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Journal articles on the topic 'Parallelogram'

Author: Grafiati

Published: 4 June 2021

Last updated: 29 May 2022

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1

Bae, Sang Won. "On the Minimum-Area Parallelogram Annulus Problem." Symmetry 14, no. 2 (February 11, 2022): 359. http://dx.doi.org/10.3390/sym14020359.

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The minimum-area parallelogram annulus problem is studied, in which one wants to compute a parallelogram annulus of minimum area that includes n input points in the plane. Extending an usual, doughnut-shaped circular annulus, a parallelogram annulus is defined to be a region between two edge-parallel parallelograms. As a parallelogram has two distinct orientations for its sides, so does a parallelogram annulus as well. In this paper, several variants of the problem are considered: (1) when both side orientations are given and fixed, (2) when one of them is fixed and the other can be freely chosen, (3) when the interior angles of the resulting parallelogram annulus is given and fixed, and (4) when both side orientations can be chosen arbitrarily. The first and efficient algorithms for each of these cases are presented, whose running times are (1) O(n), (2) O(n2logn), (3) O(n2logn), and (4) O(n4+ϵ), respectively. Further, bicriteria variants of the problem are considered, in which both width and area of the resulting parallelogram annulus are simultaneously minimized. In order to obtain these new algorithms, geometric observations, newly obtained in this paper and known in previous papers, and the symmetric nature of parallelograms and parallelogram annuli are exploited.

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2

Toumasis, Charalmpos. "When Is a Quadrilateral a Parallelogram?" Mathematics Teacher 87, no. 3 (March 1994): 208–11. http://dx.doi.org/10.5951/mt.87.3.0208.

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In most high school geometry textbooks the subject of parallelograms is usually treated in the following manner. First the definition is given: “A quadrilateral in which the opposite sides are parallel is called a parallelogram.” After this definition, some properties of parallelograms are mentioned that can serve as criteria for determining when a quadrilateral is a parallelogram.

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3

Salgado, Oscar, Oscar Altuzarra, Enrique Amezua, and Alfonso Hernández. "A Parallelogram-Based Parallel Manipulator for Schönflies Motion." Journal of Mechanical Design 129, no. 12 (December 28, 2006): 1243–50. http://dx.doi.org/10.1115/1.2779898.

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A parallelogram-based 4 degrees-of-freedom parallel manipulator is presented in this paper. The manipulator can generate the so-called Schönflies motion that allows the end effector to translate in all directions and rotate around an axis parallel to a fixed direction. The theory of group of displacements is applied in the synthesis of this manipulator, which employs parallelograms in every limb. The planar parallelogram kinematic chain provides a high rotational capability and an improved stiffness to the manipulator. This paper shows the kinematic analysis of the manipulator, including the closed-form resolution of the forward and inverse position problems, the velocity, and the singularity analysis. Finally, a prototype of the manipulator, adding some considerations about its singularity-free design, and some technical applications in which the manipulator can be used are presented.

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4

Shurtleff, Richard. "Parallelogram space." General Relativity and Gravitation 27, no. 5 (May 1995): 495–509. http://dx.doi.org/10.1007/bf02105075.

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5

Zhang, Li Nan, Shu Xin Wang, Jian Min Li, and Jin Hua Li. "Design of a Master Manipulator with Dynamical Simplification for Master-Slave Robot." Applied Mechanics and Materials 418 (September 2013): 3–9. http://dx.doi.org/10.4028/www.scientific.net/amm.418.3.

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Dynamic behavior is an important factor to affect the performance of surgical robot, especially force-feedback master manipulator. In this paper, a force-feedback master manipulator with parallelogram is developed, which can realize self-gravity balance; Compare the dynamics of the force-feedback master manipulator with parallelogram mechanism and another one without parallelogram mechanism. The result shows that the dynamical equation of the master manipulator with parallelogram mechanism is simpler than the one without parallelogram mechanism. This parallelogram mechanism can be generally used in all the mechanical design that is needed to simplify the dynamics.

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6

Chao, Wu Wei, and Li Zhou. "Parallelogram Circumcenters: 10874." American Mathematical Monthly 109, no. 7 (August 2002): 669. http://dx.doi.org/10.2307/3072446.

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7

Boussicault, Adrien, and Patxi Laborde-Zubieta. "Periodic parallelogram polyominoes." Electronic Notes in Discrete Mathematics 59 (June 2017): 177–88. http://dx.doi.org/10.1016/j.endm.2017.05.013.

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8

Yuan, Liping, Yuqin Zhang, and Ren Ding. "Trisecting a parallelogram." Applied Mathematics-A Journal of Chinese Universities 17, no. 3 (September 2002): 307–12. http://dx.doi.org/10.1007/s11766-002-0009-7.

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9

Wang, Feng Hui, Qian Liu, and Hai Ming Wang. "Clamp Equipment Design and Motion Analysis with ANSYS for Large Cylindrical Segment." Applied Mechanics and Materials 197 (September 2012): 110–13. http://dx.doi.org/10.4028/www.scientific.net/amm.197.110.

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In this research, a kind of clamp for large cylindrical segment slinging and transportation was designed. Instead of the traditional theory that based of friction to slinging and transport, a new designing method that slinging cylindrical segment by grasping double hooks was taken in this research. Parallelogram structure was used to keep the clamp synchronous and horizontal movement. The design process is that Using principles of Parallelogram structure, Parallelogram structure is initially established. Parallelogram structure Motion analysis function of the ANSYS software was used to analyze the motion status of this parallelogram structure under the load. Ensure rationality of design.

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10

Griffiths, A. Fuzz, and Qasim Zaidi. "Perceptual Assumptions and Projective Distortions in a Three-Dimensional Shape Illusion." Perception 29, no. 2 (February 2000): 171–200. http://dx.doi.org/10.1068/p3013.

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We examine a shape illusion, in which the balconies of a building appear to tilt up or down, depending on the viewpoint. The balconies are actually level parallelogram shapes, but appear as tilted rectangles. We measured the illusory tilts observed when parallelogram shapes are viewed above the line of sight, using three-dimensional stimuli consisting of parallelograms of various tilts viewed at different orientations. Under perspective projection, parallelism and orthogonality are not preserved. However, perspective distortions alone cannot account for the perceived tilts measured in these experiments, since observers perceived illusory tilts even for stimuli in the frontoparallel plane. We introduce a model, based on the theory that observers assume ambiguously projected three-dimensional angles to be equal to 90°, but revise their predictions on the basis of observation. In the model, perceived tilt is predicted as a weighted sum of the tilts predicted by the assumptions that the shape is rectangular, and that the shape is level (ie that the angle between the shape and the vertical backboard is equal to 90°). We prove that it is mathematically impossible for a planar rectangle to share a projection with a nonrectangular parallelogram. A less restrictive assumption that just the two leading internal angles are equal to 90° is suggested as an alternative, and it is further proven that this new configuration of angles leads to a unique perceived tilt. The relative weights in the model reflect the amount that each prediction is revised, and are shown to vary systematically with stimulus orientation. For some observers a better fit was found by replacing the level-tilt assumptions with an assumption that physical tilt was equal to the projected tilt.

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11

Bair, Sherry L., and JoAnn Cady. "Parts of a Parallelogram." Mathematics Teaching in the Middle School 20, no. 5 (December 2014): 267–71. http://dx.doi.org/10.5951/mathteacmiddscho.20.5.0267.

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12

Nash, Alan. "A Generalized Parallelogram Law." American Mathematical Monthly 110, no. 1 (January 2003): 52. http://dx.doi.org/10.2307/3072345.

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13

Gasparyan, A. G., and V. K. Ohanyan. "Covariogram of a parallelogram." Journal of Contemporary Mathematical Analysis 49, no. 4 (July 2014): 194–206. http://dx.doi.org/10.3103/s1068362314040050.

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14

Nash, Alan. "A Generalized Parallelogram Law." American Mathematical Monthly 110, no. 1 (January 2003): 52–57. http://dx.doi.org/10.1080/00029890.2003.11919938.

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15

Lord, Nick. "99.34 A special parallelogram." Mathematical Gazette 99, no. 546 (November 2015): 530–32. http://dx.doi.org/10.1017/mag.2015.96.

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16

Tian, Yaobin, Xiangzhi Wei, Ajay Joneja, and Yan-An Yao. "Sliding–crawling parallelogram mechanism." Mechanism and Machine Theory 78 (August 2014): 201–28. http://dx.doi.org/10.1016/j.mechmachtheory.2014.03.013.

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17

Benvenuto, Edoardo. "The parallelogram of forces." Meccanica 20, no. 4 (December 1985): 322. http://dx.doi.org/10.1007/bf02352689.

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18

Eğecioğlu, Ömer. "Parallelogram-law-type identities." Linear Algebra and its Applications 225 (August 1995): 1–12. http://dx.doi.org/10.1016/0024-3795(93)00301-f.

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19

Benvenuto, Edoardo. "The parallelogram of forces." Meccanica 20, no. 2 (June 1985): 99–109. http://dx.doi.org/10.1007/bf02337628.

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20

Delest, M., J. P. Dubernard, and I. Dutuor. "Parallelogram Polyominoes and Corners." Journal of Symbolic Computation 20, no. 5-6 (November 1995): 503–15. http://dx.doi.org/10.1006/jsco.1995.1062.

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21

Yang, Qi, and Chuanming Zong. "Multiple Lattice Tilings in Euclidean Spaces." Canadian Mathematical Bulletin 62, no. 4 (November 16, 2018): 923–29. http://dx.doi.org/10.4153/s0008439518000103.

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AbstractIn 1885, Fedorov discovered that a convex domain can form a lattice tiling of the Euclidean plane if and only if it is a parallelogram or a centrally symmetric hexagon. This paper proves the following results. Except for parallelograms and centrally symmetric hexagons, there are no other convex domains that can form two-, three- or four-fold lattice tilings in the Euclidean plane. However, there are both octagons and decagons that can form five-fold lattice tilings. Whenever $n\geqslant 3$, there are non-parallelohedral polytopes that can form five-fold lattice tilings in the $n$-dimensional Euclidean space.

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22

Hines, Ellen, and Jesse Bridges. "Explorations with a Functioning Flex-O-Gram." Mathematics Teaching in the Middle School 8, no. 6 (February 2003): 294–99. http://dx.doi.org/10.5951/mtms.8.6.0294.

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23

Edakin, A. I., T. V. Edakina, V. V. Samoilova, and V. S. Ramzhaev. "Structural Synthesis and Analysis of Mechanisms with an Output Link Performing Two Rotational and One Translational Movements." Proceedings of Higher Educational Institutions. Маchine Building, no. 11 (740) (November 2021): 43–49. http://dx.doi.org/10.18698/0536-1044-2021-11-43-49.

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The article considers mechanisms based on a hinged flat parallelogram with an additional link, ensuring the ability to maintain the insertion point of the tool installed on the output link. A rotational kinematic pair coupled to the base allows the plane of rotation of the articulated parallelogram to change the angle of inclination. The proposed design should have a greater load capacity than the available analogues, since the rotational kinematic pair mating the articulated parallelogram with the base is made in the form of two semi-axes, and the output link is located between the intermediate links of this parallelogram. The equality of the rotation angles of the output link and the intermediate links of the articulated parallelogram is ensured by the presence of additional links or belt drives. Three-dimensional models of these mechanisms are presented, and their structural synthesis is carried out in various modifications. Depending on the modification, it becomes possible to apply such mechanisms not only in industry, including additive technologies, but also in the field of medicine during surgical operations and in the study of plasma properties.

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24

Hao, Guangbo, Xianwen Kong, and Xiuyun He. "A planar reconfigurable linear rigid-body motion linkage with two operation modes." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 228, no. 16 (February 11, 2014): 2985–91. http://dx.doi.org/10.1177/0954406214523754.

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A planar reconfigurable linear (also rectilinear) rigid-body motion linkage (RLRBML) with two operation modes, that is, linear rigid-body motion mode and lockup mode, is presented using only R (revolute) joints. The RLRBML does not require disassembly and external intervention to implement multi-task requirements. It is created via combining a Robert’s linkage and a double parallelogram linkage (with equal lengths of rocker links) arranged in parallel, which can convert a limited circular motion to a linear rigid-body motion without any reference guide way. This linear rigid-body motion is achieved since the double parallelogram linkage can guarantee the translation of the motion stage, and Robert’s linkage ensures the approximate straight line motion of its pivot joint connecting to the double parallelogram linkage. This novel RLRBML is under the linear rigid-body motion mode if the four rocker links in the double parallelogram linkage are not parallel. The motion stage is in the lockup mode if all of the four rocker links in the double parallelogram linkage are kept parallel in a tilted position (but the inner/outer two rocker links are still parallel). In the lockup mode, the motion stage of the RLRBML is prohibited from moving even under power off, but the double parallelogram linkage is still moveable for its own rotation application. It is noted that further RLRBMLs can be obtained from the above RLRBML by replacing Robert’s linkage with any other straight line motion linkage (such as Watt’s linkage). Additionally, a compact RLRBML and two single-mode linear rigid-body motion linkages are presented.

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25

DUECK, Daniela. "The Parallelogram and the Pinecone." Ancient Society 35 (December 1, 2005): 19–57. http://dx.doi.org/10.2143/as.35.0.2003840.

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26

Kearnes, Keith A., and Ágnes Szendrei. "Dualizable algebras with parallelogram terms." Algebra universalis 76, no. 4 (October 12, 2016): 497–539. http://dx.doi.org/10.1007/s00012-016-0410-3.

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27

Vagin, V. A., and B. E. Moshkin. "Parallelogram interferometer for Fourier spectrometers." Journal of Optical Technology 86, no. 2 (February 1, 2019): 105. http://dx.doi.org/10.1364/jot.86.000105.

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28

Liang, Yuh-jeng, and Chih-wen Weng. "Parallelogram-Free Distance-Regular Graphs." Journal of Combinatorial Theory, Series B 71, no. 2 (November 1997): 231–43. http://dx.doi.org/10.1006/jctb.1997.1787.

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29

Sulanke:, Robert A. "Three recurrences for parallelogram polyominoes." Journal of Difference Equations and Applications 5, no. 2 (January 1999): 155–76. http://dx.doi.org/10.1080/10236199908808178.

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30

Bogart, Kenneth P., Joshua Douglass Laison, and Stephen P. Ryan. "Triangle, Parallelogram, and Trapezoid Orders." Order 27, no. 2 (April 27, 2010): 163–75. http://dx.doi.org/10.1007/s11083-010-9144-6.

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31

Zheng, Gangfeng, Bin Wu, and Cunfu He. "Shape reconstruction of parallelogram flaw." Frontiers of Mechanical Engineering in China 3, no. 1 (March 2008): 17–22. http://dx.doi.org/10.1007/s11465-008-0015-4.

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32

Aval, J. C., F. Bergeron, and A. Garsia. "Combinatorics of labelled parallelogram polyominoes." Journal of Combinatorial Theory, Series A 132 (May 2015): 32–57. http://dx.doi.org/10.1016/j.jcta.2014.12.003.

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33

Power. "Parallelogram Frameworks and Flexible Quasicrystals." Mathematical Proceedings of the Royal Irish Academy 121A, no. 1 (2021): 9. http://dx.doi.org/10.3318/pria.2021.121.02.

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34

Power, Stephen C. "Parallelogram Frameworks and Flexible Quasicrystals." Mathematical Proceedings of the Royal Irish Academy 121, no. 1 (2021): 9–31. http://dx.doi.org/10.1353/mpr.2021.0000.

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35

Trochimczuk, R. "Analysis of Parallelogram Mechanism used to Preserve Remote Center of Motion for Surgical Telemanipulator." International Journal of Applied Mechanics and Engineering 22, no. 1 (February 1, 2017): 229–40. http://dx.doi.org/10.1515/ijame-2017-0013.

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Abstract This paper presents an analysis of a parallelogram mechanism commonly used to provide a kinematic remote center of motion in surgical telemanipulators. Selected types of parallel manipulator designs, encountered in commercial and laboratory-made designs described in the medical robotics literature, will serve as the research material. Among other things, computer simulations in the ANSYS 13.0 CAD/CAE software environment, employing the finite element method, will be used. The kinematics of the solution of manipulator with the parallelogram mechanism will be determined in order to provide a more complete description. These results will form the basis for the decision regarding the possibility of applying a parallelogram mechanism in an original prototype of a telemanipulator arm.

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36

Hao, Guangbo. "EXTENDED NONLINEAR ANALYTICAL MODELS OF COMPLIANT PARALLELOGRAM MECHANISMS: THIRD-ORDER MODELS." Transactions of the Canadian Society for Mechanical Engineering 39, no. 1 (March 2015): 71–83. http://dx.doi.org/10.1139/tcsme-2015-0006.

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This paper proposes extended nonlinear analytical models, third-order models, of compliant parallelogram mechanisms. These models are capable of capturing the accurate effects from the very large axial force within the transverse motion range of 10% of the beam length through incorporating the terms associated with the high-order (up to third-order) axial force. A case study of the compound compliant parallelogram mechanism, composed of two basic compliant parallelogram mechanisms in symmetry, is also implemented. It is shown that in the case study the slenderness ratio affects the result discrepancy between the third-order model and the first-order model significantly, and the third-order model can illustrate a non-monotonic transverse stiffness curve if the beam is thin enough.

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37

Chouaibi, Y., A. H. Chebbi, Z. Affi, and L. Romdhane. "Analytical modeling and analysis of the clearance induced orientation error of the RAF translational parallel manipulator." Robotica 34, no. 8 (December 8, 2014): 1898–921. http://dx.doi.org/10.1017/s0263574714002653.

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SUMMARYThis paper deals with the analytical modeling and the analysis of the orientation error of the RAF translator due to the clearances in the joints. This model presents the orientation error as a function of the nominal pose, the external load applied to the platform, the manipulator structural parameters, and the joints clearances. Based on this model, an algorithm is developed in order to map the pose error within a desired workspace of the manipulator. It is shown that the orientation error variation depends essentially on the parallelogram configuration of the passive legs out of its plane. The orientation error magnitude is mainly caused by the parallelogram revolute joints radial clearances. Moreover, the orientation error around the z-axis presents some discontinuities due to the contact mode change of the parallelogram revolute joints.

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38

Fitri, Nur Lailatul, and Rully Charitas Indra Prahmana. "Pembelajaran Luas Segiempat untuk Siswa Kelas VII Menggunakan Reallotment Activities." Jurnal Review Pembelajaran Matematika 3, no. 1 (June 6, 2018): 18–28. http://dx.doi.org/10.15642/jrpm.2018.3.1.18-28.

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This research uses reallotment activities that already designed by previous research to know the role of reallotment activities in great rectangular learning. This research uses descriptive research method implemented in class 7th at SMP N 3 Banguntapan, Bantul, Yogyakarta. The data collection techniques used are documentation, observation, and test. Furthermore, the researcher analyzed the data obtained through video recording, observation, and student test answers. The results show that reallotment activities can assist students in finding the square formula by changing the shape of a rectangle into a rectangular shape. The learning activities that use reallotment activities consist of action comparing the area of an irregular shape, replacing the regular form into squares, determining the area of the rectangle and the parallelogram, finding the formula of the breadth of the parallelogram, and also determining the area of the trapezium, the parallelogram, and kite.

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39

ITO, Shunji, and Makoto OHTSUKI. "Parallelogram Tilings and Jacobi-Perron Algorithm." Tokyo Journal of Mathematics 17, no. 1 (June 1994): 33–58. http://dx.doi.org/10.3836/tjm/1270128186.

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40

Bair, Sherry L., and JoAnn Cady. "Solve It!: Parts of a Parallelogram." Mathematics Teaching in the Middle School 19, no. 8 (April 2014): 460. http://dx.doi.org/10.5951/mathteacmiddscho.19.8.0460.

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41

Holgate, Philip. "Lattice points in a random parallelogram." Advances in Applied Probability 22, no. 02 (June 1990): 484–85. http://dx.doi.org/10.1017/s0001867800019686.

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42

Frettlöh, Dirk, and Edmund Harriss. "Parallelogram Tilings, Worms, and Finite Orientations." Discrete & Computational Geometry 49, no. 3 (March 2, 2013): 531–39. http://dx.doi.org/10.1007/s00454-012-9478-5.

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43

KEARNES, KEITH A., and ÁGNES SZENDREI. "CLONES OF ALGEBRAS WITH PARALLELOGRAM TERMS." International Journal of Algebra and Computation 22, no. 01 (February 2012): 1250005. http://dx.doi.org/10.1142/s0218196711006716.

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We describe a manageable set of relations that generates the finitary relational clone of an algebra with a parallelogram term. This result applies to any algebra with a Maltsev term and to any algebra with a near unanimity term. One consequence of the main result is that on any finite set and for any finite k there are only finitely many clones of algebras with a k-ary parallelogram term which generate residually small varieties.

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44

Oliver, Peter N. "Pierre Varignon and the Parallelogram Theorem." Mathematics Teacher 94, no. 4 (April 2001): 316–19. http://dx.doi.org/10.5951/mt.94.4.0316.

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45

Oliver, Peter N. "Consequences of the Varignon Parallelogram Theorem." Mathematics Teacher 94, no. 5 (May 2001): 406–8. http://dx.doi.org/10.5951/mt.94.5.0406.

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46

Gür, Şebnem, Koray Korkmaz, and Gökhan Kiper. "Design of Anti-Parallelogram Loop Assemblies." Journal of the International Association for Shell and Spatial Structures 60, no. 3 (September 15, 2019): 232–40. http://dx.doi.org/10.20898/j.iass.2019.201.006.

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Scissor mechanisms are frequently used for deployable structures and many studies have been conducted on the subject. Most of the studies consider scissor units as modules in the design process. An alternative approach is to utilize loops as the modules for design. In this paper, the design alternatives of single degree-of-freedom planar linkages comprising anti-parallelogram loops using the loop assembly method is presented. First, scissor mechanisms are reviewed. Next, the types of four-bar loops and the resulting linkages in the literature are introduced and those which are yet to be explored, anti-parallelogram being one of them, are identified. Then the loop assembly method and the examples in the literature are reviewed. As a method to form as many alternatives as possible, symmetry operations are proposed. Suitable frieze symmetry groups utilized for obtaining the assemblies are explained and the anti-parallelogram loop patterns are derived. Next, the single degree-of-freedom linkages are obtained from the loop assemblies. Finally, a selection of the resulting linkages with novel properties are presented. This study shows that loop assemblies are efficient in systematic type synthesis of scissor linkages, some types of which could not be foreseen by using units as modules.

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47

Holgate, Philip. "Lattice points in a random parallelogram." Advances in Applied Probability 22, no. 2 (June 1990): 484–85. http://dx.doi.org/10.2307/1427547.

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48

Zakharov, E. N., I. A. Nesmiyanov, and M. E. Nikolaev. "Manipulator-tripod on mounted parallelogram mechanism." IOP Conference Series: Materials Science and Engineering 489 (March 26, 2019): 012062. http://dx.doi.org/10.1088/1757-899x/489/1/012062.

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49

Duatepe-Paksu, Asuman, Esra İymen, and Gül Sinem Pakmak. "How well elementary teachers identify parallelogram?" Educational Studies 38, no. 4 (October 2012): 415–18. http://dx.doi.org/10.1080/03055698.2011.643106.

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50

Zhou, Xing, María J. Garzarán, and David A. Padua. "Optimal Parallelogram Selection for Hierarchical Tiling." ACM Transactions on Architecture and Code Optimization 11, no. 4 (January 9, 2015): 1–23. http://dx.doi.org/10.1145/2687414.

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