ComputerAided_Design_Engineering_amp_Manufactur.pdf

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2a Reversible: Let M� � in , then where A is the incidence matrix and x a firing vector. Since is reversible, such that � 0 and equation is . Now add some tokens to some places in to result in . The relevant 2a N 2a � a x 2a Ax 2a 2a M� � 2a M0 N 2a N b The above firing vector x also makes since � 0. Now choose the least positive integer u such that ; i.e., every component of x is nonnegative. We have 2a b M� � M0 Ax 2a x ux 2a x b � � � 0 N b Thus is reversible. N b R 2a N 2a b M� 2a M� Live: The proof of being live is exactly the same as that in Theorem 3. b M� The bounded property can also be proven by deriving the P-invariants 15 for the synthesized nets. Theorem 6: The class synthesized PN belongs to the class of synchronized-choice (SC) nets. 2a M0 Ax 2a � Proof: A basic process is obviously an SC. Then assuming is an SC, we need to prove that is also an SC. Prove for the TT-rule first. The proofs for PP rules are similar. In order to satisfy the first (second) requirements, we need to show that for any pair of PT (TP) handles, there are two TP bridges across them. If all nodes and arcs of the two handles are in N , then by assumption they satisfy the two requirements. We need only consider the case where only part of the handles are in the new paths. Such handles are called mixed handles. 1 Consider the generations by TT-rules first. The case of PP-rules is similar. We need not consider the pure-TT generation, because the new path forms a PP-handle to N . For a generation by Rule TT.3, inside the new paths, there are only place joints formed by TP-path generations using Rule TT.3.1. But there are no pairs of TP-handles containing these TP-paths. This is because the TP-paths start from s and all of LEX1 are places. The only pairs of fixed PT-handles have their and �the of LEX1. One handle of the pair is in ; part of the other is in the new path. Two of the TP-paths generated using the Rule TT.3.1 form the two bridges between the above two TP-handles, thus satisfying the first requirement. Note that an SC may not be synthesized; this happens when the SC is not well-behaved. For instance, when the PT-path (TP-path) generated using Rule TT.4.2 (PP.2.2) is not a virtual one, the is an SC but with deadlocks. 1 tg nps npe�t g nps pps N 1 N 2 8.4 Temporal Matrices for Petri Nets � � b b M0 Ax b � � Ax M0 A ux 2a � � ( ) � M0 The rules should be implemented as an interactive and visual-aid tools. The designer can view the PN model being designed on the screen and use a mouse to input paths according to the design specification. Each time a path is generated, the system should check the new path generation against the rules. If some b N 1 b N 2
ule is violated, a warning should be issued to the designer to request either deletion of this new path or addition of more PSPs. In order to automate this process, a mechanism is needed to • Record the relationship between any two PSPs, • Determine the applicable rule upon a path generation, and generate additional paths and entries, if necessary, or, if no rules are applicable, delete this path. We use matrix to perform the first function. Instead of recording connectivity between places and transitions, the matrix in our algorithm records structural relationship between PSPs. Before a path is generated, the T-Matrix needs to be consulted to verify that no rule is violated. Whenever a new path is created, a PSP may be separated into several new PSPs, and relationships between some PSPs are changed. Therefore, the total number of PSPs needs to be updated, as do the matrix entries. Ex<strong>amp</strong>le: Figure 8.4(a) shows a PN model with its matrix shown in Figure 8.4(b). Originally there are five PSPs in solid paths �1 to �5 ; �6 in a dashed path is to be added by IG. �1 is concurrent to all other PSPs. Therefore, all entries in the first column and the first row are CN. �2 and �3 are exclusive to each other, as are and . Therefore, � 6 � 4 � 5 Notice returns to form cycles; therefore, some entries need to be updated. Prior to generation, �3 is structurally sequentially earlier (SE) to both �4 and �5 . After the addition, �6 , �4 , and �5 become SE to �3 , implying the formation of cycles. We have described how the T-Matrix records the relationship. The next section presents the algorithm and the associated time complexity for updating the T-matrix. 8.5 The Algorithm and Its Complexity The algorithm consists of two steps: A23 � A32 � A45 � A54 � EX. 1. Create new entries in the T-Matrix for each NP. 2. Determine the applicable rule; generate additional NPs if necessary and update the T-Matrix accordingly. If no rule is applicable or some rules are violated, delete the path. For ex<strong>amp</strong>le, if a PP-path is generated between pg and pj and pg � pj , then Rule PP.0 dictates that this path should be deleted. It is easy to find the structural relationship between the new PSP � and the PSPs directly involved with the generation, but not obvious as to the structural relationship between PSPs far away from (no direct connection with) the . In the following, we will develop techniques for new entries for PG and IG, respectively. w � w Determination of Entries for Pure-Generation After the PG of a �l from �g, �g is split into three new PSPs: �g1 → �g2 → �g3. The entries related to should be deleted. The values for the new entries are � g A�ik � Agk, A�ki � Akg where �k is any PSP other than �g, �l, �g1, �g2 and �g3 , and �i is one of the newly created PSPs. Note that �g1 and/or �g2 may be empty. The other new entries are the relationships among the newly created PSPs: A� g2 g 1 A� g1 g 2 � � � A� g3 g 1 A� g2 g 3 A� g3 g 2 A� g1 g 3 SL, � � � SE � 6
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COMPUTER-AIDED DESIGN, ENGINEERING,
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Library of Congress Cataloging-in-P
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Editor Cornelius T. Leondes, B.S.,
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Chapter 1 Chapter 2 Chapter 3 Chapt
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the implementation of the IPD syste
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In our IPD system implementations,
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2. Specification of analysis-specif
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FIGURE 1.2 base or the design insta
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FIGURE 1.4 System architecture of t
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of a beam is considered for FEA. Th
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FIGURE 1.7 through the control expe
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2. machining facility (e.g., gang m
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from the FBDS. The user also specif
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Depending on the type of feature to
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TABLE 1.6 Tolerance synthesis is de
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FIGURE 1.12 Display of the NC tool
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component geometric entities and va
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FIGURE 1.14 The system architecture
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TABLE 1.10 User Input for the Toler
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TABLE 1.11 Tolerance Specifications
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7. Z. Young and I. R. Groose. A rul
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FIGURE 2.1 Tool paths generated for
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FIGURE 2.2 sented by instances of f
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TABLE 2.1 A CAD-Generated Hole Conf
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FIGURE 2.6 mounted on the rotary ta
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FIGURE 2.8 fixture for the machinin
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FIGURE 2.10 or best-fit, or the cur
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FIGURE 2.11 Linear approximation of
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FIGURE 2.13 Circular approximation
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FIGURE 2.14(b) Circular approximati
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FIGURE 2.16 Types of biarcs. FIGURE
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FIGURE 2.18 Approximation of scanne
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FIGURE 2.20 A touch trigger probe c
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TABLE 2.4 Substitute Elements in CM
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FIGURE 2.21 CMM planning requiremen
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Product Model Representation for Co
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© 2001 by CRC Press LLC TABLE 2.5
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TABLE 2.7 Partial Listing of Dimens
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24. Makinouchi, S., Okamoto, M., an
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Bijan Shirinzadeh Monash University
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FIGURE 3.1 Trends in flexible manuf
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FIGURE 3.3 and constrain different
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Other Fixturing Techniques There ar
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FIGURE 3.6 contact point. The geome
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FIGURE 3.8 The vertical support fix
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and moments about the contact point
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een identified, the normals are use
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one of choosing the variables: such
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Fixture Module Location An importan
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FIGURE 3.15 Illustration of functio
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FIGURE 3.18 Minimum separation test
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direction) the face, respectively.
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FIGURE 3.21 Software structure for
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3.8 Conclusion A reconfigurable fix
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Heui Jae Pahk Seoul National Univer
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FIGURE 4.1(b) Conceptual framework
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4.3 Measurement Points Sampling and
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Surface S2 Measurement Path FIGURE
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FIGURE 4.4 Rough phase alignment ba
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deviation between the nominal CAD d
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FIGURE 4.6(a) Sum of squares distan
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FIGURE 4.7(c) Trailing edge. (c) th
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FIGURE 4.8(a) Profile tolerance of
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The calculated minimum form error i
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FIGURE 4.11(a) A typical mold havin
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FIGURE 4.11(d) Inspection results f
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FIGURE 4.12(c) Maximum deviation (p
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5.1 Introduction Developments in th
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process plan for a part (Figure 5.3
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FIGURE 5.5 leading to the developme
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the previously stored process plan
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FIGURE 5.7 Techniques of defining a
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Feature Recognition and Extraction
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in relation to another feature (e.g
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FIGURE 5.9 Framework for building a
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FIGURE 5.10 Process plan content.
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FIGURE 5.12 Schematic sketch of the
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Several techniques of defining a fe
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TABLE 5.1 Data Structure for Repres
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FIGURE 5.16 Classification of the t
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system to ensure that the part bein
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FIGURE 5.19 Graphical model of the
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TABLE 5.4 Data Structure for Repres
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FIGURE 5.20 Mapping between machini
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algorithms. (Some details of the pr
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FIGURE 5.24 An example rotational p
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FIGURE 5.26 Down_face-turn-up_face
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FIGURE 5.27 Procedure for machine t
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FIGURE 5.28 Determining the number
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DL is needed to be set only if the
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FIGURE 5.31 Operation sequencing co
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Cutting Tool Selection Selection of
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1. A tool is searched for in the da
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FIGURE 5.32 Inputs to optimization
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When these values are substituted,
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Usually, maximum and minimum speed
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FIGURE 5.33 Solution methodology.
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TABLE 5.6 Process Plan Internal Rep
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In a strict theoretical perspective
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18. Domazet, D. S. and Lu, S. C. Y,
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63. Prasad, A. V. S. R. K., Rao, P.
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CAD systems. The sample consists of
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learn to master the new system. An
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Although researchers appear to agre
Page 209 and 210: Link and Zmud28 found that organic
Page 211 and 212: Informal Training Informal CAD trai
Page 213 and 214: informal training programs, felt th
Page 215 and 216: 6. C. A. Beatty, Tall Tales and Rea
Page 217 and 218: A.Y.C. Nee National University of S
Page 219 and 220: FIGURE 7.1 Planning, design, and ma
Page 221 and 222: A metal stamping can have the follo
Page 223 and 224: FIGURE 7.3 Strips used to notch out
Page 225 and 226: A Skeletal Approach for the Recogni
Page 227 and 228: These findings can be used to devel
Page 229 and 230: Semi-Direct Piloting In cases where
Page 231 and 232: a larger value, the die operations
Page 233 and 234: FIGURE 7.9 Symbolic relationship be
Page 235 and 236: FIGURE 7.11 The shape of the envelo
Page 237 and 238: TABLE 7.1 Schema for the Generation
Page 239 and 240: strong reasons to support a move to
Page 241 and 242: FIGURE 7.16 3-D CAD model of a part
Page 243 and 244: References Cheok, B.T. et al. (1994
Page 245 and 246: include the once forbidden generati
Page 247 and 248: A temporal matrix (T-Matrix) is pro
Page 249 and 250: FIGURE 8.1 A basic process. (From R
Page 251 and 252: FIGURE 8.4(a) Generate a new IG usi
Page 253 and 254: Note if the pair of nodes are both
Page 255 and 256: TABLE 8.1 Summary of the Rules Cond
Page 257 and 258: The correctness of these rules is e
Page 259: needs to show that after each full
Page 263 and 264: Π1 Π3 Π4 FIGURE 8.8(a) After add
Page 265 and 266: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Page 267 and 268: A ik � ‘U’ and is in a cycle
Page 269 and 270: FIGURE 8.12(a) Add [p2 t7 p7 t8 p4]
Page 271 and 272: FIGURE 8.12(c) Add a token to p8 vi
Page 273 and 274: FIGURE 8.12(e) Add [p8 t9 p14 t10 p
Page 275 and 276: FIGURE 8.13 An example of rule TT.0
Page 277 and 278: FIGURE 8.14 A GPN model of a machin
Page 279 and 280: FIGURE 8.15(b) The first exclusive
Page 281 and 282: FIGURE 8.15(d) The last exclusive T
Page 283 and 284: FIGURE 8.15(f) After entering the a
Page 285 and 286: FIGURE 8.15(h) Completion of Compon
Page 287 and 288: FIGURE 8.15(j) Two PP-generations:
Page 289 and 290: FIGURE 8.15(l) The last exclusive T
Page 291 and 292: t1 t5 p1 p5 t6 (a) t2 t3 t4 2 2 p2
Page 293 and 294: FIGURE 8.17 An example of partial f
Page 295 and 296: Theorem 10: If pi → pk in a synth
Page 297 and 298: Note that control transitions are o
Page 299 and 300: t j than the lower at , it indicate
Page 301 and 302: • Programming logic and VLSI arra
Page 303 and 304: 7. Chao, D. Y. and D. T. Wang, Appl
Page 305 and 306: 53. Villaroel, J. L., J. Martinez,
Page 307 and 308: q u : the numerator of the least ra
Page 309 and 310: geometric modeling, engineering ana
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In dimension driven or parametric d
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FIGURE 9.3 configuration of bodies
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FIGURE 9.6 FIGURE 9.7 Geometric Int
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FIGURE 9.8 Intersection of degrees
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will introduce a way to propagate p
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Completeness of Dimensions Complete
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FIGURE 9.12 3-D constraints. © 200
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The distance constraint from pt �
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therefore: Now merge the lists and
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Quantity analysis methods have the
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y a revolute joint. By selecting al
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