ComputerAided_Design_Engineering_amp_Manufactur.pdf

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FIGURE 2.15 Formulation of biarc. Solving Equation (2.4) above yields the radii of the two circular arcs, R 1 and R 2: © 2001 by CRC Press LLC R 1 R 2 sin ⎛� �� ⎞ ⎝------------------------- 2 ⎠ 2sin � � �-------------------------------------------- L ⎛⎞ � � � -- sin⎛--------------⎞ ⎝⎠ 2 ⎝ 2 ⎠ sin⎛ � � � -- ⎞ ⎝ 2⎠ � � 2sin � � � � �---------------------------------------------------------------L ⎛---------------------------⎞ � � � sin⎛--------------⎞ ⎝ 2 ⎠ ⎝ 2 ⎠ (2.5) It should be noted that R 1 and R 2 are signed quantities; positive radius indicates that the arc center lies to the left of the tangent and negative radius to the right. For �, positive value is counterclockwise and negative value clockwise. For the special case of � � 0, it means that the segment from P 1 to Q is in fact a straight line. Figure 2.16 shows the different types of biarcs formed by various combinations of R 1 and R 2. It can be observed that the angles of the circular arcs must have the same sign as the radii; in other words, the relationships R 1� � 0 and R 2(� � � � �) � 0 hold. Furthermore, restricting � to the range [��, �] for practical purposes leads to the following results: �2� �� ( ��), if �� ( ��) ��2�, if �� (2.6) Specifying the variable � determines uniquely the biarc parameters which can be obtained by solving Equation (2.5). It is possible for the system of Equation (2.4) to produce a degenerate result. This occurs when � equals � and an infinite number of solutions exists. In this case, it is necessary to specify an additional variable, e.g., R 1 , to constrain the solution. Therefore, given the end points P 1(x 1, y 1), P 2 (x 2, y 2), and the tangent angles �, �, after obtaining R 1 and R 2, the arc centers O 1 and O 2 can be obtained.
FIGURE 2.16 Types of biarcs. FIGURE 2.17 Distance between a point and biarc b. The Optimal Biarc Sub-problem Let P i be an arbitrary data point lying between the two end points P 1 and P 2 (see Figure 2.17). Let D i be the deviation between P i and the biarc passing through P 1 and P 2. This distance can be easily calculated. The sector in which point P i lies needs to be first identified. If P i is in the P 1O 1Q sector, the distance D i can be obtained by © 2001 by CRC Press LLC Di ( xi � xO1) 2 ( yi � yO1) 2 � � � R1 (2.7)
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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
Page 9 and 10: 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: FIGURE 2.14(b) Circular approximati
Page 63 and 64: FIGURE 2.18 Approximation of scanne
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
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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
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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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