0
Research Papers

# Representation, Generation, and Analysis of Mechanical Assembly Sequences With k-ary Operations

[+] Author and Article Information
Haixia Wang

Product Development & Global Technology, Caterpillar Inc., Peoria, IL USA 61629;  School of Mechanical Engineering, Shandong University, Jinan Shandong, Chinahaixia@gmail.com

Dariusz Ceglarek

The Digital Laboratory, WMG, University of Warwick, Coventry CV4 7AL, UK;  Department of Industrial and Systems Engineering, University of Wisconsin, Madison, WI 53706 d.j.ceglarek@warwick.ac.uk

In case of generating a new assembly line where number of assembly stations and part allocation for station is unknown, the method presented in “Equipment selection and task assignment” [23-26] can be used to determine a suboptimal line configuration and task assignment. Then, in the next step, the k-ary sequences can be generated using the method presented in this paper.

In Ref. [27], N is a constant value. In this paper, N is a variable which is determined by the total number of parts and the number of parts to be assembled at each station.

The name of “k-piece graph” is recommended to the authors by Professor Douglas B. West at Mathematics Department, University of Illinois - Urbana-Champaign.

A subgraph of a graph (or mixed graph) is a subset of the vertices and edges of the graph (or mixed graph). An induced subgraph is a subset of the vertices of a graph (or mixed graph) together with any edges whose endpoints are both in this subset. A connected graph is an undirected graph where there is a path from any vertex to any other vertex in the graph. A mixed graph is connected if its underlying undirected graph is connected.

An algorithm is said to run in O(f(n)) time if for some numbers c and n0 , the time taken by the algorithm is at most cf(n) for all n ≥ n0 .

An in-edge to a vertex is an edge directed to the vertex.

A source vertex of a mixed graph is a vertex which has no inward directed edge. A source edge is an edge where neither of its two end vertices has in-edge from outside.

“a←→b” means joints a and b should be joined simultaneously.

J. Comput. Inf. Sci. Eng 12(1), 011001 (Dec 16, 2011) (12 pages) doi:10.1115/1.3617441 History: Received June 10, 2010; Revised March 22, 2011; Published December 16, 2011; Online December 16, 2011

## Abstract

A new methodology is presented to generate all of the assembly sequences for a production system configured as a N-station assembly line with kn (n  = 1, 2,…, N) parts or subassemblies to be assembled at stations 1, 2,…, N, respectively. This expands current approaches in sequence generation applicable for binary assembly process to a k-ary assembly process by including: (i) nonbinary state between two parts, i.e., multiple joints between two parts or subassemblies, is taken into consideration, and (ii) simultaneous assembly of Y ($Y≥3$) parts or subassemblies. The methodology is based upon proposed k-piece graph and k-piece mixed graph approaches for the assemblies without and with assembly precedence relationship, respectively. Compared with the currently used liaisons graph (or datum flow chain) representation which shows part-to-part assembly relations, the k-piece graph (or k-piece mixed graph) shows all of the feasible subassemblies and their constituent parts and joints (pairs of mating features). Based upon the k-piece graph or k-piece mixed-graph approach, all of the feasible subassemblies for a predetermined assembly line configuration are identified, and all of the sequences for a k-ary assembly process are generated. Case studies are presented to illustrate the advantages of the presented methodology over the state-of-the-art research in assembly sequence generation.

<>
Topics: Manufacturing

## Figures

Figure 11

Representation of joining sequences for the k-ary (k1  = 2, k2  = 3) process

Figure 12

Illustration of a k-ary assembly system that cannot be reduced to a binary assembly

Figure 13

Illustration of circular doubly linked list representation of graph and mixed graph

Figure 14

The simplified SUV underbody and its part-to-part representation C1 (M1 )

Figure 15

A 3-ary assembly process with parameters k1  = k2  = k3  = k4  = k5  = 3

Figure 16

Procedure of k-ary subassembly generation of the SUV underbody assembly for the k-ary process with k1  = k2  = k3  = k4  = k5  = 3

Figure 17

Sets of k-ary operations of the SUV underbody assembly for the k-ary (k1  = k2  = k3  = k4  = k5  = 3) process

Figure 18

A k-ary assembly process with parameters k1  = 3, k2  = 2, k3  = 3, k4  = 4, k5  = 3

Figure 1

A sports utility vehicle side frame assembly and its part-joint graph (a vertex represents a part, an edge represent a pair of mating features, i.e., a joint between two parts)

Figure 2

A composite of star-shaped objects in the plane requiring four hands for assembly (from Natarajan, 1988)

Figure 3

Assemblies which can only be built by plans which are (a) nonsequential, (b) nonmonotone, and (c) noncontact coherent (from Wolter, 1991)

Figure 4

An N-part product requiring N hands to assemble (from Latombe, Wilson, and Cazals, 1997)

Figure 5

A product with (a) an interesting ternary assembly and (b) a necessary ternary assembly

Figure 6

Illustration of the iterative process of implementing k-piece graph

Figure 7

Illustration of the process of implementing k-piece mixed graph

Figure 8

The procedure of k-ary sequence generation with {k1 , k2 ,…, kN }-ary operations

Figure 9

Illustration of sequence generation for k-ary assembly processes

Figure 10

Subassembly sequences for the k-ary (k1  = 2, k2  = 3) process

Figure 19

Station sequences of the SUV underbody assembly with k1  = 3, k2  = 2, k3  = 3, k4  = 4, k5  = 3

## Errata

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections