use of a tool to affect a particular set of
parts be called an application of that tool. We assume
that each tool application fits within a single opera-
tion, i.e. it happens just before, during, or just after
a single mating of two subassemblies. We also assume
an unordered list of all tool applications required dur-
ing assembly is given as input to the assembly planner.
Then a tool-level assembly plan for a product is a se-
quence of part motions and tool applications that will
construct the product from its parts.
This paper presents a framework to answer ques-
tions of the form "Is there space for this tool to be
used?" There are many related issues regarding tools
that we do not address. Among them are the space
required for a human or robot arm to wield the tool,
how to choose the best tool among several that are fea-
sible, finding an optimal tool-level plan, how to design
new special-purpose tools for an operation, and design
changes that might allow a tool to be used.
2 Previous Work
Several previous assembly planners have addressed
problems related to tool constraints. For instance,
Homem de Mello and Sanderson's relational model of
assemblies includes attachments, which correspond to
fastening operations [9]. Each attachment specifies the
other parts whose presence prevents the parts from be-
ing fastened, but determining which parts prevent at-
tachment is not addressed. Henrioud and Bourjault [7]
defer to an engineer to determine feasibility of attach-
ing parts, in some cases causing many hundreds of
questions to be asked of the engineer.
Reasoning about the effects and use of machine tools
is a well-studied problem (see e.g. [14, 15]). But in
contrast with assembly tools, machine tools are essen-
tially subtractive in their effect, and the constraints on
machining rarely if ever appear in the same form in
assembly.
An ambitious system to reason about tools was pro-
posed by Brady et al. [4]. The system was to recognize
tools from images, determine their uses analogically or
from first principles, and even design new tools auto-
matically. However, the project was canceled before
significant progress could be made.
Special-purpose planners have been created for cer-
tain tools. For instance, in [16] the position and ap-
proach path are planned for a coordinate measuring
machine. Determining visibility regions for a camera
(an assembly tool when used to facilitate or inspect an
assembly operation) has been widely studied (e.g. [11]).
Miller and Hoffman [13] describe an assembly planner
that requires access space above screws, bolts, and nuts
before they can be removed. However, the tests used
to determine access are only approximate, and it is
unclear how they could be used for other tools.
Experiments have been performed on the time hu-
man workers take to execute screwing, nut tightening,Figure 1: An open-end wrench
and pop riveting operations under conditions ranging
from normal to obstructed access and restricted visi-
bility [3]. Diaz-Calder6n et al [6] present progress to-
ward automatically determining the difficulty of using
a screwdriver in a particular assembly operation.
In this paper we address geometric accessibility is-
sues for a wide variety of assembly tools in a single
framework. Our approach is based on now standard
configuration-space techniques introduced by Lozano-
P'rez [12].
3 Representing Tools
Our representation for tool constraints is divided
into canonical tools that are independent of any as-
sembly, and applications of tools in a particular assem-
bly. A canonical tool is defined by (1) when it is used
relative to the mating of parts, (2) a use volume that
must be free to apply the tool, and (3) placement con-
straints on where the use volume must be located. A
list of canonical tools available to a particular system
is called a tool library. This section describes canoni-
cal tools in more detail; the next section describes tool
applications.
We will illustrate each piece of the representation
with a simple open-end wrench, shown in Figure 1.
Section 5 gives other examples.
3.1 Relative Time of Application
Tools have very different characteristics depending
on when they are applied relative to when parts are
mated in the operation:
Pre-tools are applied strictly before the parts are
brought together. The best example is a glue gun
that is used to apply glue to one part before mat-
ing it with another.
In-tools are applied while the parts are moving rela-
tive to each other. Examples include a wrench or
screwdriver, or a jig used to guide one subassem-
bly.
Post-tools are applied after the parts have been
mated. Testing, inspection, and many fastening
tools such as welders and riveters are common ex-
amples.
Which of these sets a tool belongs to is called the tool's
relative time.2
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Wilson, R. H. A framework for geometric reasoning about tools in assembly, article, December 31, 1995; Albuquerque, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc664068/m1/2/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.