ComputerAided_Design_Engineering_amp_Manufactur.pdf

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Although the example in Figure 8.13 synchronizes only two mutually exclusive transitions, the same idea can apply to a set of more than two mutually exclusive transitions. As a result of synchronization, they are sequentialized; i.e., their mutual synchronic distance changes from � to one. For the net shown in Figure 8.14, this set contains three mutually exclusive transitions. Summarizing the above discussion, we have the following synchronization rule: If a TT-path ( �1) is generated from tg to tj , tg tj and tj is a control transition, then generate a series of TT-paths ( �2, �3,…) from t�g to t�j such that all above �s are in a cycle and each t�j is also a control transition with the same decision place for tg and tj . Note that tg to t�g need not be a control transition. On the other hand, if t�j is not a control transition, the token in the decision place may flow to the input place of this control transition, not matching to the token in the cycle and hence resulting in a deadlock. This rule must be checked concurrently along with other TT rules. For instance, after the above cycle (with a token) generation, the following TT-path generation may become a backward generation; then Rule TT.2 must be applied to insert a token in this TT-path. The correctness of this rule can be proved by showing that it satisfies the two guidelines. We omit the proof here because it is not the main purpose of this chapter. Similar comments apply to the rule described in the next subsection. Arc-Ratio Rules for General Petri Nets The synthesis rules of the knitting technique for ordinary PN should be modified for GPN in order to meet the guidelines. This set of rules is referred to as connection rules since the absence of any may cause some guidelines to be violated. The weight of arcs in the PN must satisfy some constraints. Consider the guideline of no-disturbance, i.e., if the NP is a TT-path from to , then the firing ratio between to of NP must equal that in N 1 . Otherwise, the firing behavior of in N1 � is disturbed. Similarly, if the NP is a PP-path from to , then the marking ratio between and of the NP must equal that in . Otherwise, the marking behavior of in is disturbed. Similar but slightly different conditions apply if the NP is a TP-path or a PT-path. Now consider the second guideline of well-behaved NP. Examples are shown in Figure 8.16(a) and 8.16(b) where the second guideline is violated; both NPs are not well-behaved. These additional rules are called the arc-ratio Rules. w tg tj tg tj tj pg pj pg pj N 1 tj N 1 Arc-Ratio Rules Again, one can develop the arc-ratio rules based on the two guidelines. The following definitions of least ratios consider a pair of nodes, transitions, or places, and all the paths between them in isolation (i.e., all nodes and arcs not in these paths are deleted). f a Definition: The least firing ratio between ti and tk , Rik � -- , where a is the least firing number of t b i for tk to fire b times with no tokens left in paths between ti and tk . m a Definition: The least marking ratio between pi and pk, Rik � -- , where a is a least number of tokens in b pi for pk to get b tokens by firing all transitions between pi and pk with no tokens left in paths between pi and pk . mf a Definition: The least marking-firing ratio between pi and tk, Rik � -- , where a is the least number of b tokens in pi such that tk fires b times with no tokens left in paths between pi and tk . fm a Definition: The least firing-marking ratio between ti and pk Rik � -- , where a is the least firing number b of ti such that pk can get b tokens by firing transitions between ti and pk, with no tokens left in paths between and . t i p k
t1 t5 p1 p5 t6 (a) t2 t3 t4 2 2 p2 FIGURE 8.16(a) An example of PP generation, which violates the arc-ratio rule ARR. 1.a. � 2/2, � . t1 t2 t3 t4 p1 p2 (b) t5 2 2 FIGURE 8.16(b) An example of TT generation, which violates the arc-ratio rule ARR.1.a. � 1/1, � 2/2, f R . f � R NP lit 12 a These ratios are referred to as least ratios q. Let q � -- be one of these ratios, then q � a and � b. b In these ratios, the numerator and the denominator may not be mutually prime. Hence, we also need to define the prime ratio of the least ratio q. Definition: The prime ratio [q]�� where a� and b� are prime to each other, where q � , , , or . u q 1 a� f m ---b� { Rik Rik fm R ik mf Rik } a 1 Definition: If [ q1]�� [ q2]�q � ---- 1 b and q2 � ---- and a and then is literally greater 1 b 1 � a2 b1 � b2 q1 2 than q2 , denoted as q1 � litq2 . m Example: Figure 8.16(a) shows an NP ( p1 t5 p5 t6 p2) with R12 � 2/2, which is literally greater than m m ( �lit) that ( R12 � 1/1) for the PP-path ( p1t 2p2) . Both [ R12]�are 1/1. The net is nonlive. Figure 8.16(b) f f shows an NP ( t2 p5 t5 p6 t4) with R 24 � 2/2, which is literally greater than ( �lit) than that ( R24) � 1/1 f for the TT-path [ t2 p2 t3 p3 t4] . Both [ R24]�are 1/1. The net is nonlive. p3 p3 p5 p6 a 2 m RNP f R12 p4 p4 m RNP f RNP R m lit 12
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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
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Link and Zmud28 found that organic
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Informal Training Informal CAD trai
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informal training programs, felt th
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6. C. A. Beatty, Tall Tales and Rea
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A.Y.C. Nee National University of S
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FIGURE 7.1 Planning, design, and ma
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A metal stamping can have the follo
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FIGURE 7.3 Strips used to notch out
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A Skeletal Approach for the Recogni
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These findings can be used to devel
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Semi-Direct Piloting In cases where
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a larger value, the die operations
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FIGURE 7.9 Symbolic relationship be
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FIGURE 7.11 The shape of the envelo
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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 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: FIGURE 8.15(l) The last exclusive T
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
Page 311 and 312: In dimension driven or parametric d
Page 313 and 314: FIGURE 9.3 configuration of bodies
Page 315 and 316: FIGURE 9.6 FIGURE 9.7 Geometric Int
Page 317 and 318: FIGURE 9.8 Intersection of degrees
Page 319 and 320: will introduce a way to propagate p
Page 321 and 322: Completeness of Dimensions Complete
Page 323 and 324: FIGURE 9.12 3-D constraints. © 200
Page 325 and 326: The distance constraint from pt �
Page 327 and 328: therefore: Now merge the lists and
Page 329 and 330: Quantity analysis methods have the
Page 331 and 332: y a revolute joint. By selecting al
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