Constructing Scissor-Like Structures and Parallelogram Linkages With 4-Crease Single-Vertex Flat-Foldable Rigid Origami and Their Thick-Panel Versions

2019 ◽  
Author(s):  
David Xing ◽  
Zhong You
Keyword(s):  
Dihedral Angle ◽  
Composite Structure ◽  
Dihedral Angles ◽  
Single Vertex ◽  
Rotation Matrices ◽  
Similar Construction ◽  
Complex Approach ◽  
Intuitive Method ◽  
Point Of Intersection ◽  
Rigid Supports

Abstract Scissor-like structures are commonly composed of two straight rigid supports in a crisscross pattern connected by a pivot at its point of intersection [1]. Opposite angles formed by the supports are equal regardless of the structure’s folded state. Parallelogram linkages have a similar property. Rigid origami can be used to create these structures by combining two identical copies of a 4-crease single-vertex flat-foldable rigid origami, a single 4C, to form a flat-foldable composite structure, a double 4C. In this paper, we prove mathematically that regardless of the folded state of a single-4C, its even dihedral angles are equal, and odd dihedral angles are equal. As a result, the double 4C consists of 2 scissor-like structures. A past method to prove these dihedral angle equalities requires a more complex approach involving rotation matrices using Denavit and Hartenberg parameters [2,3]. This paper will provide a more intuitive method that proves the same equalities. We will also show that a similar construction of the double 4C using thick-panel versions of the single 4C satisfies the same dihedral angle equalities necessary for the formation of parallelogram linkages. The construction of the double 4C can help design self-folding mechanisms and useful metamaterials.

scholarly journals Relation between photochromic properties and molecular structures in salicylideneaniline crystals

2012 ◽  
Vol 68 (3) ◽  
pp. 297-304 ◽  
Author(s):  
Kohei Johmoto ◽  
Takashi Ishida ◽  
Akiko Sekine ◽  
Hidehiro Uekusa ◽  
Yuji Ohashi
Keyword(s):  
Dihedral Angle ◽  
Steric Hindrance ◽  
Molecular Structures ◽  
Dihedral Angles ◽  
Clear Correlation ◽  
X Ray Diffraction ◽  
Photochromic Properties ◽  
X Ray ◽  
Benzene Rings ◽  
The Relationship

The crystal structures of the salicylideneaniline derivatives N-salicylidene-4-tert-butyl-aniline (1), N-3,5-di-tert-butyl-salicylidene-3-methoxyaniline (2), N-3,5-di-tert-butyl-salicylidene-3-bromoaniline (3), N-3,5-di-tert-butyl-salicylidene-3-chloroaniline (4), N-3,5-di-tert-butyl-salicylidene-4-bromoaniline (5), N-3,5-di-tert-butyl-salicylidene-aniline (6), N-3,5-di-tert-butyl-salicylidene-4-carboxyaniline (7) and N-salicylidene-2-chloroaniline (8) were analyzed by X-ray diffraction analysis at ambient temperature to investigate the relationship between their photochromic properties and molecular structures. A clear correlation between photochromism and the dihedral angle of the two benzene rings in the salicylideneaniline derivatives was observed. Crystals with dihedral angles less than 20° were non-photochromic, whereas those with dihedral angles greater than 30° were photochromic. Crystals with dihedral angles between 20 and 30° could be either photochromic or non-photochromic. Inhibition of the pedal motion by intra- or intermolecular steric hindrance, however, can result in non-photochromic behaviour even if the dihedral angle is larger than 30°.

scholarly journals Crystal structure of 3-{5-[3-(4-fluorophenyl)-1-isopropyl-1H-indol-2-yl]-1H-pyrazol-1-yl}indolin-2-one ethanol monosolvate

2016 ◽  
Vol 72 (3) ◽  
pp. 283-286
Author(s):  
Md. Lutfor Rahman ◽  
Ajaykumar D. Kulkarni ◽  
Mashitah Mohd. Yusoff ◽  
Huey Chong Kwong ◽  
Ching Kheng Quah
Keyword(s):  
Crystal Structure ◽  
Hydrogen Bonds ◽  
Dihedral Angle ◽  
Interplanar Spacing ◽  
Pyrazole Ring ◽  
Dihedral Angles ◽  
Ethanol Molecule ◽  
Compound C ◽  
Ethanol Solvate

The title indolin-2-one compound, C28H23FN4O·C2H6O, crystallizes as a 1:1 ethanol solvate. The ethanol molecule is disordered over two positions with refined site occupancies of 0.560 (14) and 0.440 (14). The pyrazole ring makes dihedral angles of 84.16 (10) and 85.33 (9)° with the indolin-2-one and indole rings, respectively, whereas the dihedral angle between indolin-2-one and indole rings is 57.30 (7)°. In the crystal, the components are linked by N—H...O and O—H...O hydrogen bonds, forming an inversion molecule–solvate 2:2 dimer withR44(12) ring motifs. The crystal structure is consolidated by π–π interaction between pairs of inversion-related indolin-2-one rings [interplanar spacing = 3.599 (2) Å].

scholarly journals 1-{2-Anilino-4-methyl-5-[5-methyl-1-(4-methylphenyl)-1H-1,2,3-triazole-4-carbonyl]thiophen-3-yl}ethanone

IUCrData ◽  
2018 ◽  
Vol 3 (3) ◽  
Author(s):  
Gamal A. El-Hiti ◽  
Bakr F. Abdel-Wahab ◽  
Rizk E. Khidre ◽  
Mohamed S. Mostafa ◽  
Amany S. Hegazy ◽  
...  
Keyword(s):  
Hydrogen Bond ◽  
Dihedral Angle ◽  
Title Compound ◽  
Dihedral Angles ◽  
Axis Direction ◽  
Π Interactions ◽  
Compound C ◽  
Phenyl Rings

In the title compound, C24H22N4O2S, the dihedral angle between the triazole and thiophene rings is 4.83 (14)°. The dihedral angles between the triazole and tolyl rings and between the thiophene and phenyl rings are 48.42 (16) and 9.23 (13)°, respectively. An intramolecular N—H...O hydrogen bond closes anS(6) loop. In the crystal, molecules are stacked parallel to thea-axis direction with weak π–π interactions between adjacent thiophenyl and triazolyl groups within the stack [centroid–centroid separation = 3.9811 (16) Å].

scholarly journals 4-Chloro-5-(morpholin-4-yl)-2-[(5-phenyl-1,3,4-oxadiazol-2-yl)methyl]pyridazin-3(2H)-one

IUCrData ◽  
2017 ◽  
Vol 2 (3) ◽  
Author(s):  
Yanwen Sun ◽  
Haolei Wu ◽  
Changheng Wei ◽  
Mei Gao ◽  
Zeyi Shen ◽  
...  
Keyword(s):  
Hydrogen Bond ◽  
Hydrogen Bonds ◽  
Dihedral Angle ◽  
Title Compound ◽  
Chair Conformation ◽  
Dihedral Angles ◽  
Bond Forming ◽  
Compound C ◽  
Pyridazine Ring ◽  
Morpholine Ring

In the title compound, C17H16ClN5O3, the phenyl and the oxadiazole rings are almost coplanar, subtending a dihedral angle of 4.34 (19)°. These rings lie almost normal to the pyridazine ring, making dihedral angles of 87.35 (16) and 89.06 (15)°, respectively. The morpholine ring has the usual chair conformation and its mean plane is inclined to the pyridazine ring by 39.45 (17)°. There is a short intramolecular C—H...Cl contact present. In the crystal, molecules are linked by bifurcated C—(H,H)...O hydrogen bonds and a C—H...N hydrogen bond, forming layers parallel to the ab plane.

scholarly journals Crystal structure analysis of ethyl 6-(4-methoxyphenyl)-1-methyl-4-methylsulfanyl-3-phenyl-1H-pyrazolo[3,4-b]pyridine-5-carboxylate

2020 ◽  
Vol 76 (8) ◽  
pp. 1209-1212
Author(s):  
H. Surya Prakash Rao ◽  
Ramalingam Gunasundari ◽  
Jayaraman Muthukumaran
Keyword(s):  
Crystal Structure ◽  
Dihedral Angle ◽  
Structure Analysis ◽  
Title Compound ◽  
Crystal Packing ◽  
Crystal Structure Analysis ◽  
Dihedral Angles ◽  
Pyridine Moiety ◽  
Compound C ◽  
Phenyl Rings

In the title compound, C24H23N3O3S, the dihedral angle between the fused pyrazole and pyridine rings is 1.76 (7)°. The benzene and methoxy phenyl rings make dihedral angles of 44.8 (5) and 63.86 (5)°, respectively, with the pyrazolo[3,4-b] pyridine moiety. An intramolecular short S...O contact [3.215 (2) Å] is observed. The crystal packing features C—H...π interactions.

scholarly journals Crystal structure of quinolinium 2-carboxy-6-nitrobenzoate monohydrate

2015 ◽  
Vol 71 (5) ◽  
pp. o270-o271 ◽  
Author(s):  
J. Mohana ◽  
M. Divya Bharathi ◽  
G. Ahila ◽  
G. Chakkaravarthi ◽  
G. Anbalagan
Keyword(s):  
Crystal Structure ◽  
Hydrogen Bonds ◽  
Benzene Ring ◽  
Dihedral Angle ◽  
Carboxy Group ◽  
Three Dimensional ◽  
Dihedral Angles ◽  
Π Stacking ◽  
Dimensional Network ◽  
Molecular Salt

In the anion of the title hydrated molecular salt, C9H8N+·C8H4NO6−·H2O, the protonated carboxyl and nitro groups makes dihedral angles of 27.56 (5) and 6.86 (8)°, respectively, with the attached benzene ring, whereas the deprotonated carboxy group is almost orthogonal to it with a dihedral angle of 80.21 (1)°. In the crystal, the components are linked by O—H...O and N—H...O hydrogen bonds, generating [001] chains. The packing is consolidated by weak C—H...N and C—H...O interactions as well as aromatic π–π stacking [centroid-to-centroid distances: 3.7023 (8) & 3.6590 (9)Å] interactions, resulting in a three-dimensional network.

The Molecular Geometry of Diastereoisomeric Bis[α-(9-anthryl)ethyl] Ethers

1985 ◽  
Vol 38 (9) ◽  
pp. 1417 ◽  
Author(s):  
H Becker ◽  
VA Patrick ◽  
BW Skelton ◽  
AH White
Keyword(s):  
Single Crystal ◽  
Least Squares ◽  
Dihedral Angle ◽  
Molecular Geometry ◽  
Dihedral Angles ◽  
Methyl Groups ◽  
X Ray Diffraction ◽  
X Ray ◽  
Meso Form ◽  
Aromatic Systems

The crystal structures of racemic bis [α-(9-anthryl)] ether and its meso form have been determined by single-crystal X-ray diffraction methods at 295 K, being refined by least squares to residuals of 0.053 and 0.041 for 1868 and 3568 independent 'observed' reflections respectively. Crystals of the racemate are orthorhombic, Pcab, a 23.07(1), b 19.85(2), c 10.241(8) Ǻ, Z 8. Crystals of the meso form are triclinic, Pī , a 19.032(12), b 14.207(11), c 9.451(8) Ǻ, α 79.46(6), β 89.68(6), γ 68.97(5)°, Z 4. In the racemate , the dihedral angle between the methyl groups along the ether bonds is 12°, and the short axes of the anthracene moieties lie at an angle of about 120°. In the meso compound, for the two molecules the dihedral angles between the methyl groups along the ether bonds are 90 and 93°, the angle between the two anthracene moieties is 90°, and the interplanar angles between the partly overlapping aromatic systems are 46 and 43°.

scholarly journals N-Cyclohexyl-N-{[3-(4,6-dimethoxypyrimidin-2-yloxy)pyridin-2-yl]methyl}4,6-dimethoxypyrimidin-2-amine

2012 ◽  
Vol 68 (4) ◽  
pp. o1272-o1272
Author(s):  
De-Cai Wang ◽  
Yu-Jing Wang ◽  
Jun-Song Song ◽  
Ping Wei ◽  
Ping-Kai Ou-yang
Keyword(s):  
Dihedral Angle ◽  
Title Compound ◽  
Pyridine Ring ◽  
Chair Conformation ◽  
Dihedral Angles ◽  
Stacking Interaction ◽  
Compound C ◽  
Π Stacking ◽  
Π Stacking Interaction

In the title compound, C24H30N6O5, the cyclohexyl ring adopts a chair conformation, while the remainder of the molecule adopts a U-shape. The dihedral angles between the pyridine ring and the pendant pyrimidine rings are 69.04 (12) and 75.99 (9)°. The two pyrimidine rings, however, are nearly parallel to one another, with a dihedral angle of 8.56 (15)° between them. They are also involved in an intramolecular π–π stacking interaction with a distance of 3.6627 (18) Å between the ring centroids. In the crystal, C—H...O contacts link the molecules into chains along thebaxis.

scholarly journals Crystal stucture of methyl 2-({[2-(methoxycarbonyl)phenyl]carbamoyl}amino)benzoate

2015 ◽  
Vol 71 (5) ◽  
pp. o297-o298 ◽  
Author(s):  
Hasna Yassine ◽  
Mostafa Khouili ◽  
Lahcen El Ammari ◽  
Mohamed Saadi ◽  
El Mostafa Ketatni
Keyword(s):  
Hydrogen Bonds ◽  
Dihedral Angle ◽  
Title Compound ◽  
Molecular Conformation ◽  
Dihedral Angles ◽  
Aromatic Rings ◽  
Compound C ◽  
Benzene Rings

In the title compound, C17H16N2O5, the dihedral angles between the central urea [N—C(=O)—N] fragment and its attached benzene rings are 20.20 (14) and 24.24 (13)°; the dihedral angle between the aromatic rings is 42.1 (1)°. The molecular conformation is consolidated by two intramolecular N—H...O hydrogen bonds, which both generateS(6) rings. In the crystal, inversion dimers linked by pairs of C—H...O interactions generateR22(14) loops. The dimers are linked by further C—H...O interactions into (011) sheets.

scholarly journals 4-Formyl-2-nitrophenyl 2-chlorobenzoate

2013 ◽  
Vol 69 (12) ◽  
pp. o1806-o1806 ◽  
Author(s):  
Rodolfo Moreno-Fuquen ◽  
Geraldine Hernandez ◽  
Javier Ellena ◽  
Carlos A. De Simone ◽  
Juan C. Tenorio
Keyword(s):  
Hydrogen Bonds ◽  
Nitro Group ◽  
Benzene Ring ◽  
Dihedral Angle ◽  
Title Compound ◽  
Ester Group ◽  
Dihedral Angles ◽  
Compound C ◽  
Benzene Rings ◽  
The Mean

In the title compound, C14H8ClNO5, the benzene rings form a dihedral angle of 19.55 (9)°. The mean plane of the central ester group [r.m.s. deviation = 0.024 Å] forms dihedral angles of 53.28 (13) and 36.93 (16)°, respectively, with the nitro- and chloro-substituted rings. The nitro group forms a dihedral angle of 19.24 (19)° with the benzene ring to which it is attached. In the crystal, molecules are linked by weak C—H...O hydrogen bonds, formingC(7) chains, which run along [100].

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