Data processing: structural design – modeling – simulation – and em – Modeling by mathematical expression
Reexamination Certificate
2000-06-23
2004-04-20
Teska, Kevin J. (Department: 2123)
Data processing: structural design, modeling, simulation, and em
Modeling by mathematical expression
C703S006000, C703S007000, C703S021000, C703S022000, C700S095000, C700S097000
Reexamination Certificate
active
06725184
ABSTRACT:
FIELD OF THE INVENTION
This invention relates generally to the field of automated analysis of CAD models, and more particularly, to the field of determining assembly and disassembly sequences for components within multi-component CAD models of assembled parts (i.e., multi-component assemblies).
BACKGROUND OF THE INVENTION
Selective Disassembly involves disassembling a selected set of components (C
S
) from a multi-component assembly (A) to obtain a selective disassembly sequence (S). For example, to disassemble C
S
={C
4
, C
5
} from A in
FIG. 1
, S=[C
6
, C
4
, C
5
], as shown in FIG.
2
. (Note that roster brackets { } are used to denote a non-ordered set wherein the order of its members is unimportant, whereas square brackets [ ] are used to denote an ordered set wherein the order of its members is as listed.) It should be understood that selective assembly, the “converse” of selective disassembly, is necessarily included within the selective disassembly analysis. However, the term “selective disassembly” will generally be used to describe both selective disassembly of components as well as their selective assembly. A selective disassembly sequence S satisfying a user objective such as minimal component removals, minimum disassembly time, or minimum cost is defined as an optimal sequence (OS).
Applications for selective disassembly include assembling, maintenance and recycling operations. For example, aircraft engine maintenance requires the selective disassembly of the engine—which may involve prior disassembly/removal of some parts before the engine itself may be disassembled—and it does not require the disassembly of the entire aircraft. As might be imagined, effective use of some apparata requires their rapid and efficient disassembly and assembly; for instance, if an aircraft engine cannot be rapidly disassembled and reassembled for maintenance and/or repair, the aircraft may need to be taken out of service for an extended period of time, and the effective upkeep cost of the aircraft can be greatly increased. Another concern is recycling, wherein components of one apparatus are reused in another apparatus. From the standpoint of conservation of natural resources, it is generally desirable to reuse components rather than construct new ones. However, if components to be recycled/reused cannot be quickly and efficiently disassembled from the original apparatus and installed in the new apparatus, the cost of recycling may be such that it is not worthwhile. Therefore, selective disassembly analysis of components in an assembly A, and the determination of optimal disassembly sequences OS, is an important area of research in assembly/disassembly planning.
One potential approach to determining optimal disassembly sequences OS is an exhaustive enumeration of all the possible selective disassembly sequences S for the assembly A (i.e., perform a complete disassembly analysis), and the selection of optimal sequences OS with minimal removals. However, this analysis is computationally expensive (typically exponential) and is not recommended.
Several researchers (e.g., Ashai, 1995; Beasley and Martin, 1993; Romney et al., 1995) have proposed automated complete disassembly methods, which involve disassembling all the components in assembly A. Although a selective disassembly sequence S can be obtained from a complete disassembly analysis as previously noted (i.e., by selecting optimal sequence OS from all of the selective disassembly sequences S), the complete disassembly analysis does not automatically give an optimal solution OS. For example, a selective disassembly sequence S can be obtained for a selected component set C
S
by recursively disassembling components that are disassemblable in assembly A until all the components in C
S
are disassembled. To illustrate this, consider A in
FIG. 1
with selected component set C
S
={C
4
, C
5
}. Let s=number of components in a sequence. Following the complete disassembly algorithm, the selective disassembly sequence S to disassemble the selected component set C
S
is [C
1
, C
2
, C
6
, C
3
, C
4
, C
5
] with s=6, but the optimal disassembly sequence OS=[C
6
, C
4
, C
5
] with s=3. Hence, a separate approach for selective disassembly is preferred. Nevertheless, while complete disassembly algorithms are largely inappropriate for selective disassembly analysis, it is illustrative to survey the prior work in complete disassembly analysis. Therefore, a brief overview is now provided.
Baldwin et al. (1991); De-Fazio and Whitney (1987); Henrioud and Boudjault (1991) propose an
Assembly Sequence Diagram
to represent the ability or inability to assemble a component with other components. The user is asked a number of questions regarding the precedence relation of components in order to enumerate all assembly sequences. However, the number of such questions grow exponential to the number of components in A, and therefore the computational expense of this method limits it to smaller assemblies. Further, the method is not automated insofar as users need to answer the inquiries relating to the components, and therefore the time expense of the method is further increased.
Homem de Mello and Sanderson (1991) propose an AND/OR Graph that establishes assembly conditions and precedence relationships between components. The AND/OR graph represents the sequences for assembly based on local motion analysis in three dimensions. A cut-set of the mating diagram of the assembly and subassemblies is used as a basis for disassembly questions. The AND/OR Graph method suffers from the same disadvantages as the Assembly Sequence Diagram method in that it is time-consuming to execute except for assemblies with only a small number of components.
To reduce the number of queries to the user, several authors (Lee and Shin, 1991; Huang and Lee, 1991; Swaminathan and Barber, 1996) propose
Knowledge
-
Assisted Systems
that use preexisting information (stored from earlier queries to the user) to analyze similar products. In effect, these are essentially expert systems. The part interconnections and the directional constraints of the motion that bring two parts together are analyzed based on both existing knowledge and further user queries. These methods do not significantly decrease analysis time, particularly insofar as the information stored by the expert system can only be re-used in later products of the same type.
Several researchers have utilized computational geometry techniques for assembly analysis. Arkin et al (1989) use the concept of a monotone path between obstacles to deduce a removable subassembly and a single extended translation to remove it. Shyamsundar and Gadh (1997) propose the use of a convex hull based representation of assemblies for geometric reasoning. Beasley and Martin (1993) consider the generation of disassembly motion for voxelized models of objects based on disassemblability analysis. Mattikalli and Khosla (1992) propose constraint-based (i.e., contact geometry-based) analysis to determine the translational and rotational disassemblability of components for 3D assemblies. Ashai (1995) proposes metric-based evaluation of complete disassembly sequences via disassemblability analysis of 3D assemblies. However, these proposed techniques are primarily based on analysis of contact geometry of components, and they therefore suffer from the disadvantages of contact geometry reasoning discussed later in this document (most particularly, failure to detect interference of components during linear global assembly/disassembly motions). Further, they assume sequential disassembly of components (removal of components one at a time) for generating complete disassembly and assembly sequences. These will therefore not allow determination of optimal sequences OS wherein simultaneous removals allows for more efficient disassembly. In addition, where complete disassembly results are obtained, these results must be further analyzed to ascertai
Gadh Rajit
Srinivasan Hari
DeWitt Ross & Stevens S.C.
Ferris Fred
Fieschko, Esq. Craig A.
Teska Kevin J.
Wisconsin Alumni Research Foundation
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