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Similarly, if P i is in the sector P 2O 2Q, the distance D i can be obtained. The only exception is when P i lies outside either of these sectors, in which case D i is defined as the minimum distance between P i and either of the end points P 1 and P 2. Having the deviation formula available, we can therefore find the optimal biarc which passes through two end points P 1 and P 2 by formulating it as a least square problem: © 2001 by CRC Press LLC � Minimize Di( �) i ( ) 2 (2.8a) subject to ( �min �� max) (2.8b) where �min and �max are constrained by the Equation (2.6) This is a nonlinear optimization problem of one variable with simple-bounded constraints and can be easily solved by any of the commonly available optimization algorithms such as the sequential quadratic programming method. Biarc Curve Fitting to a Large Set of Discrete Data Points Having developed the formulation of the biarc curve and the optimal biarc sub-problem, we are now in the position to tackle the approximation of a large set of data points so that the resulting biarc curves are C continuous and within a specified tolerance of the data points. We assume the data points are given in the sequence that traces out the desired profile. The approach combines both a search process and an optimization process. In the search process, the algorithm starts from an initial point and searches forward to find the largest number of consecutive data points that can be approximated by a single biarc and still not violate the tolerance constraint. The search process uses a binary search approach, whereas finding the optimal biarc within the search steps solves an optimal biarc sub-problem as formulated by the model in the previous section. The algorithm can be summarized as follows: if (max_deviation_opt_biarc(1,n) � tolerance) add optimal_biarc(start,end); else start � 1 while (start � n) end � longest_end(start, start�1, n); add optimal_biarc(start,end); start � end; endwhile endif where optimal_biarc returns the optimal biarc between two end points and longest_end is the binary search to find the furthest point that does not violate the tolerance constraint. The routine longest_end (Integer Routine longest_end(start, low, high)) can be summarized as follows: deviation � max_deviation_opt_biarc(start, high) while (deviation � tolerance) high � (low � high)/2 if (high � low) return high; else deviation � max_deviation_opt_biarc(start, high) endif endwhile return high where max_deviation_opt_biarc solves the optimal biarc subproblem and returns the maximum deviation of the optimal biarc. 1
FIGURE 2.18 Approximation of scanned head. This algorithm will provide a minimum or near-minimum number of biarcs to fit a given set of data points. Figure 2.18 shows a cross-sectional profile of a scanned head approximated 12 inches by 12 inches in size. The initial data set consists of 760 points. Using 0.1 inch, 0.05 inch and 0.01 inch tolerances, respectively, the number of biarcs needed are only 10, 17 and 47, respectively. 2.4 <strong>Design</strong> Data Extraction for Computer-Aided Measurement In terms of measurement and inspection equipment, the computer controlled coordinate measuring machine (CMM) is a highly flexible piece of equipment for inspection of different parts that effectively replaces costly and specialized gauges. There are essentially three programming methods for the CMM: • Self-teaching, whereby the inspection program is created by manually operating the CMM to inspect a part but at the same time recording the procedure as a CMM program. The drawbacks of this method include reduction of the machine productive time and requirement that the physical part must already be available. 37 • Off-line Manual Programming, whereby the operator has to manually program the CMM using programming languages such as Dimensional Measuring Interface Specification (DMIS) 38 or the native language of the specific CMM. The off-line programming method has the advantage of not incurring CMM downtime and not requiring the physical part to be available and set up in the CMM. However, the programming process is very tedious to the operator compared to the selfteaching approach. • Computer-aided Programming through interaction with a CAD/CAM system. 39,40 Although this is the most suitable approach for CMM programming in terms of having a standard platform for design and manufacture, the commercially available CMM programming option for CAD/CAM systems still requires interactive input from the programmers. Automation level in terms of path planning, selection of inspection points, and other operation parameters is still limited. All the aforementioned methods of CMM programming currently suffer from the following drawbacks: • CMM programming requires trained personnel who must be familiar with the programming system (especially for CAD/CAM system), as well as the process knowledge for CMM inspection. • The programming process is still very tedious, leading to high labor turnover—especially for highly skilled personnel. • The flexibility in programming will leave room for inconsistencies in measurement approaches by different programmers. © 2001 by CRC Press LLC
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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
Page 11 and 12: In our IPD system implementations,
Page 13 and 14: 2. Specification of analysis-specif
Page 15 and 16: FIGURE 1.2 base or the design insta
Page 17 and 18: FIGURE 1.4 System architecture of t
Page 19 and 20: of a beam is considered for FEA. Th
Page 21 and 22: FIGURE 1.7 through the control expe
Page 23 and 24: 2. machining facility (e.g., gang m
Page 25 and 26: from the FBDS. The user also specif
Page 27 and 28: Depending on the type of feature to
Page 29 and 30: TABLE 1.6 Tolerance synthesis is de
Page 31 and 32: FIGURE 1.12 Display of the NC tool
Page 33 and 34: component geometric entities and va
Page 35 and 36: FIGURE 1.14 The system architecture
Page 37 and 38: TABLE 1.10 User Input for the Toler
Page 39 and 40: TABLE 1.11 Tolerance Specifications
Page 41 and 42: 7. Z. Young and I. R. Groose. A rul
Page 43 and 44: FIGURE 2.1 Tool paths generated for
Page 45 and 46: FIGURE 2.2 sented by instances of f
Page 47 and 48: TABLE 2.1 A CAD-Generated Hole Conf
Page 49 and 50: FIGURE 2.6 mounted on the rotary ta
Page 51 and 52: FIGURE 2.8 fixture for the machinin
Page 53 and 54: FIGURE 2.10 or best-fit, or the cur
Page 55 and 56: FIGURE 2.11 Linear approximation of
Page 57 and 58: FIGURE 2.13 Circular approximation
Page 59 and 60: FIGURE 2.14(b) Circular approximati
Page 61: FIGURE 2.16 Types of biarcs. FIGURE
Page 65 and 66: FIGURE 2.20 A touch trigger probe c
Page 67 and 68: TABLE 2.4 Substitute Elements in CM
Page 69 and 70: FIGURE 2.21 CMM planning requiremen
Page 71 and 72: Product Model Representation for Co
Page 73 and 74: © 2001 by CRC Press LLC TABLE 2.5
Page 75 and 76: TABLE 2.7 Partial Listing of Dimens
Page 77 and 78: 24. Makinouchi, S., Okamoto, M., an
Page 79 and 80: Bijan Shirinzadeh Monash University
Page 81 and 82: FIGURE 3.1 Trends in flexible manuf
Page 83 and 84: FIGURE 3.3 and constrain different
Page 85 and 86: Other Fixturing Techniques There ar
Page 87 and 88: FIGURE 3.6 contact point. The geome
Page 89 and 90: FIGURE 3.8 The vertical support fix
Page 91 and 92: and moments about the contact point
Page 93 and 94: een identified, the normals are use
Page 95 and 96: one of choosing the variables: such
Page 97 and 98: Fixture Module Location An importan
Page 99 and 100: FIGURE 3.15 Illustration of functio
Page 101 and 102: FIGURE 3.18 Minimum separation test
Page 103 and 104: direction) the face, respectively.
Page 105 and 106: FIGURE 3.21 Software structure for
Page 107 and 108: 3.8 Conclusion A reconfigurable fix
Page 109 and 110: Heui Jae Pahk Seoul National Univer
Page 111 and 112: 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
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FIGURE 8.13 An example of rule TT.0
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FIGURE 8.14 A GPN model of a machin
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FIGURE 8.15(b) The first exclusive
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FIGURE 8.15(d) The last exclusive T
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FIGURE 8.15(f) After entering the a
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FIGURE 8.15(h) Completion of Compon
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FIGURE 8.15(j) Two PP-generations:
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FIGURE 8.15(l) The last exclusive T
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t1 t5 p1 p5 t6 (a) t2 t3 t4 2 2 p2
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FIGURE 8.17 An example of partial f
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Theorem 10: If pi → pk in a synth
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Note that control transitions are o
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t j than the lower at , it indicate
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• Programming logic and VLSI arra
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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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