ComputerAided_Design_Engineering_amp_Manufactur.pdf

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where where reaction forces at each locating contact point are denoted by F ij, and or where r ij are the moment arm of F ij and © 2001 by CRC Press LLC R x (3.7) (3.8) (3.9) (3.10) (3.11) (3.12) Combining equations (3.10) and (3.12) provides a matrix equation in the form of AX � B. In this formulation the positions of locating fixture modules may have to be reconsidered if the coefficients of the matrix A are singular. The analysis can also be carried out using screw pairs. This approach is chosen for this task because screw representation of displacement and forces emphasizes the underlying representation upon line geometry and the surface model of the workpiece. Detailed accounts of the screw theory and its development may be found in Reference 29. A set of fixture modules in contact with a workpiece can be modeled as a set of zero pitch wrenches acting on the workpiece. This stems from the fact that any system of forces and couples can be reduced to a wrench of a given intensity acting on a given screw. Therefore, we are interested in the total freedom of the workpiece when it is acted upon by a set of wrenches (see Figure 3.11). Once the contact face has FIGURE 3.11 Schematic diagram of wrenches acting on a workpiece. (From Reference 24. With permission.) � F 31 Ry � �( F21 � F22) Rz � F11 � F12 � F13 3 4�i �� M � rij � Fij i �1 j �1 M � M1� M2 � M3 3 � Mi � Fijai � 3, j j �1 �i � { 1, 2, 3}
een identified, the normals are used to determine the moment components and thus the wrench coordinates. Therefore, the Plücker coordinates for a given contact position with respect to a fixed point (e.g., center of gravity) on any surface, S, of the workpiece are determined using the following: ⎛�S⎞ ⎛�S⎞ © 2001 by CRC Press LLC ⎛�S⎞ �1, i �2, i �3, i �4, i �5, i �6, i �S � ⎛----- ⎞ ⎝�x⎠ �S � ⎛----- ⎞ ⎝�y⎠ �S � ⎛----- ⎞ ⎝�z⎠ j j j ( PCY � Ycg) �S ⎛----- ⎞ ( PCZ � Z ⎝�z⎠ cg) �S � � ⎛----- ⎞ ⎝�y⎠ (3.13) where and are the components of the surface normal (i.e., ), i defines the fixture module number (i.e., number of wrenches), and j is the face number on the workpiece. It must be noted that the components of the moment about the assembly station coordinate frame may also be found using the above formulation by deleting the expressions for the center of gravity. The components of the wrenches are used to perform the kinematic analysis. The generalized screw system is used to determine the possible movement that the workpiece may have when it is partially or fully constrained in a fixture layout. The governing equation describing the virtual coefficient may be written in general form as24 ----- ⎝�x⎠j , ----- ⎝�y⎠j , ----- ⎝�z⎠j AXj , AYj , AZj (3.14) where w �� is the virtual coefficient for the twist, �, and the wrench, �, and n is the number of wrenches (i.e., fixture modules) in contact with the workpiece. The above formulation allows us to deal with the uni-directional nature of the constraints. 28 It also allows the identification of the specific contacts that may be broken for a given twist. The equations governing the virtual coefficients are formed for various stages of the fixturing process. These relationships include the following: (3.15) (3.16) (3.17) An important design criteria is that the fixture layout must provide for ease of loading and unloading. The robot or the manipulation arm is required to place the workpiece into the fixture layout from an outside location in the “free-space” region without jamming the workpiece in the layout. The fixture layout design must therefore accommodate an initial stage where the workpiece can be moved into the fixture layout location from an outside (i.e., free-space) location. This fixture layout will be referred to as the “initial” fixture layout, and it must guide and locate the workpiece into the desired position j ( PCZ � Zcg) �S ⎛----- ⎞ ( PCX � X ⎝�x⎠ cg) �S � � ⎛----- ⎞ ⎝�z⎠ j ( PCX � Xcg) �S ⎛----- ⎞ ( PCX � Y ⎝�y⎠ cg) �S � � ⎛----- ⎞ ⎝�x⎠ w�� n,1�4 � �n,2�5 � �n,3�6 � �n,4�1 � �n,5�2 � �n,6�3 w�� 0 repelling screw pair w�� ( 0) reciprocal screw pair w�� 0 contrary screw pair j j j j
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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
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 and 62: FIGURE 2.16 Types of biarcs. FIGURE
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 moments about the contact point
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
Page 113 and 114: 4.3 Measurement Points Sampling and
Page 115 and 116: Surface S2 Measurement Path FIGURE
Page 117 and 118: FIGURE 4.4 Rough phase alignment ba
Page 119 and 120: deviation between the nominal CAD d
Page 121 and 122: FIGURE 4.6(a) Sum of squares distan
Page 123 and 124: FIGURE 4.7(c) Trailing edge. (c) th
Page 125 and 126: FIGURE 4.8(a) Profile tolerance of
Page 127 and 128: The calculated minimum form error i
Page 129 and 130: FIGURE 4.11(a) A typical mold havin
Page 131 and 132: FIGURE 4.11(d) Inspection results f
Page 133 and 134: FIGURE 4.12(c) Maximum deviation (p
Page 135 and 136: 5.1 Introduction Developments in th
Page 137 and 138: process plan for a part (Figure 5.3
Page 139 and 140: FIGURE 5.5 leading to the developme
Page 141 and 142: 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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