scholarly journals Classification and Effects of Symmetry of Mechanical Structure and its Application in Design

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 683
Author(s):  
Qingying Qiu ◽  
Xiuming Chen ◽  
Chao Yang ◽  
Peien Feng
Keyword(s):  
Point Group ◽  
Group Symmetry ◽  
Point Group Symmetry ◽  
Space Group Symmetry ◽  
Space Group ◽  
Mechanical Structure ◽  
Natural Objects ◽  
Mechanical Products ◽  
Speed Change ◽  
And Performance

Symmetry widely exists in natural objects and man-made objects. Mechanical structures, as man-made objects, have the property of symmetry without exception. The existence of symmetry affects the function and performance of mechanical products. Therefore, on the basis of analyzing a large number of examples and referring to the Schoenflies symbol of crystal, the symmetry of mechanical structures is divided into point group symmetry and space group symmetry, and these two types are further subdivided according to the types and spatial positions of the symmetry elements. Then, the general effects of symmetry are summarized according to symmetry types and functions, and several symmetry rules for design are further refined. Finally, after defining the requirements of speed change and technology background, a multispeed device for bicycle shaft drive is proposed by applying symmetry knowledge comprehensively.

scholarly journals Symmetry-extended counting rules for periodic frameworks

2014 ◽  
Vol 372 (2008) ◽  
pp. 20120029 ◽  
Author(s):  
S. D. Guest ◽  
P. W. Fowler
Keyword(s):  
Point Group ◽  
Factor Group ◽  
Unit Cell ◽  
Group Symmetry ◽  
Point Group Symmetry ◽  
Space Group ◽  
Counting Rules ◽  
Periodic Frameworks ◽  
Explicit Expressions

A symmetry-adapted version of the Maxwell rule appropriate to periodic bar-and-joint frameworks is obtained, and is further extended to body-and-joint systems. The treatment deals with bodies and forces that are replicated in every unit cell, and uses the point group isomorphic to the factor group of the space group of the framework. Explicit expressions are found for the numbers and symmetries of detectable mechanisms and states of self-stress in terms of the numbers and symmetries of framework components. This approach allows detection and characterization of mechanisms and states of self-stress in microscopic and macroscopic materials and meta-materials. Illustrative examples are described. The notion of local isostaticity of periodic frameworks is extended to include point-group symmetry.

Supramolecular networks in (9-fluoro-4H-chromeno[4,3-c]isoxazol-3-yl)methanol and its 9-chloro analogue at 100 K

2012 ◽  
Vol 68 (8) ◽  
pp. o288-o293 ◽  
Author(s):  
P. Rajalakshmi ◽  
N. Srinivasan ◽  
R. V. Krishnakumar ◽  
Ibrahim Abdul Razak ◽  
Mohd Mustaqim Rosli
Keyword(s):  
Intermolecular Interaction ◽  
Point Group ◽  
Group Symmetry ◽  
Interaction Patterns ◽  
Point Group Symmetry ◽  
Orthorhombic Space Group ◽  
Molecular Scaffold ◽  
Triclinic Space Group ◽  
Space Group ◽  
Supramolecular Networks

The title compounds, (9-fluoro-4H-chromeno[4,3-c]isoxazol-3-yl)methanol, C11H8FNO3, (I), and (9-chloro-4H-chromeno[4,3-c]isoxazol-3-yl)methanol, C11H8ClNO3, (II), crystallize in the orthorhombic space groupPbcawithZ′ = 1 and the triclinic space groupP\overline{1} withZ′ = 6, respectively. The simple replacement of F by Cl in the main molecular scaffold of (I) and (II) results in significant differences in the intermolecular interaction patterns and a corresponding change in the point-group symmetry fromD2htoCi=S2. These striking differences are manifested through the presence of C—H...F and the absence of O—H...O and C—H...O interactions in (I), and the absence of C—H...Cl and the presence of O—H...O and C—H...O interactions in (II). However, the geometry of the synthons formed by the O—H...N and O—H...X(X= F or Cl) interactions observed in the constitution of the supramolecular networks of both (I) and (II) remains similar. Also, C—H...O interactions are not preferred in the presence of F in (I), while they are much preferred in the presence of Cl in (II).

scholarly journals CSDSymmetry: a database of point group and space group symmetry relationships in crystal structures

2002 ◽  
Vol 58 (s1) ◽  
pp. c367-c367
Author(s):  
W. D. S. Motherwell ◽  
E. Pidcock ◽  
J. W. Yao ◽  
J. C. Cole ◽  
F. H. Allen ◽  
...  
Keyword(s):  
Crystal Structures ◽  
Point Group ◽  
Group Symmetry ◽  
Space Group Symmetry ◽  
Space Group

scholarly journals Beiträge zur Chemie des Bors, 153 [1] Die Kristall- und Molekülstruktur eines 1.3.2-Dioxaborolan-2-yl-1.3.2-dioxaborolans

1984 ◽  
Vol 39 (11) ◽  
pp. 1463-1466 ◽  
Author(s):  
H. Nöth
Keyword(s):  
Point Group ◽  
Group Symmetry ◽  
Monoclinic Space Group ◽  
Point Group Symmetry ◽  
Space Group ◽  
X Ray ◽  
X Ray Crystallography

Abstract The structure of the title com pound 5 has been investigated by X-ray crystallography in order to discern between two structural alternatives. 5 crystallizes in the monoclinic space group P21/c, and almost planar B-B bonded dioxaborolane rings are present in the molecule. 5 possesses a crystallographically imposed center of inversion, and approaches the point group symmetry D2h-

Vibrational spectra of arsenic triiodide

1968 ◽  
Vol 21 (10) ◽  
pp. 2379 ◽  
Author(s):  
MA Hooper ◽  
DW James
Keyword(s):  
Raman Spectrum ◽  
Solid State ◽  
Vibrational Spectra ◽  
Point Group ◽  
Group Symmetry ◽  
Space Group Symmetry ◽  
Space Group ◽  
Polarization Studies

The Raman spectrum of AsI3 has been determined in solution in CS2 and in the solid state. For the solution the assignment of Stammreich, Forneris, and Tavares has been confirmed by polarization studies. In the solid state it is shown that assignment of the spectrum is only possible on the basis of space group symmetry and an earlier assignment based on point group C3v is in error. The solid state frequencies (R3 symmetry) are v1(Ag) 185 cm-l, v2(Ag) 75 cm-l, v3(Au) 201 cm-l, v4(Au) 102 cm-1, v5(Eg) 205 cm-1, v6(Eg) 50 cm-l, v7(Eg) 216 cm-1, v8(Eg) 74 cm-1.

The atomic anisotropic displacement tensor – completing the picture

2015 ◽  
Vol 71 (4) ◽  
pp. 467-470 ◽  
Author(s):  
Gunnar Thorkildsen ◽  
Helge B. Larsen
Keyword(s):  
Point Group ◽  
Transformation Property ◽  
Group Symmetry ◽  
Site Symmetry ◽  
Tensor Representation ◽  
Space Group Symmetry ◽  
Space Group ◽  
Simplified Approach ◽  
Displacement Parameter ◽  
Isotropic Displacement Parameter

A simplified approach for calculating the equivalent isotropic displacement parameter is presented and the transformation property of the tensor representationUto point-group operations is analysed. Complete tables have been compiled for the restrictions imposed upon the tensor owing to the site symmetry associated with all special positions as listed in Hahn [(2011),International Tables for Crystallography, Vol. A,Space-group Symmetry, 5th revised ed. Chichester: John Wiley and Sons, Ltd].

scholarly journals Multiplicity, Parity and Angular Momentum of a Cooper Pair in Unconventional Superconductors of D4h Symmetry: Sr2RuO4 and Fe-Pnictide Materials

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1435
Author(s):  
Victor G. Yarzhemsky
Keyword(s):  
Angular Momentum ◽  
Cooper Pair ◽  
Point Group ◽  
Group Symmetry ◽  
Cooper Pairs ◽  
Group Approach ◽  
Angular Momentum Projection ◽  
Space Group ◽  
Unconventional Superconductors ◽  
Even Pairs

Sr2RuO4 and Fe-pnictide superconductors belong to the same point group symmetry D4h. Many experimental data confirm odd pairs in Sr2RuO4 and even pairs in Fe-pnictides, but opposite conclusions also exist. Recent NMR results of Pustogow et al., which revealed even Cooper pairs in Sr2RuO4, require reconsideration of symmetry treatment of its SOP (superconducting order parameter). In the present work making use of the Mackey–Bradley theorem on symmetrized squares, a group theoretical investigation of possible pairing states in D4h symmetry is performed. It is obtained for I4/mmm , i.e., space group of Sr2RuO4, that triplet pairs with even spatial parts are possible in kz direction and in points M and Y. For the two latter cases pairing of equivalent electrons with nonzero total momentum is proposed. In P4/nmm space group of Fe- pnictides in point M, even and odd pairs are possible for singlet and triplet cases. It it shown that even and odd chiral states with angular momentum projection m=±1 have nodes in vertical planes, but Eg is nodal , whereas Eu is nodeless in the basal plane. It is also shown that the widely accepted assertion that the parity of angular momentum value is directly connected with the spatial parity of a pair is not valid in a space-group approach to the wavefunction of a Cooper pair.

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