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home place of the basic process (called ) from which the synthesis begins (called the time-saving method). We will briefly compare the two after the presentation of the latter method. The algorithm then assigns a global variable (initialized to 1) to pbh . This variable Hc indicates the minimum tokens required in pbh for the synthesized net to be live. It also assigns two variables to each node ni in the net: upper[i] and lower [i] representing ( Rih) and , respectively. Their ratio is called the least home ratio. Lower[i] indicates the minimum tokens, among all reachable markings, required in for , if a place, to gain at least one token (actually upper [i]), or, if a transition, to fire at least one (actually upper[i]) time by firing transitions along any path from to . Whenever we generate a new arc and a new node at its end, we calculate the upper and lower of the new node using the following rule. u ( Rih) l pbh ni pbh ni Rule New-Ratio Let [ n1n 2] be an arc with only two nodes with weight w and the least home ratio of n1 is known, then n 2 (1) if is a place n 2 (2) if is a transition p bh upper[ 2] ---------------------lower[ 2] � upper[ 1]w --------------------------, lower[ 1] i.e., upper[ 2] � upper[ 1]�w, lower[ 2] � lower[ 1], and Hc unchanged. upper[ 2] 1 upper[ 1] ---------------------- � --------------------- ⎛---------------------- ⎞ , lower[ 2] lower[ 1] ⎝ w ⎠ i.e; lower[ 2] � lower[ 1]�w/gcd, and upper[ 2] � upper[ 1]/gcd, and Hc � Hc�w/gcd, where gcd is the greatest common denominatorof upper[ 1] and w. (1) is obvious; (2) is to avoid tokens left in the place between and when all tokens in are consumed and proceed to fire . When we stop at an , which is in N1 , we require that its least home ratio be primarily equal, but not necessarily literally smaller (unlike Rule Arr.1.a) than that in N1 . This is to reduce the time to find the firing ratio between and , which cannot be deferred from the mere least home ratios of and . As a result, extra time complexity would be incurred to trace all paths between and to find the firing ratio between them. By “primarily,” we mean the resulting ratio after the cancellation of the GCD (greatest common denominator) between upper and lower. By “literally,” we mean we do not perform the above cancellation of the GCD between upper and lower. The two ratios must be primarily equal and there are no restrictions on the magnitudes of upper and lower in N1 n1 n2 Hc pbh n2 nj ng nj ng nj ng nj . They may be smaller or greater than those in the NP. In the former (smaller) case, there is no need to update all uppers and lowers. In the latter (greater), there are two cases: forward and backward generations. For a backward generation, there is no need to update for a TT-generation, since it creates a new home place as will be discussed later. In the former case of a forward TT-generation plus backward PPgenerations, the updates at tj are needed for any node n1, nj → n1 must have its upper and lower updated if its lower is smaller than that of tj . And Hc must be updated also if any updated lower is greater than the current Hc. Otherwise, it will not be able to get a token or fire at least once if the amount of tokens in the home place equals the old lower (not updated) at the node. If the lower of the above is smaller n 1
t j than the lower at , it indicates that the amount of tokens at the home place required for is smaller than that for . This is impossible, because if cannot fire once, will not either if it is a transition. For a forward or backward PP-generation, there is no need for the update at ; however, Hc must be updated. This is because if the tokens do not flow through the NP, the least amount of tokens at for to get at least one token remains unchanged. Hc must be updated, otherwise, some transitions in the NP may be not live. In the case of multiple home places, there are multiple Hc’s and the above update of Hc must be extended to other home places being are sequential to . Home places resulting from single exclusive TT-generations, as well as exclusive to the above home places, need not have their Hc updated. As a matter of fact, there should be more than one upper and lower for and involved in a series of exclusive TT-generations. Note that by removing the restriction of “literally smaller” from Rule ARR.1.a, we violate Guideline 1 as N 1 is disturbed by the above updates even though N 2 tj tj n1 pj pbh pj tj tg tj remains well behaved. This is because Rule ARR.1.a restricts us to synthesizing a net in a certain order, i.e., the path with the largest literal ratios between two nodes must be constructed prior to all other paths. This restriction is certainly inflexible and certain nets may be unable to be synthesized because paths with literally greater ratios than existing paths can never be constructed. Upon a backward TT-generation, Rule ARR.1.b entails that we insert enough tokens into the new PSP per ARR.1.b. The number of tokens to be inserted into a place in is stated in the following rule. � w Updated Rule ARR.1.b Upon a backward TT-generation, insert uppern tokens into in . The rationale comes from the fact that uppern represents the maximum number of tokens that it will obtain by firing . This same amount of tokens will be completely consumed by firing . Consequently, there will be neither continuous token accumulations nor token depletion at . However, we do not need to perform updates even though the new ratios at may be literally greater than the existing ratio prior to the generation. This is because the backward TT-generation creates a new home place, and the tokens in the new PSP support the firing of unlike the forward TT-generation case where the firing of must be supported by the tokens in the home place. Although the computation and updating of upper and lower incurs extra computations compared to that for OPNs, the associated time complexity is linear to the total number of arcs in the net and does not increase the total time complexity for the synthesis. It is easy to see that the nets synthesized by the canonical method are a subset of those synthesized by the time-saving method. However, the NP by the former alters the behavior of N 1 pn � . w tg tj pn tj tj tj Synthesis Steps for the Net in Figure 8.14 Now we return to the synthesis of the net ex<strong>amp</strong>le in Figure 8.14. At various stages, message boxes will be popped up to provide warning or error messages or guidelines for the next generations. Figure 8.15(a) is constructed using the PP.1 rule. Note that least-home-ratios are 1/1; Rule arc-ratio need not apply here and we do not display the ratios. Figure 8.15(b)–(d) shows the three consecutive exclusive TT-generations making up a cycle (all nodes in the cycle turn their color from red into black) along with the least home ratios; the new home place is p9. Using the arc-ratio rule, n � 2 for p9. Note the three control transitions t1, t3, and t5 are in the same cycle. Note that we enter arc weights only after the NP is completed and we must enter them in order from ng . If we enter the arc weight for an arc with its start node’s least home ratio not yet computed, a warning message box will appear. Figure 8.15(h) is constructed using Rules PP.1 and TT.2 (a token inserted in p13). This forms Component I. Steps to synthesize Component II are shown in Figure 8.15(i)–(j) for the subactivity of robot 2 on Conveyor 2. Note that the two Components I and II are not connected. The final net is obtained using the rule for exclusive-TT generation, which requires constructing a cycle containing all control transitions. During the construction process, part of the cycle comes from Component I. Hence, Rule p n � w n 1
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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
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strong reasons to support a move to
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FIGURE 7.16 3-D CAD model of a part
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References Cheok, B.T. et al. (1994
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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 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: Note that control transitions are o
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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