ComputerAided_Design_Engineering_amp_Manufactur.pdf

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FIGURE 9.15 (a) Nodes represented by expressions, (b) nodes represented by pointers. In this example, variable z is fixed in order to have as many equations as unknowns. Two tree structures are built to have fixed value at the end of branches as shown in Figure 9.15. The equivalent tree structure is exhibited in Figure 9.15(a) and includes all parameters and variables. Notice that constants occupy the terminal nodes. In Figure 9.15(b), all nodes are numbered in pointerindices. In determining the execution sequence, the problem is breaking down into smaller subproblems. Subproblems are solved in a sequence such that any subproblems of the same type will not be solved more than once. An ‘‘and/or’’ graph algorithm is applied here that makes a list of all pointers to unknowns for each node in a given level. These lists are then sorted according to tree levels and merged roots a and b, because the adjacency matrix has all the information regarding both roots; it is possible to evaluate an individual root as well as all roots present in the system. To determine the execution sequence for this example, we have for nodes © 2001 by CRC Press LLC a: Level unknown pointers 4 none ... 3 y 1 2 x, y 3, 1 1 a 4 b: z � Constant level unknown pointers 4 none ... 3 y 1 2 x 3 1 b 2
therefore: Now merge the lists and eliminate the repeated pointers thus: The pointers are eliminated from left to right because they are listed with the pointers in the deepest level occupying the leftmost position in the list. Therefore, to solve this simple example requires evaluating the expressions in the order 1-3-4-2. Because not all systems may be solved using this technique, it is necessary to check that the system satisfies the necessary conditions. If one of the following two conditions is not satisfied then the iterative solution will be invoked. The first condition that is checked is the presence of slings, which are detected when an expression defining a variable contains the same variable as part of its definition. The second condition requires an acyclic system. In the next section, Newton-Raphson will be introduced when either of these two conditions is not satisfied. Iterative Solution There are various methods of finding roots or solutions for nonlinear equations, of which Newton’s method is one of the most commonly used because it has better convergence properties than direct iteration methods. The Newton-Raphson technique is a generalization to Newton’s method, and it is used to determine the zeros of a set of simultaneous nonlinear equations. The general formulation for nonlinear systems can be stated in the following form. Given n-functions fi in terms on n-unknowns xi: The basis for the Newton-Raphson method is a Taylor’s expansion of the n equations about some point ( x0, y0) : If the higher order terms are dropped, the problem becomes one of finding the roots of the linear system: © 2001 by CRC Press LLC root a : ( 1,3,1,4) root b : ( 1,3,2) list : ( 1,3,1,4,1,3,2) final : ( 1,3,4,2). f1( x1, x2,..., xn) � 0 f2( x1, x2,..., xn) � 0 � � � fn( x1, x2,..., xn) � 0 f1( x1 � x,…x n � x) � f1( x1,…, xn) � x1f … x � � xn fn � Higher order terms. . . fn( x1 � x,…x n � x) � fn( x1,…, xn) � x1f … x � � xnf n � Higher order terms. f 11 f 12 . . f 1n f21 f22 . . f1n . . . fn1 fn2 fnn X 1 X 2 . . X n � �f1 �f2 . . �fn
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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
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A temporal matrix (T-Matrix) is pro
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FIGURE 8.1 A basic process. (From R
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FIGURE 8.4(a) Generate a new IG usi
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Note if the pair of nodes are both
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TABLE 8.1 Summary of the Rules Cond
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The correctness of these rules is e
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needs to show that after each full
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ule is violated, a warning should b
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Π1 Π3 Π4 FIGURE 8.8(a) After add
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
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A ik � ‘U’ and is in a cycle
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FIGURE 8.12(a) Add [p2 t7 p7 t8 p4]
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FIGURE 8.12(c) Add a token to p8 vi
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FIGURE 8.12(e) Add [p8 t9 p14 t10 p
Page 275 and 276: FIGURE 8.13 An example of rule TT.0
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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: The distance constraint from pt �
Page 329 and 330: Quantity analysis methods have the
Page 331 and 332: y a revolute joint. By selecting al
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