ComputerAided_Design_Engineering_amp_Manufactur.pdf

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FIGURE 8.9(a) After the interaction-generation (IG), there are 18 PSPs in Petri nets. Each number stands for a PSP. (From Reference 2a. With permission.) For case (a), prior to the generation, no path passes through both �r and �q (otherwise �r → �q ); after the generation, there is a path passing through �r , �l , and �a. Hence, Arq � SE; this completes the proof for case (1). For case (b), note the two paths �g2… �h and �l� j2 …�q intersect at the generation point of �l ; this might change the relationship between �h and �q . However, it is easy to see that Ahq � Agj and from the structure definitions of “�”and “�”, we have A�hq � Ahq . Hence, except for mz � rq, A�mz �A mz where m, z �{r, q, u, v}. Hence case (2) proved. Case (3) can be proved similarly to cases (1) and (2). The corresponding time complexity is O n mainly incurred by the operation �SE. To complete the step of the single application of a TT or PP rule, additional TP- or PT-paths may have to be generated from/to the NPs. The matrix update after each such generation can be performed in a similar fashion to that in Lemma 6 with the same time complexity. Figure 8.9 shows the PN after the IG and the updated T-Matrix (refer to Figure 8.6). Any alphabetic number in Figure 8.9(a) stands for a PSP. in Figure 8.6 has been separated into two PSPs, and , respectively. Note this PN does not belong to the class of asymmetric-choice nets; note also that all pairs of exclusive (concurrent) PSPs have places (transitions) as their and ; i.e., the PN belongs to the class of synchronized-choice nets. The synthesized PN in Figure 8.5(a) also belogns to the class of synchronized-choice nets. 2 ( ) A�rq �3 �3 �4 nps npe Complexity of the Algorithm The complexity for the algorithm consists of the follwing components: 1. Determining which rule is applicable and checking the rule violation. 2. Updating matrix entries.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 EX SP SE SP SE EX EX EX EX EX EX EX EX EX EX EX SE 2 EX EX SE EX SE SP SE SP SE SE SE SE SE SE SE SE SE 3 SN EX SP CN CN EX EX EX EX EX EX EX EX EX SE EX SE 4 SL SL SN CN CN SL EX SL EX SL SL SN SN CN SP EX SE 5 SN EX CN CN SP EX EX EX EX EX EX EX EX EX SL EX SE 6 SL SL CN CN CN SL EX SLL EX SL SL SL CN SN SP EX SE 7 EX SN EX SE EX SE SP CN CN SP CN SE SE SE SE SE SE 8 SE SL EX EX EX EX SN CN CN EX CN EX EX EX EX SP SE 9 EX SN EX SE EX SL CN CN SP CN SP SP SE SE SE SE SE 10 EX SL EX EX EX EX CN CN SN EX EX EX EX EX EX SP SE 11 EX SL EX SE EX SE SN EX CN EX CN SP SE SE SE EX SE 12 EX SL EX SE EX SE SL EX SN EX CN SP SE SE SE EX SE 13 EX SL EX SP EX CN SL EX SL EX SN SN SP SP SE EX SE 14 EX SL EX CN EX SP SL EX SL EX SL SL SN CN SE EX SE 15 EX SL EX CN EX SP SL EX SL EX SL SL SN CN SE EX SE 16 SL SL SL SN SL SN SL EX SL EX SL SL SL SL SL EX SE 17 EX SL EX EX EX EX SL SN SL SN EX EX EX EX EX EX SP 18 SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SN SN FIGURE 8.9(b) The new T-Matrix of the net in Figure 8.9(a). (From Reference 2a. With permission.) For factor 1, it takes O(1) time to consult the T-Matrix to find Agj . For factor 2, the complexity to update entries has been shown to be O(n) for PG and O n for each PSP generation during an IG. Thus each PSP generation takes O time complexity. Let be the number of PSPs prior to the ith generation. The time complexity for the ith generation is . After a PG, one PSP is deleted, while at most four new PSPs are created. Thus after the PG, the number of PSPs increases at most from to . For an IG of an NP between two PSPs, two PSPs are deleted and at most five new PSPs are created. Hence after the IG of a single PSP, there are at most PSPs. The time complexity for the next generation is bounded by . Let � be the total number of PSPs at the end of a design. If we add the above time complexity for all steps, the total time complexity would be . However, this is overly estimated by noting that every entry is updated at most twice because the entry can only be updated when it is “CN” or “EX.” In other words, it can be updated from “CN” or “EX” to “SQ,” but not vice versa. Since we have entries, the total time complexity is therefore . Note that the T-Matrix does not include any virtual PSPs as they have no internal nodes (i.e., neither nor ) to serve as an or an . Thus any PSP in the T-Matrix must contain at least one internal node and the total number of PSPs in the T-Matrix are less than the total number of nodes, �, in the PN. Therefore, the total time complexity is . When many PSPs contain a number of internal nodes, the number of nodes outnumbers that of PSPs. Operations on the T-Matrix should result in significantly more reduction in time for synthesis than if we consider each node individually. 2 ( ) n 2 ( ) ni 2 O( ni) ni ni�3 ni � 3 O [ ni�3] 2 ( ) O � 3 ( ) � 2 O � 2 ( ) ng nj ng nj O � 2 ( ) 8.6 X-Window Implementation We have implemented the above algorithm by incorporating it into a multi-function Petri net graphics tool based on X-Window (Motif version). This software package 4,11 is a user-friendly CAD tool for designing, verifying, simulating, querying (including cycle time, invariants, incidence matrix, inputs/ outputs of neods, etc.), reducing, and synthesizing PN. The structure of this tool is shown in Figure 8.10. This tool can draw, erase, copy, move, pan, and zoom in/out objects such as places, transitions, states, rectangular and elliptical objects (filled and nonfilled), and texts (with a variety of fonts). The user can
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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
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 and 260: needs to show that after each full
Page 261 and 262: ule is violated, a warning should b
Page 263: Π1 Π3 Π4 FIGURE 8.8(a) After add
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
Page 311 and 312: In dimension driven or parametric d
Page 313 and 314: 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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