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C 12 Proof: After each � in fires once, there exists a � for one of to gain a token. By the equivalence of temporal and structural relationship, each � in C21 will gain a token. Hence the lemma. This lemma ensures that the application of Rule PP.2 will not alter the reachable markings of N . The following lemma also comes from the equivalence of temporal and structural relationship. Lemma 3: Using Rule TT.4, if one in gets a token in each of its input places except the one from , then any subsequent firing sequence, if long enough, will inject a token to and fires the above . Proof: This lemma comes from the fact that, prior to the generation, d( ) � 1, since ↔ or � . This lemma, along with Lemma 4, ensures that no tokens get accumulated in the NP indefinitely. Note: if → , then the NP is marked by Rule TT.2. can fire without the token injected by firing a . But subsequent firing will always lead to the firing of a to restore . The above firing sequence, denotd as , including both and and � t � , t � (the set of transitions in the NP), is called a complete firing sequence of the NP. Lemma 4 shows that after a , the marking of in , will be a reachable one in . The correctness of this lemma is based on the following: Observation 1: �t � , if , , and 1. 2. � pair of and � , ¬ using Rule TT.4, and ¬ using Rule PP.2. 3. Any TP (PT) generation occurs between exclusive (concurrent) PSPs. 4. Any pair of PSPs ad , joining at a node in the NP, then , if � . 1 tj Xjg n˙j n˙ j tj Xgj, Xjg Xgj Xjg tj tg tj tg w tg M0 � w tg tj � w T w � w N 1a N 2a M 1/2 N 1a T w t�ngt�n˙j t�n˙g |•t � 1. t1 t2 T w ( t1 || t2) ( t1 | t2) �1 �2 nk �1� ()� | 2 nk T w P w ( ) Proof: (1) |•t| � 1 only for transition joints within the NP. But this occurs only under Rule PP.2.1 where the joint is an n˙g . (2) Consider Rule TT.4 first. Any pair of new PSPs corresponding to the TPpath using Rule TT.4.1 are mutually exclusive since they have the same pps as the two corresponding �g . The same result applies to Rule TT.4.2 since the nps is a place pj . The case for Rule PP.2 can be proved in a dual fashion. Cases 3 and 4 can be similarly proved. The observation derives from the fact that there are only TP and PT generations beyond the first generation using Rules TT.4 and PP.2. From (2) of Observation I, any pair of PSPs �1 and �2 using Rule TT.4 (PP.2) is eithter �1 ↔ �2 or �1 ()� � 2 . Thus, a complete firing path through the NP is a single DEP using Rule TT.4 and includes all transitions in the NP using Rule PP.2. Lemma 4: For the N after applying Rule TT.4 (PP.2), after injecting a token (tokens) into the NP by firing only one (the ), the subsequent firing sequence will lead to , where both and . Proof: We first show that the injected tokens will eventually disappear from the NP due to the following facts: 1. There are no internal TP-paths whose and 2. Injected tokens can flow freely inside the NP since every t inside the NP has only one input place by Observation 1. We then show that upon the disappearing of the injected tokens from the NP, the resultant contains a � . This is true for Rule TT.4 since the subfiring sequence in leading to the firings of and is exactly the same as that in prior to the generation. For Rule PP.2, the token disappearing is equivalent to the switching of tokens from to , which leads to a submarking by Lemma 2. Lemma 5: ��, such that . 2 1a w tg n˙g ( M� , M0 )[� w 1a w → ( M� , M0 ) 1a 1a 1a M� M� �R pj � nj M 2 M 1/2 R 1a N 1/2 tg tj N 1a Cgj Cjg M 1/2 �R 1a 2 2 w [�M0 , either � ( � or � t�� , ¬ ) t�T w � ( ) M 0 Proof: This lemma comes directly from Lemmas 3 and 4. Theorem 3: Any PNs resulting from the singular applications of Rules TT.4 and PP.2 to a N synthesized from a basic process are well behaved. 1a Proof: Prove by induction. It is easy to see that a basic process is live, bounded, and reversible. Then, assuming the N i.e., N from the (N-1)th synthesis steps is bounded, live, and reversible, the proof 1a ( ) C 21
needs to show that after each full synthesis step using Rule TT.4 or PP.2, the resulting remains so. �� that does not include any node in the NP, it will fire in exactly the same manner as that in N and leads to the same reachable marking. Hence this case need not be considered. Reversible: We need to show that a � exists such that . There are two cases: (a) and (b) . (a) Two cases if � (1) does or (2) does not include any t � . For case (2), the subnets that involve � are exactly those in . Hence, the � exists. For case (1), Lemma 5 dictates that a . Let , then [ ], where . The problem then reduces to case (2) which has been proved. (b) , which implies a partial . By Lemma 5, all sbsequent firing sequences, if long enough, can complete the rest of to restore . The case then is similar to case (a) and can be proved similarly. Live: Assume to the contrary, then � , t � ; some of its input places, which are mutually concurrent, can never get tokens. But this is impossible by the equivalence between temporal and structural relationship (which ensures that all input places of t are possible to get tokens) and the requirement that the NPs in Rule TT.4.2 and PP.2.2 should be virtual (which ensures that the above possibility should be definite) by preventing uncoordinated movement of tokens in a set of concurrent places. When a token enters a place with more than one output transition, it may fire any of its output transitions and thus it may result in uncoordinated movement of tokens. That is, the two tokens generated by firing a transition may move to the input places of two exclusive transitions, respectively. Since they are mutually exclusive, none of them will be able to be fired; the N hence is not live. The virtual PSP generations in Rules TT. 4.2 and PP.2.2 prevent such uncoordinated movements. One of the above two tokens moves in ; the other in the NP. Uncoordinated movements of these two tokens intrude the marking behavior of ; this is impossible by Lemma 5, which states that guideline (2) is satisfied. Note that Guideline (1) can only be revoked when the a has input places from the NP. Then, by Rule TT.2, the NP will have a token in its initial marking, which allows to be potentially able to be fired from . Thus both guidelines are satisfied. Based on this, we can show that the t is potentially able to be fired. If (1) , then by Lemma 4, the presence of NPs does not change the markings of ; hence, if t is not in the NP, t is potentially able to be fired. If t is in the NP, then by Observation 1 and Guideline (1), t is also potentially able to be fired. Now if (2) , then also by Lemma 4 there exists a subsequent firing sequence to drive back to and then is a reachable marking in . The case then degenerates to case (1). 1a 1a w 1a w ( M� , M ) [� � ( M0 , M0 ) M w w � M0 M w w �M0 T w N 1a � w � � � �c� w 1a w � �d ( M� , M0 ) �1� w 1a w 1a 1a � ( M� , M0 ) M� �R M w w �M0 � w � w w M0 � a R 2a 1a w ( M� ,M ) � T 2 N 1a N 1a tg tg 2a M0 M w w � M0 N 1a M w w �M0 M w w M0 M 1/2 M 1a Theorem 4: Any PN resulting from a singular application of Rule TT.3 to an synthesized from a basic process is well-behaved. Proof: Lemma 5 does not hold for Rule TT.3.1 because Lemma 3 does not either. This is because may fire infinitely often relative to tj . Now Rule TT.3.2 prevents such infinite firings of tg with respect to tj and forces dgj � 1. Lemma 3, and hence Lemma 5 also hold for Rule TT.3. The rest of proof follows that for Rule TT.4 in Theorem 3. Theorem 5: Any PNs resulting from the applications of the TT and PP rules to a basic process are bounded, live, reversible, and marking monotonic. Proof: Prove by induction. It is easy to see that a basic process is live, bounded, and reversible. Then, assuming the N from the (N-1)th synthesis steps is bounded, live, and reversible, the proof needs to show that after each full synthesis step using a certain TT or PP rule, the resulting N remains so. The correctness of this is established by Theorems 1–4. Note that we have been assuming that there is only one token in every home place. Now prove the property of marking monotonic by showing that is well-behaved. 1a N b N 1a N 2a t g
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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
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 and 256: TABLE 8.1 Summary of the Rules Cond
Page 257: The correctness of these rules is e
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,
Page 307 and 308: 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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