ComputerAided_Design_Engineering_amp_Manufactur.pdf

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In this application, the objectives of computational kinematics comprise the following aspects: • Automatic formulation of the governing kinematic equations • Solving nonlinear equations for kinematic response • Analysis of the kinematic characteristics of mechanical systems. Kinematic modeling of a mechanism involves the definition of the geometry of the bodies that make up the mechanism, the selection of kinematic constraints that act between pairs of bodies, and the specification of time-depended drivers to reduce the number of degrees of freedom of the mechanism to zero. Intuitively, a CAD system appears to be an appropriate tool to model not only static mechanical systems, but also assemblies that contain moving parts. However, certain requirements must be met by the CAD system in order to be useful in the process of kinematic modeling and analysis. It is essential that the constraints on the relative motion of bodies in the mechanism imposed by the physical joints can be captured in the CAD knowledge base. The formulation of the governing kinematic equations of the system can then be achieved automatically after the desired input motion is specified. Thus, the user is freed from the tedious and error-prone process of translating the physical characteristics of a mechanism into a valid mathematical model. It is important to note that, rather than creating an animation of the mechanism’s motion on a computer screen after the input of relevant data by the user, this approach is based on placing the CAD data into the center of the kinematic analysis process. The advantages of this philosophy derive from the flexibility of utilizing neutral data to perform a variety of tasks without any redundancy of information stored in a data base. Design with spatial relationships is ideally suited to support computer-aided kinematic modeling and analysis of mechanisms. By assigning spatial relationships between individual components, the designer not only defines the relative position of a component in the final assembly, but he also specifies the degrees of freedom implied by a joint. Since spatial relationships constitute a pair-wise operation under assumption that both components, initially, are unconstrained free bodies, it is not able to close up an open-chain assembly where the degrees of freedom of components are retrained. In a four-bar linkage example, the first three joints can be assembled with spatial relationships in order to assemble the fourth joint to generate a closed chain. This has to be achieved by an inverse kinematics operation (Prinz, 1994). The following example illustrates the process of assembling a closed kinematic chain using spatial relationships. The four-bar mechanism that is to be assembled and its kinematic diagram are shown in Figure 9.16. The assembly of the open kinematic chain consisting of base a, crank b, coupler c, and follower d is considered first. Each of the revolute kinematic pairs {a,b}, {b,c}, and {c,d} can be modeled by using the spatial relationships aligned and against. Then the position of base e is specified by parallel offset spatial relationships. In order to close the kinematic chain, base e and follower d must be connected (d) (e) FIGURE 9.16 Assembled four-bar mechanism and its kinematic diagram with joint coordinate frames. © 2001 by CRC Press LLC (a) (c) (b) y2 y1 z2 z1 x2 x1 y3 z3 y4 z4 x3 x4
y a revolute joint. By selecting aligned and against as post-spatial relationships, the user defines the desired kinematic pair {d,e} and initiates the solution process for this inverse kinematics problem. Further input required is the selection of those parts that are fixed to the ground, i.e., the bases a and e. Once the user has specified the spatial relationships between the components of the mechanism, local coordinate frames are automatically attached to each joint in the mechanism (see Figure 9.16). The 4 � 4 transformation matrix Ak( k� 1) relates the position and orientation of two adjacent joints k and k + 1 in the kinematic loop that describes the mechanism. In order to close a loop, the coordinate system at the end of the loop must be congruent with the one at the beginning. That is, for a kinematic loop consisting of n joints, the product of the transformation matrices must be the identity matrix: This equation is called the loop-closure equation. It is important to note that this matrix equation is automatically derived from the set of spatial relationships that define the kinematic constraints between the parts of the mechanism. The joint variables in this equation may be considered as belonging to one of two groups. We have simplified the expression here in order to show that the formulated system equations can be solved by the same techniques introduced in sections above, the direct substitution method and the iterative solution. The detailed solutions can be found in Prinz (1994) and Aguwa (1997). 9.7 Conclusion Existing computer-aided design systems focus on the design and analysis of components in isolation. Since these design systems are unable to support early conceptual design, designer’s intent cannot be captured, represented, and propagated to down-stream activities. The consequence of this inability is that existing design systems are not capable of optimizing the product against life-cycle constraints. Assembly is the final manufacturing stage and is also the most complicated and cost-effective process. The early evaluation of the assembly process that is in the design stage may reduce the time and cost of production. In this chapter, we introduce a new type of mechanical product modeling system that is not only capable of capturing and integrating the designer’s intent at conceptual design level, but also of propagating these intentions as constraints to guide the development and detailing of product design and manufacturing processes. We introduced spatial relationships, an assembly representation scheme embedded with geometric information and nongeometric constraints, to carry design criteria and to serve as the common language between design engineers and manufacturing engineers in design considerations. We also introduced the 3-D variational geometry modeling technique, a constraint-based modeling revision technique that simplifies the design alternation processes. Constraints are derived from design and manufacturing specifications such that the violation will be detected automatically and communicated to both design and manufacturing engineers. Finally, we showed three applications of ProMod in computer-aided assembly: stability analysis of assembly, feasible-approach directions and precedence constraints, and kinematic modeling. Further Information The development of ProMod originated at the Automation and Robotics Laboratory at the University of Massachusetts at Amherst, and continued at the University of Pittsburgh where B. Nnaji works at the time of this writing. References Aguwa, C., Spatial Kinematics Modeling and Analysis of Spherical and Cylindrical Joints and Applications in Automated Assembly Systems, Master’s Thesis, University of Massachusetts, Amherst, February 1997. © 2001 by CRC Press LLC A00 � A01A12…A n � 1 � ( )nA n0 I
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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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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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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 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 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: Quantity analysis methods have the
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