ComputerAided_Design_Engineering_amp_Manufactur.pdf

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to generate a new contact line with respect to itself. So, the degree of freedom for p1 with respect to p2 is {plane_z::rot_x,rot_z} . For p2 with respect to p1, p2 can translate along the cylindrical surface of p1, and p2 can move itself along the x-axis and rotate about the z-axis. The degree of freedom for p2 is {cyl_x::lin_y,rot_z} . A rule-based system is adopted for assisting in the process of selecting an appropriate set of spatial relationships and for inferring the final state of degrees of freedom. From the above definitions, surfaces characterize degrees of freedom. For a plane_n_a degree of freedom, a body may move on a planar surface along two lin_n directions. When a new plane_z_b is introduced, the remaining degree of freedom is derived by intersecting these two planes. For example, if plane_z_a is parallel to plane_z_b, then the degree of freedom may be either plane_z_a or plane_z_b; if they are not parallel, then lin_n is the degree of freedom obtained from the intersection of plane_z_a and plane_z_b. The intersection degrees of freedom are obtained by intersection of two geometry entities, (e.g., circle_n is the result of intersecting plane_n with cyl_n (or sph_n) together). In the intersection of two rotational degrees of freedom, e.g., rot_z_a and rot_z_b, if they share the same rotational axis, then rot_z_a or rot_z_b remains; if not, they cancel each other. In the above examples, we demonstrate some simple rules for the reduction of degrees of freedom, but in some cases, such as combining the spatial relationships with numbers of rotational degrees of freedom, the solution becomes complicated. We show some general reduction rules based on our earlier work as follows: 1. {{plane_z_a::rot_za}�{plane_z_b::rot_z_b} | |vec_of(z_a) . vec_of(z_b)| �� 1} � {lin_n_c| lin_n_c � intersect(plane_z_a, plane_z_b)} 2. {{plane_z_a::rot_z_a}�{lin_v_b}| | vec_of(z_a) . vec_of(z_a)| �� 0} � {fix_c} 3. {{plane_z_a::rot_x_a,rot_z_a}�{plane_z_b::rot_x_b,rot_z_b}| x_a � x_b, |vec_of (z_a) . vec_of (z_b)|�1} � {lin_x_c::rot_x_c| lin_x_c � cent_of(x_a) � cent_of(x_b), rot_x_c � rot_x_a � rot_x_b} 4. {{plane_z_a::rot_z_a} � {lin_x_b::rot_x_b}| |vec_of(z_a) . vec_of (z_b)| � 1} � {fix_c:: rot_x_c | rot_x_c � rot_x_b} 5. {{plane_z_a::rot_x_a,rot_y_a,rot_z_a}�{plane_z_b::rot_x_b,rot_y_b,rot_z_b}| cent_of(x_a,y_a, z_a) � cent_of (x_b,y_b,z_b), vec_of (z_a) � vec_of(z_b), |vec_of (rot_z_a) � vec_of(rot_z_b)| � 0} � {plane_z_c::rot_z_c, rot_x_c| plane_z_c � plane_z_a or plane_z_b, rot_z_c � rot_z_a or rot_z_b, x_c � axis (cent_of(rot_x_a), cent_of(rot_x_b))} 6. {{plane_z_a::rot_x_a,rot_z_a}�{plane_z_b::rot_x_b,rot_y_b, rot_z_b}|vec_of(z_a) � vec_of (z_b), vec_of(rot_z_a) � vec_of(rot_z_b) � 0} � {plane_z_c::rot_z_c|plane_z_c � plane_z_a: or: plane_z_b, rot_z_c � rot_z_a: or :rot_z_b} 7. {{plane_z_a::rot_z_a} � {plane_z_b::rot_x_b, rot_y_b,rot_z_b}| 0�|vec_of (z_a)cdot vec_of (z_b)| �� 1} � {lin_n1_c::rot_n2_c| lin_n1_c � intersect (plane_z_a, plane_z_b), point_of(n2_c) � cent_of(x_b,y_b,z_b), vec_of(n2_c) � vec_of(z_a)} 8. {{lin_n1_a::rot_n2_a} � {plane_z_b::rot_x_b,rot_y_b,rot_z_b}| vec_of(n2_a) cdot vec_of(z_b) � 0} � {lin_n1_c | lin_n1_c � lin_n1_a} 9. {{lin_n1_a} � {plane_z_b::rot_x_b,rot_y_b,rot_z_b}| vec_of(n1_a) cdot vec_of(z_b) � 0} � {fix_c} where Axis is a translation or rotation axis that contains a start and a vector. point_of(Axis) returns start point of Axis. vec_of(Axis) returns vector of Axis. cent_of(Axis_x, Axis_y, Axis_z) returns origin of the Axis_x, Axis_y, Axis_z coordinate frame. (Also, this origin is a center point of a sphere.) axis(Point_a, Point_b) returns an Axis with Point_a as start point and Point_b-Point_a as direction. intersect(Dof_a, Dof_b) returns intersection of two degrees of freedom. fix is the origin of degrees of freedom representation. Figure 9.8 shows an example of assembly with spatial relationships and the intersection of degrees of freedom. Degrees of freedom are the allowable relative motion between mating components derived from © 2001 by CRC Press LLC
FIGURE 9.8 Intersection of degrees of freedom. (From Nnaji, B.O. and Liu, H.C., 1994. With permission from the Society of Manufacturing Engineers.) assembly constraints. Mating frames are the coordinate frames attached to mating components to describe the degrees of freedom between them (Nnaji, 1994). A mating frame is a coordinate frame of a part relative to the base coordinate frame of that part. Each component, as well as each subassembly, has its own mating frame (see Figure 9.9). We would like to find the mating frames by studying two approaches where one is to locate the origin of a mating frame and the other one is to find its orientation. Origin of mating frames can be derived from the intersection of the features that have spatial relationships assigned to them, which is the same as the intersection of degrees of freedom. The orientation of a mating frame can be derived from the normal vector of features. For three planar faceagainst relationships, if the mating face normals of one of the part’s faces are fa_1, fa_2, and fa_3, and none of them is parallel, then the Xm_a, Ym_a, and Zm_a axes of a mating frame can be decided upon as follows: Zm_a � fa_1 � fa_ V_a � fa_1 � a_3 Xm_a � Zm_a � V_a Ym_a � Zm_a � Xm_a © 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
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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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Page 267 and 268: A ik � ‘U’ and is in a cycle
Page 269 and 270: FIGURE 8.12(a) Add [p2 t7 p7 t8 p4]
Page 271 and 272: FIGURE 8.12(c) Add a token to p8 vi
Page 273 and 274: 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 281 and 282: FIGURE 8.15(d) The last exclusive T
Page 283 and 284: FIGURE 8.15(f) After entering the a
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Page 287 and 288: FIGURE 8.15(j) Two PP-generations:
Page 289 and 290: FIGURE 8.15(l) The last exclusive T
Page 291 and 292: t1 t5 p1 p5 t6 (a) t2 t3 t4 2 2 p2
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: FIGURE 9.6 FIGURE 9.7 Geometric Int
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 and 326: The distance constraint from pt �
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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