ComputerAided_Design_Engineering_amp_Manufactur.pdf

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FIGURE 9.13 The point-to-plane constraints. measured from implicit data. Position, orientation, and runout tolerances are measured from explicit data. Based on this point of view, the variational constraints should be derived from implicit or explicit data, accordingly. Figure 9.13 shows an ex<strong>amp</strong>le of how to derive the point-to-plane constraints with an explicit datum. Given 1. a datum which is A_d X + B_d Y + C_d Z � D_d, 2. a plane with four points, pt_1, pt_2, pt_3, and pt_4, 3. point pt, 4. the distance between datum and plane is d_1, and 5. the distance between plane to point is d_2, six geometric constraints can be derived. Plane function A_p X + B_p Y + C_p Z + D_p, can be generated from points of pt_1 � (x_1, y_1, z_1), pt_2 � (x_2, y_2, z_2), and pt_3 � (x_3, y_3, z_3). We have, The plane constraints thus are Point pt_4 � (x_4, y_4, z_4) is on plane A_p X + B_p Y + C_p Z � D_p which is © 2001 by CRC Press LLC A_p � ( �y_2 � z_1 � y_3 � z_1 � y_1 � z_2 � y_3 � z_2 �y_1 � z3_ � y_2 � z_3 ) � Norm_p B_p � ( x_2 � z_1 � x_3 � z_1 � x_1 � z_2 � x_3 � z_2 � x_1 � z_3 � x_2 � z_3 )/Norm_p C_p � ( �x _2 � y_1 � x_3 � y_1 � x_1 � y_2�x_3 � y_2�x_1 � y_3 � x_2 � y_3 )/Norm_p D_p � ( �x_3 � y_2 � z_1 � x_2 � y_3 � z_1 � x_3 � y_1 � z_2 � x_1 � y_3 � z_2 � x_2 � y_1 � z_3 � x_1 � y_2 � z_3 )/Norm_p Norm_p A_p 2 B_p 2 � � � C_p 2 A_p � A_d B_p � B_d C_p � C_d D_p � D_d�d_1 A_px_4 � B_py_4 � C_pz_4 � D_p
The distance constraint from pt � (x, y, z) to plane is Given a distance d, the positive or negative of d will determine the direction of variation along with (A_d, B_d, C_d) or (�A_d, �B_d,�C_d). Systems of Equations Once constraints are translated into a set of equations, the next step is to solve for the variables part of the equations. For a simplified ex<strong>amp</strong>le, to solve the system equation of point-to-plane (as described in the previous section), if datum plane d is coincident with plane p, pt_1, pt_2, pt_3, pt_4, and d_2 are given, then the value of point pt (x, y, z) can be solved directly. When multiple dimensions are applied and with fewer fixed variables, the solution scheme becomes complicated. Two methods are available for solving a system of equations. One is a direct solution using substitution algorithm and the other is numerical iteration. The direct solution has the advantage that, in general, it is faster and more precise. The direct solution has the main disadvantage that it may not be used to solve all systems of equations because it may not be possible to define a variable explicitly in an expression for its subsequent substitution in other expressions (Serrano, 1984). The Newton-Raphson method that can solve simultaneous nonlinear equations does not have substitution problems. The disadvantage of the Newton-Raphson method is that it requires the user to input the initial guess close to the actual solution in order to converge to a solution, and it may not converge to the desired solution if multiple solutions are possible (Lin, 1981). Direct Substitution Method In order to determine if a direct solution is possible, it is necessary to determine if all the variables may be defined explicitly by an expression. Given a set of system equations, to solve this set of equations we need the same number of equations and unknowns, and explicit definition for each unknown in terms of other variables; therefore, no slings should appear in the resulting digraph (directed graph). A sling would be formed if an unknown is defined in terms of itself. The system must be acyclic because the process of determining the order of execution is analogous to that of scheduling a network of activities. An activity originating at a node cannot start before all activities terminating at that node are completed. Using network path scheduling, it is possible to solve systems with more than one root, i.e., systems with subsets of expressions that are not related among themselves. An adjacency matrix as shown in Figure 9.14 is constructed to describe the digraph of the above system equations. FIGURE 9.14 Adjacent matrix. © 2001 by CRC Press LLC A_px � B_py � C_pz � D�d_2 y b x a z y � y( z) b � b( x,z) x � x( y,z) a � a( x,y,z) y b x a z 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 0 1 0 1 0 0 0 0 0
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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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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
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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
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Page 321 and 322: Completeness of Dimensions Complete
Page 323: FIGURE 9.12 3-D constraints. © 200
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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