ComputerAided_Design_Engineering_amp_Manufactur.pdf

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FIGURE 4.9 Form error and setup error for sculptured surface. 2. Calculate the Euclidean distance from the measured point to the points of 1/4 and 3/4 location 3. Assign the shortest distance point as the nearest point (Qi � Ri). 4. Choose the subsection having the shortest distance point for further subdivision. 5. Calculate � | ( Qi � Ri) where is the currently determined nearest point and is the previously determined nearest point. 6. Repeat steps 1 to 5 until the calculated � is not greater than the assigned tolerance. n ( ) n 1 ( Qi � Ri) � ( ) � � | , ( Qi � Ri) n ( ) n 1 ( Qi � Ri) � ( ) Profile Tolerance (Form Error) Evaluation When the actual measurement points are found, the Euclidean distance can be calculated using Equation (4.27), and the dimensional errors for the parts can be obtained from the Euclidean distance data. There are two types of error in the sculpture surface affecting dimensional accuracy of the products: (1) The form error (profile tolerance), which is one of the characteristics unique to the sculptured surface, and (2) The setup error involved in tilting or translation of the sculptured surface. Generally, the form error and the setup error are combined to give the dimensional errors for the sculptured surface. The relationship between the profile tolerance (form error) and the setup error is illustrated in Figure 4.9. In the case of mold cavity manufacturing, the profile tolerance is unique to the machined cavity of the sculptured surface, and the setup error is associated with the adjustment of the cavity in the mold. As an ex<strong>amp</strong>le of the metrological meaning of the setup error, consider the case of flatness analysis of a plane. A mathematically defined reference plane is derived so that the maximum deviation is minimum for all possible transformations, and thus the evaluated maximum deviation is unique to the plane. Similarly, a mathematically defined sculptured surface having a setup error from the CAD-defined sculptured surface can be determined so that the maximum Euclidean distance is minimum for all possible transformations. For the given total error of sculptured surface, the form error and the setup error are dependent on the transformation matrix T because the Euclidean distance between the measurement points and the CAD-defined points is dependent on the T matrix as in Equation (4.27). The transformation matrix T is also dependent on the actual measurement points, (Q i � R i). Thus recursive iteration can be used for determining the transformation matrix and the Euclidean distance. For a trial transformation matrix T the trial form error D can be calculated as the maximum distance between the measurement points and the points on the offset curve: D max|T (4.28) An optimal transformation matrix T can be found such that the trial form error D is minimum, which is the profile tolerance. Thus, the profile tolerance is 1 � � Pi � ( Qi � Ri) | for i � 1, 2,…, n Profile tolerance � min D for all possible transformation (4.29)
The calculated minimum form error is the profile tolerance which is unique to the sculptured surface. The optimal transformation matrix giving the minimum form error then becomes the optimal setup. In this section, an iterative algorithm, MINIMAXSURF 11 , is explained using the Chebyshev norm between the measured points and the corresponding closest points. Again, let P i be the measured points data, Q i � R i be the calculated closest points on the offset surface defined by the CAD geometry, and T be the transformation matrix between the two data. The Chebyshev norm of power p, L p, can be defined as (4.30) The L p can be minimized with respect to the transformation matrix T and the optimum transformation matrix T 0 can be found. The profile tolerance E is then The algorithm for the profile tolerance evaluation is implemented as (4.31) 1. Set the iteration index k as 0, and the initial transformation matrix as the multiplication of T1 and T2 in case of the rough-phase and fine-phase alignment. 2. Input the measured point data Pi for i � 1, 2, …, n, where n is the total number of measured points on the surface. 3. Assign the initial closest point corresponding to the Pi as the measurement target point. 4. Calculate the initial profile error for i � 1, …, n. 5. Increase the iteration index k by 1. 6. Find the closest point corresponding to the transformed 7. Calculate the kth iterative transformation matrix, such that the Chebyshev norm, be minimum using the universal alignment algorithm. 11 ( Qi � Ri) 8. Calculate the kth iterative profile error, for i � 1, 2, …, n. 9. Evaluate the incremental maximum deviation, . 10. If the incremental maximum deviation is less than the assigned tolerance TOL then proceed to the end; otherwise increase k by 1. 11. Repeat steps 5 through 10 until the criterion is met. 0 ( ) Eo max | T 0 ( ) [ ] 1 � Pi ( Qi � Ri) 0 ( ) � � | ( Qi � Ri) k ( ) T k�1 ( ) [ ] 1 � Pi T k ( ) , �| T k ( ) [ ] 1 � [ Pi ( Qi � Ri) k ( ) � | p ] 1�p E k ( ) � max | T k ( ) [ ] 1 � Pi ( Qi � Ri) k ( ) � | DEk |E k ( ) E k�1 ( ) � � | The flowchart of the implemented algorithm is shown in Figure 4.10. Error Evaluation for Basic Features L p � � |T 1 � Pi � Qi � Ri �1 Pi Qi Ri ( )| E � max |T0 � ( � ) | for i � 1, 2… , , N Flatness is the deviation of measured points with respect to the mathematically determined reference plane; the flatness error is evaluated as the distance between the maximum and minimum deviation. Squareness tolerance is the tolerance zone limited by two perpendicular planes to the given reference plane, where the two perpendicular planes contain the whole measured feature. The reference plane can be determined as the best fit plane by using the least squares technique. Parallelism tolerance is defined as the tolerance zone limited by two parallel planes which are parallel to the reference plane; the reference plane can be constructed as the best fit plane by using the least squares technique. The straightness tolerance is defined by the minimum distance between two parallel lines containing the measured datum. The slope of two parallel lines can be mathematically determined as the best fit line by using the least squares technique. The roundness tolerance is defined as the tolerance zone limited by two concentric circles; the circles can be calculated by the least squares circle (LSC), the minimum zone circle (MZC), the minimum circumscribed circle (MCC), and the maximum inscribed circle (MIC). p 1�p T 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
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 92: and moments about the contact point
Page 93 and 94: een identified, the normals are use
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: FIGURE 4.8(a) Profile tolerance of
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
Page 143 and 144: FIGURE 5.7 Techniques of defining a
Page 145 and 146: Feature Recognition and Extraction
Page 147 and 148: in relation to another feature (e.g
Page 149 and 150: FIGURE 5.9 Framework for building a
Page 151 and 152: FIGURE 5.10 Process plan content.
Page 153 and 154: FIGURE 5.12 Schematic sketch of the
Page 155 and 156: Several techniques of defining a fe
Page 157 and 158: TABLE 5.1 Data Structure for Repres
Page 159 and 160: FIGURE 5.16 Classification of the t
Page 161 and 162: system to ensure that the part bein
Page 163 and 164: FIGURE 5.19 Graphical model of the
Page 165 and 166: TABLE 5.4 Data Structure for Repres
Page 167 and 168: FIGURE 5.20 Mapping between machini
Page 169 and 170: algorithms. (Some details of the pr
Page 171 and 172: FIGURE 5.24 An example rotational p
Page 173 and 174: FIGURE 5.26 Down_face-turn-up_face
Page 175 and 176: 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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