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Generating complete disassembly sequences byutilising two-dimensional viewsR. Giria & M. Kanthababua

a Department of Manufacturing, Anna University, Chennai, IndiaPublished online: 02 Feb 2015.

To cite this article: R. Giri & M. Kanthababu (2015): Generating complete disassembly sequences by utilising two-dimensional views, International Journal of Production Research, DOI: 10.1080/00207543.2015.1005249

To link to this article: http://dx.doi.org/10.1080/00207543.2015.1005249

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Generating complete disassembly sequences by utilising two-dimensional views

R. Giri* and M. Kanthababu

Department of Manufacturing, Anna University, Chennai, India

(Received 5 April 2014; accepted 30 December 2014)

This research work proposes a novel method to generate the complete disassembly sequences for mechanical productsby utilising the part interference matrix which contains the removal directions of the parts and the part connection graphwhich indicates the contact among the parts in the assembly. Contrary to the earlier methods, the proposed method con-siders the two-dimensional views generated from the computer-aided design assembly model for automatically identify-ing the part removal directions and for generating the part connection graph. Rules are formulated in the proposedmethod to identify the part removal directions effectively and also to reduce the size of part connection graph, since themethod of identifying the part removal directions and the size of the formulated graph plays a vital role in the generationof disassembly sequence. Finally, a heuristic method is developed to generate the best feasible disassembly sequences.The effectiveness of the approach is illustrated with three examples.

Keywords: CAD; image analysis; disassembly sequence generation

1. Introduction

A product consists of a number of discrete parts, which are called the components and a mechanical assembly is a sta-ble unit consisting of more than one part. Removing a part or more than one part from the assembly is called as disas-sembly process. The disassembly operation is carried out for the purpose of accessing components for maintenance,replacement or repair, or for reuse and as a tool for assembly optimisation. Brennan, Gupta, and Taleb (1994) havestated that the disassembly process is the systematic removal of desirable constituent parts from an assembly, whileensuring that there is no impairment of parts due to the process. The disassembly operation can be subdivided as eitherdestructive disassembly or non-destructive disassembly.

Non-destructive disassembly operations are disassembly operations that do not impair the components. In the caseof destructive disassembly, parts are just pulled or cut. Non-destructive disassembly can be further classified into threedistinct categories as follows:

� Complete disassembly: the entire product is disassembled into its constituent components.� Selective disassembly: selective disassembly is defined as the reversible dismantling of complex products into less

complex subassemblies or single parts (Lambert 1999).� Partial Disassembly: this is usually done to gain access to a particular component for servicing and/or

maintenance.

Many complex manufacturing processes like crude oil refining, contains different kinds of units and all these processingunits require periodic maintenance activities in order to keep the performance at a good level. Most of the units will beshutdown from operation to perform replacing, repairing, cleaning, modifying and inspecting the machine parts, sincethese maintenance activities cannot be performed during the operation of the unit, and normally the unit must be closedwhile these activities are to be carried out. These maintenance periods are known in the industry as turnarounds orshutdowns. During shutdown, even the performing critical machines will be subjected to complete disassembly by non-destructive operations to inspect the level of the corrosion, wear and tear of the parts, and necessary replacement ofparts will be done so that the machines can function up to next shutdown period without any failure.

The most common application of computer aided design (CAD) software is designing and drafting, and it is usedthroughout the design phase in all industries. In this paper, a novel method is proposed to automatically generate disas-sembly sequences for complete disassembly from two-dimensional CAD views in which the part removal directions and

*Corresponding author. Email: giri_ie@yahoo.comR. Giri is employed at Department of Mechanical Engineering, Rajalakshmi Engineering College, Chennai, India.

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parts connection graph is formulated by using CAD views. The proposed method is developed for complete disassemblysequence generation through non-destructive operations only and the method did not consider the precedence informa-tion of parts for generating the disassembly sequence, since the present day CAD software could not provide it effec-tively. The purpose of this work is to identify the feasible disassembly sequence in less computational time.

2. Literature survey

The choice of the sequence in which parts or subassemblies are put together in the mechanical assembly of a productcan drastically affect the efficiency of the assembly/disassembly process (Homem de Mello and Sanderson 1991). Tilltoday, most of the assembly and disassembly operations are carried out by human beings. The research work ondisassembly sequence generations is based on AND/OR graph, graph-based, connector-based, CAD-integrated andoptimisation techniques (refer Table 1).

Table 1. Type of methods.

Type ofapproach Author Objective of the approach Remark

AND/ORgraph

Hoeme de Mello andSanderson (1990)

Assembly and disassembly generation AND/OR graph is the input

Hoeme de Mello andSanderson (1991)

Disassembly sequence generation Cutset method is applied on partconnection graph

Lambert (1997) Disassembly sequence generation Generated disassembly processZwingmann et al.(2008)

Optimal disassembly sequencing graph using AND/OR graph usingconstraint programming approach

Graph Ong and Wong (1999) Disassembly sequence generation Requires interference and connectivitymatrix as input

Li, Khoo, and Tor(2002)

Generation of disassembly sequence Requires DCG graph

Li et al. (2010) Disassembly precedence constraint generation Unigraphics CAD model is the inputConnector

basedYin et al. (2003) Assembly sequence planning Requires connector graph as input

Li et al. (2010) Disassembly precedence constraint generation Precedence rules are formed based onconnectors

CADintegrated

Lin and Chang (1993) Automated assembly planning Interferences are found by sweep method

Gottipolu and Ghosh(1997)

Assembly sequence generation Input CAD file is PADL-2 package

Gungor and Gupta(2001)

Disassembly sequence plan generation Precedence matrix formed from CAD

Sung (2001) Assembly and disassembly sequencegeneration

Applies Octree model on CAD model

Dong et al. (2005) Generation of disassembly sequence Requires simplification of CAD modelPan, Smith, and Smith(2006)

Determining the interference matrix Projection and ray tracing algorithm isused for interference identification

Briceno and Pochiraju(2007)

Automatic disassembly plan generation Applies ray triangle algorithm forinterference identification

Li et al. (2010) Disassembly precedence constraint generation Unigraphics CAD model is the inputSu and Lai (2010) Assembly sequence generation Oriental bounding box for interference

identificationOptimizationtechniques

Gungor and Gupta(2001)

Disassembly sequence plan generation Requires disassembly precedence

Gupta and Lambert(2006)

Optimum disassembly sequences Requires disassembly precedence

Imtanavanich andGupta (2007)

Disassembly sequence generation Genetic algorithm is applied

Lambert and Gupta(2008)

Methods for optimum and near optimumdisassembly sequencing

Requires disassembly precedence

Zwingmann et al.(2008)

Optimal disassembly sequencing strategy usingconstraint programming approach

AND/OR disassembly graph

Tseng, Ting, andHuang (2010)

Assembly and disassembly sequence planningusing Genetic algorithm

Requires disassembly precedence

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AND/OR Graph has been extensively used for disassembly sequence generation by various researchers (Homem deMello and Sanderson 1990, 1991; Lambert 1997; Zwingmann et al. 2008). Homem de Mello and Sanderson (1990,1991) generated the assembly and disassembly sequences from the AND/OR graph. Lambert (1997) has utilised AND/OR graphs to generate disassembly process graphs. Zwingmann et al. (2008) have developed an optimal disassemblysequencing strategy using constraint programming approach. Other types of graph-based techniques are also developedfor disassembly sequence planning (Ong and Wong 1999; Li, Khoo, and Tor 2002; Li et al. 2010). Although the graph-based approaches are effective in identifying the disassembly sequences but the computational time of the methodsincreases exponentially when the number of parts in the assembly increases. For example, a simple assembly with 10components contains 75 nodes and 221 arcs in a strongly connected AND/OR graph (Homem de Mello and Sanderson1990). Ong and Wong (1999) have presented an effective method for detecting subassemblies automatically based onthe criteria of connectivity and interference relationships of the components in a subassembly from a user-definedproduct model, but the major limitation of this method is the manual inputting of the connectivity and interference infor-mation between the parts in the assembly. Li, Khoo, and Tor (2002) have generated the disassembly sequence usingdisassembly constraint graph in which nodes represent the components of the product, the constraints between contactcomponents and the precedence information are represented by undirected and directed edges, respectively.

A few researchers have developed connector-based algorithm for assembly sequence generation (Yin et al. 2003; Liet al. 2010). Yin et al. (2003) approach requires user input for generating connector graph. Li et al. (2010) method iden-tifies connectors and precedence constraints for Unigraphics CAD software users.

Many researchers used different CAD files for generating assembly and disassembly sequences (Lin and Chang 1993;Gottipolu and Ghosh 1997; Gungor and Gupta 2001; Sung 2001; Dong et al. 2005; Pan, Smith, and Smith 2006; Bricenoand Pochiraju 2007; Li et al. 2010; Su and Lai 2010). CAD is used by researchers for identifying the connectors or forpart feature recognition or for identifying the mating data or for generating precedence matrix. Sung (2001) developed anoctree-based algorithm for generating disassembly sequences by using the virtual reality modelling language files.

The obstructions to a part during disassembly operation can be found out from CAD files by space subdividingmethods (Sung 2001), three-dimensional to two-dimensional projection (Pan, Smith, and Smith 2006), sweeping (Linand Chang 1993) and ray triangle (Briceno and Pochiraju 2007). Generating the best disassembly sequence in shortertime for any given product requires the direct interaction with CAD files to identify the collision-free disassembly direc-tions of the parts. Prior studies have adequately addressed the problem of identifying the collision-free directions duringdisassembly operation by using three- dimensional geometry analysis or ray-firing algorithm or by combining two-dimensional geometry analysis with ray-firing algorithm. For the first time, an attempt is made in the proposed methodfor identifying the collision-free part removal directions by using two-dimensional views alone and it is found that theproposed technique is superior (discussed in detail at section 3.2) and takes less time to find solutions, since thetwo-dimensional shape processing requires less data to process.

Optimisation techniques are also used for generating the disassembly sequences (Gungor and Gupta 2001; Guptaand Lambert 2006; Imtanavanich and Gupta 2007; Lambert and Gupta 2008; Zwingmann et al. 2008; Tseng, Ting, andHuang 2010).The optimisation techniques require assembly or disassembly precedence information either in a matrix orgraph format. The shortcoming of these approaches is the lack of algorithmic nature in the development of the prece-dence formation (Gottipolu and Ghosh 1997). Vigano and Gomez (2013) have observed that due to nature of presentday CAD system and their procedures used in the creation of the three-dimensional assembly models, it is very difficultto establish the assembly precedence automatically.

Most of the previous research works have generated disassembly sequences by assuming that the precedence rela-tions of the parts are available as input. The main disadvantages of using precedence relations are the enormous increasein search space for generating possible disassembly sequences and inability of present day CAD software to provideprecedence information. Research works using CAD files have identified the collisions among the parts during disassem-bly by analysing the three-dimensional geometry of parts or by using the computer graphics algorithms like ray-tracingand ray-triangle algorithms. The disadvantages of collision identification methods followed by previous researchers arediscussed in section 3. In order to overcome these limitations, the proposed method is developed to generate disassem-bly sequences by utilising two- dimensional view-based collision identification technique and undirected part connectiongraph.

The main stages in the generation of disassembly sequence generations are (1) identification of part removal direc-tions in matrix form; (2) representing the parts connectivity in the assembly as undirected simple graph; and (3) generat-ing the best feasible disassembly sequences using heuristic method. In order to reduce the computational time, theproposed method reduces the size of the graph by grouping the parts based on similarity and inaccessibility (explainedin section 4) and the heuristic method provides a systematic way for finding good solutions.

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3. Part interference matrix

The part interference matrix is a matrix in which the obstruction during the disassembly of a part with all other parts isrepresented and it is generated from the CAD assembly model of a stable assembly. For P = {p1, p2, … pm} parts in anassembly, ‘m’ part interference matrices have to be generated. The elements in the matrix are either ‘1’ or ‘0’. Theobstruction of one part with the other while removing it is represented as ‘1’. The absence of obstruction is representedas ‘0’. The six columns in the part interference matrix represent the part removal directions in x+, x−, y+, y−, z+ andz−, respectively, and the rows in the matrix represent the parts in the assembly.

3.1 Identification of Type 1 and Type 2 assembly

The CAD modelling software has facility to convert three-dimensional assembly models to two-dimensional views bymeans of orthographic projection. Orthographic views are two-dimensional drawings used to represent or describe athree-dimensional object. The views represent the exact shape of an object seen from one side at a time as viewer islooking perpendicularly to it without showing any depth to the object. The six types of orthographic views are front,back, top, bottom, left and right side view. The viewer position is opposite for front and back view, top and bottomview and left and right side view, respectively.

To find the interference between two parts in the assembly, the parts are classified as Type 1 or Type 2 assemblybased on their intersection in bounding volume and the formulated rules for the assembly type helps to identify theobstructions during disassembly. If there is no intersection of the bounding volumes of two parts in the assembly posi-tion, then the two parts are identified as Type 1 assembly else the parts are called as Type 2. The Figure 1 contains theexamples for two types of assembly. The examples of Figure 1(a)–(c) are of Type 1 assembly and the Figure 1(d) and(e) are of Type 2 assembly.

The method for categorising the relation of any two parts in the assembly as Type 1 and Type 2 are as follows:Step 1: The two parts for which collision has to be identified are rendered in different colours in the assembly CADmodel.Step 2: Save the individual orthographic views of each part without changing the assembly position in tagged imagefile format (TIFF) file format.Step 3: Save the orthographic views of both parts without changing the assembly position in TIFF file format.Step 4: Using the image-processing software, identify the regions of the image by thresholding the image.Step 5: Encloses the region by forming a rectangular bounding area. Identify the coordinates of upper and lowervertices, centroid and the bounding area of all regions.

Figure 1. Assembly examples.

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Step 6: Copy the region of part 1 in front view and paste it in the front view of part 2 without changing thecoordinate location.Step 7: Identify any intersection between the parts.Step 8: Identify intersection in other views also.Step 9: If there is no regional intersection in any two views, then consider the assembly as Type 1 else consider asType 2.

3.1.1 Identifying collision for Type 1 assembly

To find the collision between the two parts of Type 1 assembly, the bounding area of a part is enlarged along the hori-zontal and vertical directions. The bounding rectangle of the part may intersect with other part during the enlargement.The intersection at right and left side is identified by horizontal extension of the bounding rectangle. The vertical exten-sion of the bounding rectangle is used to identify the intersection at upward and downward direction. Collisions of partsduring disassembly are identified based on the rules formulated in the Table 2.

3.1.2 Identifying collision for Type 2 assembly

Since the parts in Type 1 assembly are of non-intersecting bounding volume, the image enlargement is only needed tofind the collision direction. The level of obscurity in the views and the machining feature information are needed to findthe part removal direction for the Type 2 assembly. The level of obscurity is classified by comparing the assembly andpart model views. In an orthographic view, any surface which is nearer to the projected plane is made visible and thesurface which is placed behind is obscured. With respect to the position and geometry of the assembled parts,orthographic view of a part in the assembly position may remain same or differ from its individual views. A part in anorthographic view of an assembly can be completely visible (V) or split into two or more regions (S) or distorted (D) orinvisible (I) or matching (M) when compared with its original orthographic view.

The classification of the views based on view matching is required for Type 2 assembly and it is explained with twoexamples shown in Figures 2 and 3. Although the two examples belong to Type 2 assembly, the part removal directionsdiffer in each assembly.

For the assembly shown in Figure 2, the front view and back view of both parts are Visible and Matching (VM)and it indicates that no single surface of any part is obstructing the other when moved along the viewer direction. It isunderstood that the two parts can be removed independently moved along Z+ and Z− direction without any obstruction.

The assembly shown in Figure 3 is taken as second example. Part 2 is visible in front view and the region of part 2in the assembly view matches with the front view when part 1 is hidden. Region of part 1 in assembly view does notmatch with the front view region when part 2 is hidden. The front view classification for part 1 is Visible and Distorted(VD). The front view classification for part 2 is VM. The back view classification for part 1 is VD. The back view clas-sification for part 2 is VM. The part 1 is behind part 2 in both front and back view. Since the part 1 is obscured by part2 in both views, they cannot be moved along the viewer direction in both front (X+) and back view (X−). The part 1and part 2 are classified as VM and VDS in left view. The part 1 and part 2 are classified as VDS and VM in right

Table 2. Type 1 assembly rules.

Rule no. Translation 1 Translation 2Inference based on the satisfaction oftranslation 1 and 2

1. Part 1 in contact with part 2 athorizontal extension of boundingrectangle in front view

Part 1 in contact with part 2 athorizontal extension of boundingrectangle in top view

Part 1 and 2 collide along X direction. If part1 is at right side of part 2, then part 1 cannotbe moved in X− direction else Part 1 cannotbe moved in X+ direction.

2. Part 1 in contact with part 2 atvertical extension of boundingrectangle in front view

Part 1 in contact with part 2 atvertical direction extension ofbounding rectangle in right or leftside view

Part 1 and 2 collide along Y direction. If part1 is above of part 2, then Part 1 cannot bemoved in Y− direction else Part 1 cannot bemoved in Y+ direction.

3. Part 1 in contact with part 2 atvertical extension of boundingrectangle in top view

Part 1 in contact with part 2horizontal extension of boundingrectangle in right or left side view

Part 1 and 2 collide along Z direction. If part1 is above of part2 in top view, then Part 1cannot be moved in Z+ direction else Part 1cannot be moved in Z− direction.

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Figure 2. Cylinder in concentric contact with plate.

(a) (d)

Figure 3. Assembly of Type 2.

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view. From right view, it is understood that part 2 is not obstructed towards the viewer, because the joining of the splitportion of part 1 is taking place at the other end, i.e. on left side. In bottom view and top view, the part 1 and part 2are classified as VM and VDS, respectively. The classification of two objects assembly is identified by using imageprocessing techniques in 50 ms and the results are shown in Figure 4.

All the parts in an assembly have different shapes and sometimes may contain machining features like hole, slot,channel, thread and boss. Two parts with contact at machining features can restrict the disassembly operation. Manyapproaches are used to identify the machining features. Meeran and Taib (1999) proposed a generic approach to identifythe isolated, non-isolated and interacting features using two-dimensional orthographic views. In this work, it is assumedthat the machining features are available by using their approach. The standard fasteners like bolt, studs, nut, circlips,pin and machine screws are identified from their orthographic views by analysing their shapes, and the removal direc-tions are identified based on their contact with their mating part. On the basis of the parts classification, rules are formu-lated to identify the collision direction of the parts. The parts classification and the contacts restriction of the parts inthe assembly are considered for identifying the disassembly removal directions and accordingly, rules are formulated toidentify the removal directions for Type 2 assembly. By studying various types of assembly, the rules are presented inthe Table 3. The assembly types of each part with other parts are identified and using the rules, the part interferencematrix for each part is formulated.

3.2 Comparison of part interference matrix generation method with STEP

The previous researchers have applied the methods like sweeping, space subdivision, three-dimensional–two-dimensionalprojection method and ray-tracing algorithm for collision identification. Sweeping method used to find interference iscomputationally expensive because interference calculations have to be performed on all entities (vertices, edges, faces,shells and lumps) that make up the solid. Space subdividing method subdivides the spaces surrounding the componentsof the assembly into smaller spaces and the size of the subdivision has direct effect on the interference identificationand its computation time. Pan, Smith, and Smith (2006) developed an effective method for identifying the collision-freedirection for a part during disassembly using Standard for the Exchange of Product Model Data (STEP) CAD files. Thesteps involved in their method are identifying part-geometrical data of each part from STEP file, extracting the verticesof each part, converting the data to two-dimensional views and finding the collision-free matrices. In their method, bothtwo-dimensional projection techniques and ray-tracing algorithm are used. Ray-tracing algorithm is a simple method,but in many situations it turns out to be a brute-force approach. Plane equation of the faces is needed to apply the ray-tracing algorithm and firing a ray will find out only the hit point on the plane of the other part’s face, and whether thepoint lies inside or outside the part has to be checked. Intersection cannot be identified if rays are fired from the verticesof the parts in some assembly like the one shown in Figure 5. The intersection in z direction can be identified if fired

Figure 4. View classification.

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from each pixel points and the method turns out to be a brute-force method for solving the problem. Ray-trianglemethod requires the part geometry to be tessellated to triangles and the processing of the triangles is computationallyexpensive.

The proposed method is compared with the STEP–CAD method by taking the assembly shown in Figure 6 as a testproblem. The proposed method is faster since it requires two-dimensional views for establishing the removal directionsand it identifies the collision matrix for all parts of the assembly in 4.4 s, whereas the STEP–CAD identifies in 7.771 s.The performance of the proposed method with Pan, Smith, and Smith (2006) is compared in Table 4.

4. Generating the part connection graph

Parts positioned in an assembly can have the physical contact with other parts. Based on its position, a part can haveinternal contact or rested over other part or screwed inside the other part. The part connection graph formulated in thisapproach is a simple graph with undirected edges. A graph that has at most one edge joining each pair of distinct vertices

Table 3. Type 2 assembly rules.

Ruleno.

Orthographicview comparisonin plane (plane 1)

Orthographicview comparisonin opposite plane(plane 2)

InferencePart 1 Part 2 Part 1 Part 2

1. VM VM VM VM Part 1 and 2 can be removed towards viewer2. VD VD VD VD Part 1 and 2 cannot be removed on viewer direction3. VM VD VM VD Part 1 and 2 cannot be removed on viewer direction4. VM VDS VDS VM Part 1 can be removed towards viewer in plane 1 provided the machining features

permit the removal of parts. Part 2 can be removed towards viewer in plane 2provided the machining features permit the removal of parts

5. VM VDS VM VDS Part 1 and 2 cannot be removed on viewer direction6. VM I VM I Part 1 and 2 cannot be removed on viewer direction7. VM VD VD VM Part 1 can be removed towards viewer in plane 1 provided the machining features

permit the removal of parts. Part 2 can be removed towards viewer in plane 2provided the machining features permit the removal of parts

8. VM VD I VM Part 1 can be removed towards viewer in plane 1 provided the machining featurespermit the removal of parts. Part 2 can be removed towards viewer in plane 2provided the machining features permit the removal of parts

9. VM VDS I VM Part 1 can be removed towards viewer in plane 1 provided the machining featurespermit the removal of parts. Part 2 can be removed towards viewer in plane 2provided the machining features permit the removal of parts

10. VM I I VM Part 1 can be removed towards viewer in plane 1 provided the machining featurespermit the removal of parts. Part 2 can be removed towards viewer in plane 2provided the machining features permit the removal of parts

Figure 5. Assembly of two parts.

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or nodes and has no loop edges is called as simple graph. It describes the relation between the parts of the assembly andcan be defined as 2-tuple: G = {P, E}.The node P = {p1, p2, …, pm} denotes the parts in the assembly. E = {e1, e2, … ,ek}denotes the edges. An edge between the two vertices is formed if there is a contact between the parts. The contactsbetween parts are identified from the orthographic views. Since the size of the formulated graph plays a vital role in thegeneration of disassembly sequence, the part connection graph can be reduced based on the following two rules:

(1) Group the hidden and unapproachable fasteners with their contact part in to one subassembly.(2) Fasteners with similar contact of nodes are grouped as one node.

Figure 7 shows an assembly with nine parts and the part connection graph for the assembly is shown in Figure 8(a).Initially the graph has 13 edges and using the above said rules, the graph size is reduced. The main aim of usingmachine screws or bolt and nut in an assembly is to join at least two different parts. Since part 2 and part 3 are fasten-ers with similar node contacts, they are merged as one unit (f1). Practically, a bolt which is in contact with a nut is tobe removed together. Part 5 and part 6 are combined as f2. Rule 2 is used to group f1 and f2. The hexagonal head of abolt and part 7 is not visible in the front, top and side views of the assembly and it indicates that the parts are notapproachable initially. The part 7 and f2 are merged with part 4 to form a subassembly sa1 by utilising rule 1. Finally,the part connection graph is reduced to six edges and shown in Figure 8(d).

5. Proposed method

The flowchart of the proposed method is shown in Figure 9 and the steps are explained below:Step 1: Model the parts pi … m in CAD software and create the assembly model.Step 2: Create orthographic views of each part in the assembly using the CAD software by hiding the other parts inthe assembly mode.

Figure 6. Assembly with six holes.

Table 4. Part interference comparison.

AssemblyComputational time in secondsPan, Smith, and Smith (2006) Proposed method

7 parts Pan, Smith, and Smith (2006) 7.771 4.413 parts Pan, Smith, and Smith (2006) 9.875 6.354

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Figure 7. Nine-components assembly.

(a) (b)

(c) (d)

Figure 8. Connection graph.

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Figure 9. Flow chart of the method.

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Step 3: Consider any parts say, p1 and p2 in the assembly. Using HALCON machine vision software, identify therelationship between p1 and p2 as Type1 or Type 2 assembly. Apply the formulated rules based on the assembly typeto identify the collision directions.Step 4: Repeat the step 3 for all parts in the assembly and identify the collisions for all parts. Develop the part inter-ference matrix.Step 5: Formulate the part connection graph. Using the part connection graph and part interference matrix, applyheuristic method (explained in the next section) to generate the feasible disassembly sequences.Step 6: Calculate the scoring value of each disassembly sequences using Equation (1) (explained in the nextsection), and the sequence with the lowest scoring value is considered as the best disassembly sequence.The assumptions considered in this approach are as follows:

� All the parts in the assembly are rigid and the assembly is not made of any permanent fasteners.� No part is separated by the effect of gravity.� During disassembly the parts are removed along the X, Y and Z axes.� Every subassembly or assembly is provided with a manipulator.� Information on disassembly tools usage is available.

The interference matrix and part connections are generated using HALCON machine vision software and the heuristicmethod is implemented using Visual Basic software.

6. Disassembly sequence generation

The final step in the proposed approach is the generation of feasible disassembly sequences which is achieved by utilis-ing the part connection graph and part interference matrix. The heuristic method identifies the disassembly sequences byselecting the possible disassembly operations only and the best disassembly sequence among the feasible disassemblysequences is arrived finally by using the Equation (1). The number of connections in a part connection graph may varyfrom n − 1 to (n2− n)/2, where ‘n’ indicates number of parts in the assembly. A part is called as removable part if thesum value of any column in its part interference matrix is zero. If the sum value of column is zero then the part can beremoved along that direction without any obstruction. Similarly, the subassembly is considered to be fit to disassembleon the basis of the interference matrix only. A mechanical assembly has fasteners and screwed joints which create ahierarchy in removing the parts and hence, the mechanical assembly has limited feasible disassembly sequences only.Removing a node is considered as removing a part from assembly/subassembly or removing a subassembly from theassembly.

The flowchart of the heuristic method used to generate disassembly sequences is shown in Figure 10 and the proce-dures for the method are given below.

Step 1: Initially, the removable nodes are identified. If more than one node is available, then list all nodes as (Ni).Step 2: Remove the node N1 form the part connection graph and update the interference matrix of all parts.Step 3: List the available removable nodes as Ri. Rearrangement of Ri is carried out by prioritising subassemblynode as first, similar tool usage with the last removed node as second, connectivity with the last removed node asthird and other nodes to follow.Step 4: Remove R1 and update the interference matrix of all parts.Step 5: Rearrangement of Ri is again carried out. Removal of R1 and rearrangement of Ri is repeated until all thenodes become isolated vertex.Step 6: If any subassembly is an isolated node then expand the node and convert the nodes to isolated vertices. Theremoved parts are noted down in the disassembly sequence (SEQi). The procedures used to identify the disassemblysequence by considering N1 as first node to remove is followed for all Ni.The nine-component assembly is considered as a first example to explain the heuristic method. The tool require-

ments for removing parts of the assembly are shown in Table 5. Table 6 contains the disassembly operations when f1 isselected as first operation to disassemble, and the table has six columns namely, disassembly operation, part connectiongraph before, task performed, part connection graph after, possible parallel operations performed and remarks. Part 9and f1 has zero in Z+ column of the interference matrix (refer Table 7) which indicate that the disassembly operationcan be carried out in Z+ direction without any obstruction and therefore, Ni= (f1,9). After removing the node N1(f1)from the part connection graph, the interference matrix of the parts is updated and shown in Table 6. From the updatedinterference matrix, sa1 and 9 can be removed without any collision and sa1 is preferred over 9, since it is a subassem-bly and considered as R1. Removing sa1is the second disassembly operation and as result of this, the graph is split in totwo sub-graphs in which 1, 9 and 8 form one group and subassembly sa1 as other group. Once the graph is split into

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Figure 10. Disassembly heuristic.

Table 5. Disassembly tool requirement.

Disassembly tool Parts

1 2,3 and 92

5, 6

34,7,1,8, & 1, 8 1,9,8

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Table

6.Disassemblysteps.

Disassembly

operation

Partconn

ectio

ngraphbefore

Taskto

beperformed

Partconn

ectio

ngraphafter

Possibleparallel

operations

performed

Rem

ark

1sa

1 f1

1 8

9

Rem

oving

f1sa

1

1 8

9 –

Parts2and3aretogether

know

nas

f1.Rem

ovingf1

means

part2remov

edfirstfollo

wed

bypart3or

part3remov

edfirstfollo

wed

bypart2.

2sa

1

1 8

9 Rem

oving

sa1

sa1

1 8

9 –

sa1Twosubassem

bliesareform

ed.Parts4,5andf2

(6,7)are

insa1

3

1 8

9 Rem

oving

91

8 Disassembly

operation4can

beperformed

Parts9andf2

areremov

edin

parallel.

4

4

f2

5 Rem

oving

f2(6,7)

4

5 Disassembly

operation3can

beperformed

51

8 Rem

oving

81

8 Disassembly

operation6can

beperformed

Parts8and5areremov

edin

paralllel.

6

4

5 Rem

oving

5

4

5 Disassembly

operation5can

beperformed

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Table

7.Interference

matrix.

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two groups, they can be further disassembled in parallel. This procedure is repeated for the two groups. In the third dis-assembly operation, part 9 and part f2 (5–6) are removed parallel in their groups. Finally, part 8 and part 5 are alsoremoved in parallel. Removing f1 from the assembly includes the task of dismantling part 2 and 3 in any order and as aresult of this the first two sequences in the Table 8 are formed.

Table 8. Sequences with scoring value.

S.no SequenceTotal disassembly

timeNumber of parallel

operationsTotal toolchange

Scoringvalue

1 7 2 3 5.3

2 7 2 3 5.3

3 7 1 2 6.2

4 7 1 2 6.2

5 7 1 2 6.2

6 7 1 2 6.2

7 7 1 2 6.2

8 7 1 2 6.2

9 9→2→8→3→1→5,6→7→4 7 0 5 7.510 9→3→8→2→1→5,6→7→4 7 0 5 7.511 9→8→2→3→1→5,6→7→4 7 0 5 7.512 9→8→3→2→1→5,6→7→4 7 0 5 7.513 2→3→9→8→1→5,6→7→4 7 0 3 7.314 2→9→3→8→1→5,6→7→4 7 0 3 7.315 2→9→8→3→1→5,6→7→4 7 0 5 7.516 9→3→2→8→1→5,6→7→4 7 0 3 7.317 3→2→9→8→1→5,6→7→4 7 0 3 7.318 3→9→2→8→1→5,6→7→4 7 0 3 7.319 3→9→8→2→1→5,6→7→4 7 0 5 7.520 9→2→3→8→1→5,6→7→4 7 0 3 7.3

Table 9. Comparison of the proposed method.

S·no Assembly Method Input Computational time

1. Nine part assembly Co-ASP Dong et al. (2005) Modification in CAD model is required. Not mentionedProposed method Orthographic views are required 8.5 s

2. Butterfly valve Octree method Sung (2001) Virtual reality modelling language 110 minProposed method Orthographic views are required 11 s

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Figure 11. Butterfly valve.

(a)

(b)

(c)

Figure 12. Various views of Feed check valve.

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The sequences 3 and 4 shown in the Table 8 are formed when N2 (part 9) is selected as first disassembly operation.Although the table contains 20 feasible disassembly sequences for the assembly, the proposed method generates the firstfour best sequences and it avoids the processing of other inferior solutions due to the prioritised task selection.

The feasible disassembly sequences are evaluated based on the Equation (1).

SV ¼ td�Xn

i¼1

pot(i)þ m�ptc (1)

where SV is the scoring valve;n is the number of parallel operations carried out;m is the number of times the tool is changed;td is the total disassembly time;pot is the parallel disassembly time;ptc is the penalty for tool change, respectively.

Figure 13. Modified part connection graph.

Table 10. Tools requirement.

Disassembly tool Parts

1bg1&ng1

2 24 and ng23 bg24 1,2,3,4,5,6,74

3 & 2

42,3,6,7,bg2 &ng2

42,3,bg2 &ng2

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Penalty for tool change is considered as 0.1 and the sequence with minimum scoring value among the feasibledisassembly sequences is declared as best sequence.

The comparison of the proposed method with two well known methods is presented in Table 9. Dong et al. (2005)proposed collaborative assembly sequence planning system (Co-SAP) in which assembly sequence is generated by usingthe connection semantic assembly tree. In their method, B-REP models are not taken directly as input but the three-dimensional models are simplified by removing the inner surfaces and then taken as input. The nine part-assemblymodel was discussed in Co-SAP method, but the computational time was not mentioned in their paper. The time takento generate the disassembly sequences by the proposed method is 8.5 s.

The Butterfly valve shown in Figure 11 was taken as second example. The assembly has totally 11 parts. Thisassembly was studied by Sung (2001) and in his method, Octree-based algorithm is used to find the disassemblysequence. Octree algorithm subdivides the CAD assembly model in to cubes to find the contact and spatial adjacencies,and based on the adjacencies the disassembly sequence is generated. The computational time taken for the second exam-ple by the Octree method is 110 min in a 400 MHZ CPU and the proposed method took 8 s to generate the disassemblysequence in a 2.4 GHZ CPU (refer Table 8). The three screws (3, 9 and 10) are having similar contact in the connectiongraph and hence, combined as f1 in this approach. The two screws (6 and 11) joining the parts 7 and 8 are combinedas f2.The first part to be removed is 1. The second, third, fourth and fifth parts are 2, f1, f2, 4 and 8 respectively.

(a)

(b)

(c)

Figure 14. Generated disassembly sequences.

Table 11. Comparison of sequences.

Sequence number Total tool changes Parallel operations

1 6 22 6 23 6 1

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Finally, the parts 5 and 7 are separated out. The proposed method is faster in identifying the removal directions for theparts and is taking less time to generate the disassembly sequences.

The feed check valve is taken as third example. The various assembly views and modified part connection graph areshown in Figure 12 and 13. Total number of parts in the assembly is 24 and the disassembly tool requirement is shownin Table 10. Modified part connection graph has reduced the nodes of initial graph from 24 to 10 and the edgesare reduced from 47 to16. Part numbers 8, 10, 12, 14, 16 and 18 are grouped as ng1 and parts 9, 11, 13, 15, 17 and19are grouped as bg1, parts 20 and 22 are grouped as bg2, and parts 21 and 23 are grouped as ng2. The parts 1, 5 and 4are grouped as a subassembly (sa1). It is considered that the disassembly task time is same for all operations. The threedisassembly sequences identified by this approach are shown in the Figure 14 and are compared in Table 11. It is foundthat the first two sequences contain six tool changes and two parallel operations, and the last sequence contains six toolchanges and one parallel operation.

7. Conclusion

In this method, disassembly sequences are identified by using orthographic views as input. The approach identifies thecollision-free directions to remove the parts by utilising two-dimensional views only. The part removal directions areeffectively identified and found to be superior over other methods. Rules formulated in the method helps to identify thesubassemblies and as a result of this the computational time is reduced significantly. The application of the approach tothe illustrative examples confirms the superiority of the method in identifying the best disassembly sequences. Theproposed work can be extended further for generating the optimal disassembly sequence by considering the distancetravelled by the disassembly tools, tool selection among the available tools and its accessibility during the removal oper-ations.

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