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n g n j Definition: The and of a TT (PP, TP, and PT) generation are transition (place, transition, place) and transition (place, place, and transition), respectively. For factor 2, ng and nj can be in the same or different PSPs. For the latter case, there are five possibilities: (1) sequential earlier (SE), (2) sequential later (SL), (3) concurrent (CN), (4) exclusive (EX), and (5) cyclic (CL). Definition: Let �g ( �j) denote the PSP that contains the generation point (joint). Pure generation (PG) generates paths within a single PSP (Figure 8.2), i.e., �g � �j . Interactive generation (IG) generates paths between two PSPs (Figure 8.4), i.e., �g ��j . Definition: If ng → nj prior to the generation, then it is a forward generation; otherwise it is a backward generation. In Figure 8.2, [t1 p4 t3] is a forward generation; �6 in Figure 8.4(a) is a backward generation. A backward TT generation needs the addition of tokens to the NP to avoid the resulting N being nonlive. This constitutes Rule TT.2. The idea of constructing the rules is simple. An eligible generation upon N to produce should not alter the marking and firing behavior of . Furthermore, the new PSP must be live and bounded. One of the following three actions is taken depending on the type of generation: (1) forbidden, (2) permitted, or (3) permitted but need more generations. For instance, a TP generation causes an extra token to be injected into the original net whenever the NP gets a token. This alters the marking behavior of and the net is unbounded. A PT generation robs a token from and causes to be nonlive, hence changing its firing behavior. To avoid this problem, add more generations or forbid such generations. The rules are complete in the sense that all possible generations have been considered. The following definitions for TT and PP rules have considered all possible structural relationships between and . Some generations are forbidden, some require the addition of tokens, while others require further generations. 1 N 2 N 1 N 1 N 1 N 1 N 1 ng nj Definition: TT Rule: For an NP from tg � �g to tg � �j generated by the designer, (0) TT.0 If tg � tj or only one of them is in a cycle, which was solely generated using Rule PP.1, then signal “forbidden, delete the � ” and return. (1) TT.1 If � , signal “a pure TT generation;” otherwise signal “an interactive TT generation.” (2) TT.2 If ← , signal “forming a new cycle.” If, without firing , there does not exist a firing sequence � to fire , then insert token in a place of NP. If � , return and the designer may start a new generation. (3) TT.3 If the structure synchronic distance � � then (a) TT.3.1 Apply Rule TT.4. (b) TT.3.2 Generate a new TT-path path to synchronic and such that after step 3.c, changes from � to 1. (c) TT.3.3 Go to step 2. (4) TT.4 (a) TT.4.1 Generate a TP-path from a transition of each in to a place in the NP. (b) TT.4.2 Generate a virtual PSP, a PT-path, from the place to a transition of each in . w �g �j tg tj tj tg �g �j s dgj s tg tj dgj tg �g Xgj pk n˙ j tj �j Xjg Definition: PP Rule: For an NP from pg � �g to pj � �j generated by the designer,
TABLE 8.1 Summary of the Rules Conditions of Generations PP Rule TT Rule A. cycles created — TT.2 B. no cycles created — — B.1 only one of ng and nj in a cycle from PP.1 — TT.0 B.2 exclusive PP.2 TT.0 B.3 concurrent PP.0 — B.3.1 neither ng nor nj in a cycle from PP.1 — TT.4 B.3.2 both ng and nj in a cycle from PP.1 — TT.3 B.4 sequential or cyclic PP.1 (PG) TT.1 (PG) PP.2 (IG) TT.4 (IG) (0) PP.0 If pg pj , then signal “forbidden, delete the � ” and return. (1) PP.1 if (2) PP.2 , signal “a pure PP generation;” otherwise signal “an interactive PP generation.” (a) PP.2.1 Generate a TP-path from a transition of NP to a place of each in . (b) PP.2.2 Generate a virtual PSP, a PT-path, from a place of each in to the transition of NP. w �g � �j tk pj �j Cjg pg �g Cgj n˙ g Note that some generations may require the application of more than one rule. For instance, a backward IG may need both Rules TT.2 and TT.4. Note also the partial dual relationship between the TT and PP rules. Replacing transitions with places (and vice versa) reversing each arc in Rule TT.4, we obtain Rule PP.2. The rules are summarized in Table 8.1. Section 8.6 demonstrates the application of these rules to an automated manufacturing system. Note that during each application of a rule, more than one new PSP may be generated; we call such a generation a macro generation. Otherwise, it is a singular generation. In the remainder of this chapter, all nets mentioned refer to nets synthesized using the rules presented above. Below, we explain the rules starting with the rules that forbid generations. Forbidden TT and PP generations come from synchronic and concurrency mismatches, respectively, which cause uncoordinated actions. For a TT generation, a single parameter, the synchronic distance between tg and tj , can unify all cases of the structural relationships between and . n g Definition: Synchronic Mismatch: A TT generation causes a synchronic mismatch of , where 1 w ( dgj) denotes the synchronic distance between tg and tj and N (NP). 1 d gj Definition: Concurrency Mismatch: A PP generation causes a concurrency mismatch if ( pg � pj ) and � a p � P, p � pg , and ¬ (p � pj ). There are three possible synchronic distances: 1, �, and the integers in between. A TT generation should not alter the synchronic distance between tg and tj . But a TT-path implies a synchronic distance of 1 between tg and tj . Thus, if the synchronic distance between tg and tj is 1 prior to the generation, the TT generation will not alter the reachable markings of N . If ( ) can fire infinitely often without firing , then the NP will get unbounded tokens (become nonlive due to deficiency of tokens). In terms of structural relationship, �� for the following cases: (1) � , (2) and/or is in a cycle generated earlier using the PP rule, (3) ↔ or � , such that , and/or , and , and (4) tg and are in two separate PNs. For cases (1) and part of (2) where only one of and is in a cycle, the generation is chosen to be forbidden to make Rule TT.0. The rest of the cases need additional generations to make Rules TT.3 and TT.4. 1 tg tj tj ( tg) dgj tg tj tg tj tg tj tg tj �tx tg tx tj tx tg tj tg tj n j 1 w dgj � dgj
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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.
Page 203 and 204: 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: Note if the pair of nodes are both
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 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
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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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