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FIGURE 9.9 Derivation of mating frames. With the same sequence of calculations, one can find the direction of mating frame axes of the mating part. Relationships such as parallel-offset, incline-offset, and include-angle may use this method of reversing one of the normal directions of a face of a part. For a cylindrical (spherical) feature, the normal directions of the feature are infinite; the orientation can be finite through the intersection of other features’ spatial relationships. Product Specification Attributes Product specifications describe the constraints of form and function of a product. Tolerances are form specifications that specify the available range for position, orientation, and form of a product or component. Function specifications describe the functional performance of a product or its individual components. Form specifications influence the functional performance; function is the product of interaction of forms. For example, in order to fasten two blocks with a screw, the bolt of the screw must have the same type of thread as the threaded hole of the block below. Based on design principles, the hole for the block above has to be a smooth cylindrical surface. The outside diameters should be the same for the threaded holes and the depth of thread of the bolt should move far enough to make contact with the threaded hole of the bottom block. It can be seen that the form specifications needed are: thread type, thread length, and the diameter tolerance. In assembling the forms, the fasten function can thus be achieved. In this example, if designers assign the screw-fasten function between threaded hole and bolt with a specified load, then they provide enough information for searching the form specifications for both bolt and threaded hole. We propose that the most appropriate time to assign the specifications to a product is in the assembly mode, which saves human effort and clarifies the intention of the designer. Product specification attributes such as functional descriptions and positional specifications can be specified by the designers. Others can be automatically (or interactively, when the default information is insufficient) generated through the specifications assigned. These specification attributes contain the information about the methods of assembly (such as glue, weld, snap fit, etc.) and the tolerances associated with positioning the parts. Through assignment of the spatial relationships, these attributes are inferred. For example, in Figure 9.2, the positional tolerances Da � ta and Db � tb are assigned with association of parallel-offset, and then the tolerance Dc � tc and Dd � td of components are decided upon. With complete specifications represented and assigned, this information can be propagated to a postprocessor such as tolerance propagation and process planning. In the next section, we © 2001 by CRC Press LLC
will introduce a way to propagate product specification into dimensional constraints of the part model. These dimensions are shown on the final drawings, and they are also the constraints used by 3-D variational geometry. Tolerance Propagation and Control In this section, we will briefly outline Bjorke’s (1989) theories on tolerance analysis. This will lead to the basis of tolerance propagation and control that help a designer attach dimensions to components. Tolerance control is the process of fitting a sum dimension tolerance to that specified by the designer; tolerance propagation allocates the specified tolerance to individual dimension tolerances. Tolerance propagation and control both require the identification of one or more sum dimensions. A sum dimension, or functional dimension, is any dimension that affects the functionality of the assembly more than the other dimension (Bjorke, 1989). The sum dimension tolerance (T_s) will be influenced by the tolerances on any individual dimension in the assembly, which affect the sum dimension. The relationship between these individual tolerances and the sum dimension tolerance is known as the fundamental equation. For a particular assembly, there may be several sum dimensions, each of which will have a fundamental equation of the form: where T_i is the ith sum dimension tolerance, T_j is the tolerance of the jth dimension influencing the sum dimension. The fundamental equations can be used to generate tolerance chains that can be shown visually using graphs in which arcs represent chain links and vertices represent the connections between the chain links. There are two types of tolerance chains of interest, namely the simple chain, in which no element is encountered twice, and the interrelated chain, which covers all other cases in which at least one endpoint is encountered twice. An example of an assembly generating an interrelated tolerance chain is shown in Figure 9.10. The dimensions S1 and S2 in the diagram denote sum dimensions, while the dimensions D1 to D3 show part dimensions. The data A and B, the tolerance on the sum dimensions, and the geometric tolerance of parallelism between faces A-F_1 and B-F_2 are originally specified by the designer when the assembly model is generated. Note that, due to the against- and clearance-fit spatial relationships and the riveting of parts B and C into position, any eccentricity between the holes in part A and the shafts of parts B and C will not affect the sum dimensions. This tolerance chain is interrelated. We see that the tolerances T_S1 and T_S2 are propagated into T_D1, T_D2 and T_D3, while the tolerance TP_S1 is propagated into TP_D1 and TP_D2 such that TP_S1 � f(TP_D1, TP_D2). Proper datum selection by the designer is important since this is the basis of the determination of the individual dimensions affecting the sum dimension and hence the fundamental equations. The steps required in order to carry out tolerance propagation are as follows: 1. Break down sum dimension to component dimension by analyzing dimension data and spatial relationships within the assembly that affect sum dimension. 2. Establish a cost function by identifying the contribution of each individual tolerance to the manufacturing cost of the assembly. 3. Prepare fundamental equations of sum tolerances. 4. Solve fundamental equations that minimize cost function. It is envisaged that the ability to represent traditional and geometric tolerances will enable the analysis of the effect of a given geometric tolerance on a particular sum dimension, thus providing this tolerance analysis module. © 2001 by CRC Press LLC T_i � f_i(T_1,T_2,…T_j,…T_n)
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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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Page 271 and 272: 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: 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 and 330: Quantity analysis methods have the
Page 331 and 332: y a revolute joint. By selecting al
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