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FIGURE 8.6(a) An ex<strong>amp</strong>le of the completeness rule 2 involving interactions between two exclusive PSPs using PP rule. LCN (� 4, � 5) � {� 3, � 4}, LCN (� 5, � 6) � {� 5, � 6}. (From Reference 2a. With permission.) 1 2 3 4 5 6 7 8 9 1 EX SP SP EX EX SE EX SE 2 EX EX EX SP SP EX SE SE 3 SN EX EX EX SP EX SE 4 SN EX CN EX EX SP EX SE 5 EX SN EX EX CN EX SP SE 6 EX SN EX EX CN EX SP SE 7 SL SL SN SN EX EX EX SP 8 EX SL EX EX SN SN EX SP 9 SL SL SL SL SL SL SN SN FIGURE 8.6(b) The T-Matrix of Figure 8.6(a). (From Reference 2a. With permission.) Rule PP.0 forbids concurrent mismatch. Since , they need to cooperate to complete the task. But the NP diverts the token away to break the coordination and induces a deadlock; hence, Rule PP.0 forbids a PP generation between concurrent PSPs. Rules TT.4 and PP.2 model the messages exchange between two parties and the context switching between two processes, respectively. They are called completeness rules 1 and 2, respectively. To satisfy the completeness requirement1 �g � �j in communication protocols, each PSP in Xgj ( Xjg) , if executed, must send (receive) a token by firing the relevant tg ( tj) . In the context switching, all local contexts in Cgj must switch to those in Cjg. See Figures 8.5 and 8.6 for the application of these two rules.
The correctness of these rules is established in the sequel. We first show the correctness for a synthesized net where each home place holds eactly one token. Let N denote such a net, the net after adding tokens to , and and also . We then show that the synthesized net is marking monotonic; that is, it remains well-behaved by adding tokens to places in the synthesized net. Rules TT.1, TT.2, and PP.1 do not require further generations. They are simple and have been dealt with in much of the literature using the concept of reductions and expansions. The rest rules are established to satisfy the following guidelines for adding NPs. a N b N a N 1a N a N 1 1. No disturbance to : inhibiting any intrusion into normal transition firings of prior to the generations. This guarantees that neither unbounded places nor dead transitions would occur in N1 since it was live and bounded prior to the generations. 2. Well-behaved NP: inhibiting any dead transitions and unbounded places in NP. There are two kinds of intrusions. One is to chnage the marking of ; the other is to eliminate some reachable markings. In order for NP to be live, it must be able to get enough tokens from pg or by firing tg . When tokens in NP disappear, the resultant marking of the subnet N1 in N2 must be reachable in N1 prior to the generation of NP. Furthermore, the marking of NP must be reversible in N2. The second intrusion may occur when the joint is a transition that may not be enabled in case of backward TT generation, hence, causing some markings in N1 to be unreachable. Thus if the joint is a transition, NP must be able to get tokens from a generation point within each iteration. Based on the concept of no intrusion, the rules are constructed according to the following guidelines: 1. From M0, each tg must be potentially able to be fired (always fires or has fired �� in N1 enabling the joint that is a transition). 2. These tokens must disappear from NP before it gets unbounded tokens, and return to an N1 to reach a marking M2. The marking of the subnet N1 in N2, M2( N1) of all possible sets of such M2 is identical to those in without the new paths. N 1 Theorem 1: Any PN resulting from a singular application of Rules TT.1 and PP.1 to an synthesized from a basic process is well-behaved. Proof: This theorem can be proved by repetitively applying reduction and expansion. 30,34,36 Theorem 2: Any PN resulting from a singular application of Rules TT.2 to a synthesized from a basic process is well-behaved. Proof: This theorem can be proved by repetitively applying reduction and expansion. 30,34,36 N 2 Lemma 1: For an , any pair of PSPs cannot be both concurrent and exclusive to each other. Proof: If one assumes to the contrary, then there are two , one a t � T and another a p � P. This can only happen when they are PT or PP generations between concurrent PSPs or TP or TT generations between exclusive PSPs. These four types of generations are forbidden. This lemma implies that any time start node of a pair of PSPs must be either transition or place and cannot be both. Thus, similar to an SC, the two prime nodes of a pure pair must both be transitions or places. This lemma leads to the equivalence of structural and temporal relationship, which is markingor time-related, rather than structurally related. Two transitions (places) are temporally concurrent to each other if they can fire (have tokens) simultaneously in a safe PN. Without this lemma, p1 and p2 may not (may) be able to hold tokens simultaneously, even if p1�(�) p2 since there may be two DEPs from a pps ( tps) to p1 and p2, respectively. Lemma 2: For an , let M� � (the R for ), where all �s in C12 are marked, then M� � 2 M� � � ( C12) � � ( C21) is a reachable marking, where � ( C12) (� ( C21) ) denotes that each � in C12 ( ) holds exactly one token. C 21 N 2 2 R 2 N 2 n ps N 1 N 1a N 1 N 1a 2
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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
Page 205 and 206: learn to master the new system. An
Page 207 and 208: 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: TABLE 8.1 Summary of the Rules Cond
Page 259 and 260: needs to show that after each full
Page 261 and 262: ule is violated, a warning should b
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,
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q u : the numerator of the least ra
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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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