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Journal articles on the topic 'Geometrical constraints'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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1

TROMBETTONI, GILLES, and MARTA WILCZKOWIAK. "GPDOF — A FAST ALGORITHM TO DECOMPOSE UNDER-CONSTRAINED GEOMETRIC CONSTRAINT SYSTEMS: APPLICATION TO 3D MODELING." International Journal of Computational Geometry & Applications 16, no. 05n06 (December 2006): 479–511. http://dx.doi.org/10.1142/s0218195906002154.

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Our approach exploits a general-purpose decomposition algorithm, called GPDOF, and a dictionary of very efficient solving procedures, called r-methods, based on theorems of geometry. GPDOF decomposes an equation system into a sequence of small subsystems solved by r-methods, and produces a set of input parameters.1. Recursive assembly methods (decomposition-recombination), maximum matching based algorithms, and other famous propagation schema are not well-suited or cannot be easily extended to tackle geometric constraint systems that are under-constrained. In this paper, we show experimentally that, provided that redundant constraints have been removed from the system, GPDOF can quickly decompose large under-constrained systems of geometrical constraints. We have validated our approach by reconstructing, from images, 3D models of buildings using interactively introduced geometrical constraints. Models satisfying the set of linear, bilinear and quadratic geometric constraints are optimized to fit the image information. Our models contain several hundreds of equations. The constraint system is decomposed in a few seconds, and can then be solved in hundredths of seconds.

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2

Suzuki, H., T. Ito, H. Ando, K. Kikkawa, and F. Kimura. "Solving regional constraints in components layout design based on geometric gadgets." Artificial Intelligence for Engineering Design, Analysis and Manufacturing 11, no. 4 (September 1997): 343–53. http://dx.doi.org/10.1017/s0890060400003267.

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AbstractThis paper proposes a new method for dealing with geometrical layout constraints. Geometrical layout constraints are classified into three classes of dimensional, regional, and interference constraints. Dimensional constraints are handled by using an existing methodology. A method is proposed to translate the other two classes of constraints into dimensional constraints. Thus, it is possible to uniformly deal with all of those geometrical layout constraints. The method is twofold. First, it converts regional, interference constraints into a set of simple inequalities. Then each inequality is solved by a geometric gadget, which is a structured set of dimensional constraints. A prototype system is developed and applied to some layout design examples.

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3

Hördt, Andreas, Katharina Bairlein, Matthias Bücker, and Hermann Stebner. "Geometrical constraints for membrane polarization." Near Surface Geophysics 15, no. 6 (October 1, 2017): 579–92. http://dx.doi.org/10.3997/1873-0604.2017053.

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4

Pauly, Daniel. "Geometrical constraints on body size." Trends in Ecology & Evolution 12, no. 11 (November 1997): 442. http://dx.doi.org/10.1016/s0169-5347(97)85745-x.

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5

Evans, A. K. D., I. K. Wehus, Ø. Grøn, and Ø. Elgarøy. "Geometrical constraints on dark energy." Astronomy & Astrophysics 430, no. 2 (January 20, 2005): 399–410. http://dx.doi.org/10.1051/0004-6361:20041590.

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6

de Luis-García, Rodrigo, Carl-Fredrik Westin, and Carlos Alberola-López. "Geometrical constraints for robust tractography selection." NeuroImage 81 (November 2013): 26–48. http://dx.doi.org/10.1016/j.neuroimage.2013.04.096.

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7

Maia, M. D., and G. S. Silva. "Geometrical constraints on the cosmological constant." Physical Review D 50, no. 12 (December 15, 1994): 7233–38. http://dx.doi.org/10.1103/physrevd.50.7233.

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8

Peng, Heping, and Zhuoqun Peng. "Concurrent design and process tolerances determination in consideration of geometrical tolerances." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 19-20 (August 1, 2019): 6727–40. http://dx.doi.org/10.1177/0954406219866866.

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Concurrent design and process tolerances determination may ensure the manufacturability of products, improve the design efficiency, lower the overall production cost, reduce the quantity of unqualified products, and shorten product development cycle. Yet most of the current concurrent tolerancing models focus on the concurrent design of dimensional tolerances without taking into consideration geometrical tolerances. The objective of this study is to extend the concurrent tolerancing model to consider geometrical tolerance requirements. Firstly, the geometrical tolerances are either converted into equivalent dimensional tolerances or only treated as additional machining constraints based on their respective characteristics. Then, a concurrent tolerancing model is established based on ensuring the fulfillment of the product's functional requirements, taking the combination of expected quality loss and manufacturing cost as target function, and taking the functional constraints, geometrical tolerance constraints and process bound constraints as the constraint conditions. After having established the concurrent tolerancing model, the nonlinear programming technique is employed to solve this model to gain the optimal design and process tolerances. Finally, an example of wheel assembly is given to illustrate the validity of the suggested method.

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9

SATO, Yuki, Takayuki YAMADA, Kazuhiro IZUI, and Shinji NISHIWAKI. "Topology optimization with geometrical constraints based on fictitious physical models (The geometrical constraint for molding and milling)." Transactions of the JSME (in Japanese) 83, no. 851 (2017): 17–00081. http://dx.doi.org/10.1299/transjsme.17-00081.

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10

Dong, Yan, and Mei Li. "The Geometrical Feature Recognition Method of Part Drawing." Advanced Materials Research 415-417 (December 2011): 523–26. http://dx.doi.org/10.4028/www.scientific.net/amr.415-417.523.

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This paper put forward a geometry feature recognition method of part drawing based on graph matching. Describe the constraints structure of geometric feature in geometric elements and those constraint relationships. Match sub-graph in contour closure graphics and those combination. Using linear symbol notation of chemical compounds in chemical database for reference, encode to constraint structure of geometry graphics, establish recognition mechanism of geometric characteristics by structure codes. Taking the fine-tune screw and fork parts for example, this method has been proved to be effective.

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11

Zimiao Zhang, 张子淼, 孙长库 Changku Sun, 孙鹏飞 Pengfei Sun, and 王鹏 Peng Wang. "Pose measurement method based on geometrical constraints." Chinese Optics Letters 9, no. 8 (2011): 081501–81505. http://dx.doi.org/10.3788/col201109.081501.

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12

Wang, De Lun, Jian Liu, and Da Zhun Xiao. "Geometrical characteristics of some typical spatial constraints." Mechanism and Machine Theory 35, no. 10 (October 2000): 1413–30. http://dx.doi.org/10.1016/s0094-114x(99)00077-4.

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13

Suzuki, Emiko L., Jahnavi Chikireddy, Serge Dmitrieff, Bérengère Guichard, Guillaume Romet-Lemonne, and Antoine Jégou. "Geometrical Constraints Greatly Hinder Formin mDia1 Activity." Nano Letters 20, no. 1 (December 4, 2019): 22–32. http://dx.doi.org/10.1021/acs.nanolett.9b02241.

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14

Troshin, S. M., and N. E. Tyurin. "Unitarity constraints and role of geometrical effects." Nuclear Physics A 711, no. 1-4 (December 2002): 236–39. http://dx.doi.org/10.1016/s0375-9474(02)01224-1.

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15

Shpitalni, M., and H. Lipson. "Automatic Reasoning for Design under Geometrical Constraints." CIRP Annals 46, no. 1 (1997): 85–88. http://dx.doi.org/10.1016/s0007-8506(07)60781-1.

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16

Lund, Ole, Jan Hansen, Søren Brunak, and Jakob Bohr. "Relationship between protein structure and geometrical constraints." Protein Science 5, no. 11 (November 1996): 2217–25. http://dx.doi.org/10.1002/pro.5560051108.

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17

CHAU, LING-LIE, and CHONG-SA LIM. "GEOMETRICAL CONSTRAINTS FOR D = 10, N = 1 SUPERGRAVITY." International Journal of Modern Physics A 04, no. 15 (September 1989): 3819–31. http://dx.doi.org/10.1142/s0217751x89001540.

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A set of geometrical constraints for D = 10, N = 1 supergravity is formulated. It has the meaning as integrability conditions on "hyperplanes" determined by light-like lines in the superspace. The dynamical consequence of these geometrical constraints is studied via Bianchi identities. Since no equations of motion have resulted, these geometrical constraints can form an off-shell set of constraints for the theory. We also discuss additional constraints that lead to Poincare supergravity equations of motion. The relation of the theory with D = 4 N = 4 supergravity is also illuminated.

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18

Baksa, Aleksandar. "Ehresmann connection in the geometry of nonholonomic systems." Publications de l'Institut Math?matique (Belgrade) 91, no. 105 (2012): 19–24. http://dx.doi.org/10.2298/pim1205019b.

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This article deals with a dynamic system whose motion is constrained by nonholonomic, reonomic, affine constraints. The article analyses the geometrical properties of the ?reactions" of nonholonomic constraints in Voronets?s equations of motion. The analysis shows their link with the torsion of the Ehresmann connection, which is defined by the nonholonomic constraints.

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19

Udwadia, F. E., and R. E. Kalaba. "Explicit Equations of Motion for Mechanical Systems With Nonideal Constraints." Journal of Applied Mechanics 68, no. 3 (October 9, 2000): 462–67. http://dx.doi.org/10.1115/1.1364492.

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Since its inception about 200 years ago, Lagrangian mechanics has been based upon the Principle of D’Alembert. There are, however, many physical situations where this confining principle is not suitable, and the constraint forces do work. To date, such situations are excluded from general Lagrangian formulations. This paper releases Lagrangian mechanics from this confinement, by generalizing D’Alembert’s principle, and presents the explicit equations of motion for constrained mechanical systems in which the constraints are nonideal. These equations lead to a simple and new fundamental view of Lagrangian mechanics. They provide a geometrical understanding of constrained motion, and they highlight the simplicity with which Nature seems to operate.

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20

YAMADA, Takayuki, Jun MASAMUNE, Hiroshi TERAMOTO, Takahiro HASEBE, and Hirotoshi KURODA. "Topology optimization with geometrical feature constraints based on the partial differential equation system for geometrical features (Overhang constraints considering geometrical singularities in additive manufacturing)." Transactions of the JSME (in Japanese) 85, no. 877 (2019): 19–00129. http://dx.doi.org/10.1299/transjsme.19-00129.

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21

NAKANO, Hisashi, Noriyuki TANI, and Masatake HIGASHI. "Compound-Feature Modeling Using Topological and Geometrical Constraints." Journal of the Japan Society for Precision Engineering, Contributed Papers 72, no. 3 (2006): 331–36. http://dx.doi.org/10.2493/jspe.72.331.

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22

Lunova, Mariia, Vitalii Zablotskii, Nora M. Dempsey, Thibaut Devillers, Milan Jirsa, Eva Syková, Šárka Kubinová, Oleg Lunov, and Alexandr Dejneka. "Modulation of collective cell behaviour by geometrical constraints." Integrative Biology 8, no. 11 (2016): 1099–110. http://dx.doi.org/10.1039/c6ib00125d.

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During tissue development and growth, cell colonies may exhibit a wide variety of exquisite spatial and temporal patterns. We demonstrated that the geometrical confinement caused by topographically patterned substrates modulates cell and nuclear morphology and collective cellular behavior.

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23

Le, Van-Hung, Hai Vu, Thuy Thi Nguyen, Thi-Lan Le, and Thanh-Hai Tran. "Acquiring qualified samples for RANSAC using geometrical constraints." Pattern Recognition Letters 102 (January 2018): 58–66. http://dx.doi.org/10.1016/j.patrec.2017.12.012.

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24

HIGASHI, Masatake, Hiroki SENGA, Hisashi NAKANO, and Mamoru HOSAKA. "Parametric Design Based on Topological and Geometrical Constraints." Journal of the Japan Society for Precision Engineering 67, no. 2 (2001): 229–34. http://dx.doi.org/10.2493/jjspe.67.229.

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25

Chou, Aaron, Henry Glass, H. Richard Gustafson, Craig J. Hogan, Brittany L. Kamai, Ohkyung Kwon, Robert Lanza, et al. "Interferometric constraints on quantum geometrical shear noise correlations." Classical and Quantum Gravity 34, no. 16 (July 20, 2017): 165005. http://dx.doi.org/10.1088/1361-6382/aa7bd3.

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26

Bishop, Adrian N., Baris Fidan, Brian D. O. Anderson, Kutluyil Dogancay, and Pubudu N. Pathirana. "Optimal Range-Difference-Based Localization Considering Geometrical Constraints." IEEE Journal of Oceanic Engineering 33, no. 3 (July 2008): 289–301. http://dx.doi.org/10.1109/joe.2008.926960.

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27

LONGUET-HIGGINS, MICHAEL S. "Geometrical Constraints on the Development of a Diatom." Journal of Theoretical Biology 210, no. 1 (May 2001): 101–5. http://dx.doi.org/10.1006/jtbi.2001.2301.

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28

Dorninger, D., and W. Timischl. "Geometrical constraints on Bennett's predictions of chromosome order." Heredity 59, no. 3 (December 1987): 321–25. http://dx.doi.org/10.1038/hdy.1987.138.

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29

Porrill, John. "Optimal Combination and Constraints for Geometrical Sensor Data." International Journal of Robotics Research 7, no. 6 (December 1988): 66–77. http://dx.doi.org/10.1177/027836498800700606.

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30

Toroker, Z., V. M. Malkin, A. A. Balakin, G. M. Fraiman, and N. J. Fisch. "Geometrical constraints on plasma couplers for Raman compression." Physics of Plasmas 19, no. 8 (August 2012): 083110. http://dx.doi.org/10.1063/1.4745868.

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31

Suzuki, Hiromasa, Hidetoshi Ando, and Fumihiko Kimura. "Geometric constraints and reasoning for geometrical CAD systems." Computers & Graphics 14, no. 2 (January 1990): 211–24. http://dx.doi.org/10.1016/0097-8493(90)90033-t.

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32

Heckman, C. A. "Geometrical constraints on the shape of cultured cells." Cytometry 11, no. 7 (1990): 771–83. http://dx.doi.org/10.1002/cyto.990110703.

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33

Xing, Hongjun, Kerui Xia, Liang Ding, Haibo Gao, Guangjun Liu, and Zongquan Deng. "Unknown geometrical constraints estimation and trajectory planning for robotic door-opening task with visual teleoperation assists." Assembly Automation 39, no. 3 (August 5, 2019): 479–88. http://dx.doi.org/10.1108/aa-08-2018-109.

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Purpose The purpose of this paper is to enable autonomous door-opening with unknown geometrical constraints. Door-opening is a common action needed for mobile manipulators to perform rescue operation. However, it remains difficult for them to handle it in real rescue environments. The major difficulties of rescue manipulation involve contradiction between unknown geometrical constraints and limited sensors because of extreme physical constraints. Design/methodology/approach A method for estimating the unknown door geometrical parameters using coordinate transformation of the end-effector with visual teleoperation assists is proposed. A trajectory planning algorithm is developed using geometrical parameters from the proposed method. Findings The relevant experiments are also conducted using a manipulator suited to extreme physical constraints to open a real door with a locked latch and unknown geometrical parameters, which demonstrates the validity and efficiency of the proposed approach. Originality/value This is a novel method for estimating the unknown door geometrical parameters with coordinate transformation of the end-effector through visual teleoperation assists.

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34

Mohammadi, Mohammad Hossain, Tanvir Rahman, and David Lowther. "Restricting the design space of multiple-barrier rotors of synchronous reluctance machines." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 36, no. 5 (September 4, 2017): 1338–50. http://dx.doi.org/10.1108/compel-02-2017-0109.

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Purpose This paper aims to propose a numerical methodology to reduce the number of computations required to optimally design the rotors of synchronous reluctance machines (SynRMs) with multiple barriers. Design/methodology/approach Two objectives, average torque and torque ripple, have been simulated for thousands of SynRM models using 2D finite element analysis. Different rotor topologies (i.e. number of flux barriers) were statistically analyzed to find their respective design correlation for high average torque solutions. From this information, optimal geometrical constraints were then found to restrict the design space of multiple-barrier rotors. Findings Statistical analysis of two considered SynRM case studies demonstrated a design similarity between the different number of flux barriers. Upon setting the optimal geometrical constraints, it was observed that the design space of multiple-barrier rotors reduced by more than 56 per cent for both models. Originality/value Using the proposed methodology, optimal geometrical constraints of a multiple-barrier SynRM rotor can be found to restrict its corresponding design space. This approach can handle the curse of dimensionality when the number of geometric parameters increases. Also, it can potentially reduce the number of initial samples required prior to a multi-objective optimization.

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35

Peng, Weibing, Liangliang Song, and Guoshuai Pan. "Solving topological and geometrical constraints in bridge feature model." Tsinghua Science and Technology 13, S1 (October 2008): 228–33. http://dx.doi.org/10.1016/s1007-0214(08)70154-8.

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36

CLEAVER, G. B., D. V. NANOPOULOS, J. T. PERKINS, and J. W. WALKER. "ON GEOMETRICAL INTERPRETATION OF NON-ABELIAN FLAT DIRECTION CONSTRAINTS." International Journal of Modern Physics A 23, no. 22 (September 10, 2008): 3461–92. http://dx.doi.org/10.1142/s0217751x0804161x.

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In order to produce a low-energy effective field theory from a string model, it is necessary to specify a vacuum state. In order that this vacuum be supersymmetric, it is well known that all field expectation values must be along so-called flat directions, leaving the F- and D-terms of the scalar potential to be zero. The situation becomes particularly interesting when one attempts to realize such directions while assigning vacuum expectation values to fields transforming under non-Abelian representations of the gauge group. Since the expectation value is now shared among multiple components of a field, satisfaction of flatness becomes an inherently geometrical problem in the group space. Furthermore, the possibility emerges that a single seemingly dangerous F-term might experience a self-cancellation among its components. The hope exists that the geometric language can provide an intuitive and immediate recognition of when the D and F conditions are simultaneously compatible, as well as a powerful tool for their comprehensive classification. This is the avenue explored in this paper, and applied to the cases of SU (2) and SO (2N), relevant respectively to previous attempts at reproducing the MSSM and the flipped SU (5) GUT. Geometrical interpretation of non-Abelian flat directions finds application to M-theory through the recent conjecture of equivalence between D-term strings and wrapped D-branes of Type II theory.1 Knowledge of the geometry of the flat direction "landscape" of a D-term string model could yield information about the dual brane model. It is hoped that the techniques encountered will be of benefit in extending the viability of the quasirealistic phenomenologies already developed.

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37

Zhang, J. Y., and M. Ohsaki. "Form-Finding of Tensegrity Structures Subjected to Geometrical Constraints." International Journal of Space Structures 21, no. 4 (December 2006): 183–95. http://dx.doi.org/10.1260/026635106780866024.

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38

Lomax, Jamie R., Jennifer L. Hoffman, Nicholas M. Elias II, Fabienne A. Bastien, and Bruce D. Holenstein. "GEOMETRICAL CONSTRAINTS ON THE HOT SPOT IN BETA LYRAE." Astrophysical Journal 750, no. 1 (April 16, 2012): 59. http://dx.doi.org/10.1088/0004-637x/750/1/59.

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39

Soteros, C. E., and S. G. Whittington. "Lattice models of branched polymers: effects of geometrical constraints." Journal of Physics A: Mathematical and General 22, no. 24 (December 21, 1989): 5259–70. http://dx.doi.org/10.1088/0305-4470/22/24/014.

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40

Chau, Ling-Lie, and Chong-Sa Lim. "Geometrical constraints and equations of motion in extended supergravity." Physical Review Letters 56, no. 4 (January 27, 1986): 294–97. http://dx.doi.org/10.1103/physrevlett.56.294.

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41

Calvo-López, José, and Macarena Salcedo-Galera. "Geometrical Proportion in the Sixteenth Century: Methods and Constraints." Nexus Network Journal 19, no. 1 (February 10, 2017): 155–78. http://dx.doi.org/10.1007/s00004-017-0329-9.

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42

Doodhi, Harinath, Eugene A. Katrukha, Lukas C. Kapitein, and Anna Akhmanova. "Mechanical and Geometrical Constraints Control Kinesin-Based Microtubule Guidance." Current Biology 24, no. 3 (February 2014): 322–28. http://dx.doi.org/10.1016/j.cub.2014.01.005.

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43

Porwal, Gaurav, Swapnil Jain, S. Dhilly Babu, Deepak Singh, Hemant Nanavati, and Santosh Noronha. "Protein structure prediction aided by geometrical and probabilistic constraints." Journal of Computational Chemistry 28, no. 12 (2007): 1943–52. http://dx.doi.org/10.1002/jcc.20736.

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44

Rajagopal, K. R., and A. R. Srinivasa. "On the nature of constraints for continua undergoing dissipative processes." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2061 (July 28, 2005): 2785–95. http://dx.doi.org/10.1098/rspa.2004.1385.

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When dealing with mechanical constraints, it is usual in continuum mechanics to enforce ideas that stem from the seminal work of Bernoulli and D'Alembert and require that internal constraints do no work. The usual procedure is to split the stress into a constraint response and a constitutively determined response that does not depend upon the variables that appear in the constraint response (i.e. the Lagrange multiplier), and further requiring that the constraint response does no work. While this is adequate for hyperelastic materials, it is too restrictive in the sense that it does not permit a large class of useful models such as incompressible fluids whose viscosity depends upon the pressure—a model that is widely used in elastohydrodynamics. The purpose of this short paper is to develop a purely mechanical theory of continua with an internal constraint that does not appeal to the requirement of worklessness. We exploit a geometrical idea of normality of the constraint response to a surface (defined by the equation of constraint) in a six-dimensional Euclidean space to obtain (i) a unique decomposition of the stress into a determinate and a constraint part such that their inner product is zero, (ii) a completely general constraint response—even constraint equations that are nonlinear in the symmetric part of the velocity gradient D as well as when the coefficients in the determinate part depend upon the constraint response and (iii) a second order partial differential equation for the determination of the constraint response. The geometric approach presented here is in keeping with the ideas of Gauss concerning constraints in classical particle mechanics.

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45

Mark, Earl, and Zita Ultmann. "Environmental footprint design tool: Exchanging geographical information system and computer-aided design data in real time." International Journal of Architectural Computing 14, no. 4 (September 28, 2016): 307–21. http://dx.doi.org/10.1177/1478077116670740.

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The pairing of computer-aided design and geographical information system data creates an opportunity to connect an architectural design process with a robust analysis of its environmental constraints. Yet, the geographical information system data may be too overwhelmingly complex to be fully used in computer-aided design without computer-assisted methods of filtering relevant information. This article reports on the implementation of an integrated environment for three-dimensional computer-aided design and environmental impact. The project focused on a two-way data exchange between geographical information system and computer-aided design in building design. While the two different technologies may rely on separate representational models, in combination they can provide a more complete view of the natural and built environment. The challenge in integration is that of bridging the differences in analytical methods and database formats. Our approach is rooted in part in constraint-based design methods, well established in computer-aided design (e.g. Sketchpad, Generative Components, and computer-aided three-dimensional interactive application). Within such computer-aided design systems, geometrical transformations may be intentionally constrained to help enforce a set of design determinants. Although this current implementation modestly relates to geometrical constraints, the use of probabilistic risk values is more central to its methodology.

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46

Anco, Stephen C., and Bao Wang. "Geometrical Formulation for Adjoint-Symmetries of Partial Differential Equations." Symmetry 12, no. 9 (September 19, 2020): 1547. http://dx.doi.org/10.3390/sym12091547.

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A geometrical formulation for adjoint-symmetries as one-forms is studied for general partial differential equations (PDEs), which provides a dual counterpart of the geometrical meaning of symmetries as tangent vector fields on the solution space of a PDE. Two applications of this formulation are presented. Additionally, for systems of evolution equations, adjoint-symmetries are shown to have another geometrical formulation given by one-forms that are invariant under the flow generated by the system on the solution space. This result is generalized to systems of evolution equations with spatial constraints, where adjoint-symmetry one-forms are shown to be invariant up to a functional multiplier of a normal one-form associated with the constraint equations. All of the results are applicable to the PDE systems of interest in applied mathematics and mathematical physics.

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Nishida, Isamu, Shogo Adachi, and Keiichi Shirase. "Automated Process Planning System for End Milling Operation Constrained by Geometric Dimensioning and Tolerancing (GD&T)." International Journal of Automation Technology 13, no. 6 (November 5, 2019): 825–33. http://dx.doi.org/10.20965/ijat.2019.p0825.

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To realize autonomous machining, it is necessary to focus on machining tools and also on the automation of process planning in the preparation stage. This study proposes a process planning system that automatically defines the machining region and determines the machining sequence. Although previous studies have explored computer-aided process planning, only a few have considered geometric tolerances. Geometric tolerances are indicated on product drawings to eliminate their ambiguity and manage machining quality. Geometric dimensioning and tolerancing (GD&T) is a geometric tolerance standard applied to a three-dimensional computer-aided design (3D CAD) model and are expected to be used for the digitization of manufacturing. Therefore, this study developed an automated process planning system by using GD&T as a sequencing constraint. In the proposed system, the machining sequence is automatically determined by the geometrical constraints, which indicate whether the tool can approach, and GD&T, which indicates the geometric tolerance and datum in a 3D CAD model. A case study validated the proposed method of automated process planning constrained by GD&T. The result shows that the proposed system can automatically determine the machining sequence according to the geometric tolerance in a 3D CAD model.

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48

Ma, T. Q., K. T. Ooi, and T. N. Wong. "Geometrical optimization of bare tube heat exchangers for process industries." Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 219, no. 2 (May 1, 2005): 139–47. http://dx.doi.org/10.1243/095440805x8584.

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This paper presents simulation results on the geometrical optimization design of bare tube heat exchangers. By linking a mathematical model with an optimization alogorithm, it is possible to predict which combination of five geometrical variables would produce a given coil capacity of a heat exchanger, the minimum core volume size operating at the minimum pressure drop. A constrained multivariable direct search technique is used in which the five geometrical variables and a mixture of five explicit and implicit constraints are accommodated. Using this design method, three typical sizes of bare tube optimization cases have been studied. The simulation results predict significant performance improvements for heat exchanger design. The range of tube outer diameter in this optimization study is from 4.9 to 9.0 mm.

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BARCELOS-NETO, J., and C. WOTZASEK. "SYMPLECTIC QUANTIZATION OF CONSTRAINED SYSTEMS." Modern Physics Letters A 07, no. 19 (June 21, 1992): 1737–47. http://dx.doi.org/10.1142/s0217732392001439.

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It is shown that the symplectic two-form, which defines the geometrical structure of a constrained theory in the Faddeev-Jackiw approach, may be brought into a non-degenerated form, by an iterative implementation of the existing constraints. The resulting generalized brackets coincide with those obtained by the Dirac bracket approach, if the constrained system under investigation presents only second-class constraints. For gauge theories, a symmetry breaking term must be supplemented to bring the symplectic form into a non-singular configuration. At present, the singular symplectic two-form provides directly the generators of the time independent gauge transformations.

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Liu, Xia, Luling An, Zhiguo Wang, Changbai Tan, and Xiaoping Wang. "Tolerance Analysis of Over-Constrained Assembly Considering Gravity Influence: Constraints of Multiple Planar Hole-Pin-Hole Pairs." Mathematical Problems in Engineering 2018 (November 14, 2018): 1–18. http://dx.doi.org/10.1155/2018/2039153.

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Over-constrained assembly of rigid parts is widely adopted in aircraft assembly to yield higher stiffness and accuracy of assembly. Unfortunately, the quantitative tolerance analysis of over-constrained assembly is challenging, subject to the coupling effect of geometrical and physical factors. Especially, gravity will affect the geometrical gaps in mechanical joints between different parts, and thus influence the deviations of assembled product. In the existing studies, the influence of gravity is not considered in the tolerance analysis of over-constrained assembly. This paper proposes a novel tolerance analysis method for over-constrained assembly of rigid parts, considering the gravity influence. This method is applied to a typical over-constrained assembly with constraints of multiple planar hole-pin-hole pairs. This type of constraints is non-linear, which makes the tolerance analysis more challenging. Firstly, the deviation propagation analysis of an over-constrained assembly is conducted. The feasibility of assembly is predicted, and for a feasible assembly, the assembly deviations are determined with the principle of minimum potential energy. Then, the statistical tolerance analysis is performed. The probabilities of assembly feasibility and quality feasibility are computed, and the distribution of assembly deviations is estimated. Two case studies are presented to show the applicability of the proposed method.

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