Relevant bibliographies by topics / Spherical chain

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Spherical chain'

Author: Grafiati
Published: 3 June 2025
Last updated: 22 June 2025

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Journal articles on the topic "Spherical chain"

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Lee, C.-C., and J. M. Hervé. "Discontinuously Movable Seven-Link Mechanisms Via Group-Algebraic Approach." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 219, no. 6 (2005): 577–87. http://dx.doi.org/10.1243/095440605x31436.

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Combining planar and spherical 4R chains generates three kinds of new discontinuously movable (DM) seven-link mechanisms. The mobility analysis is based on algebraic concepts of set theory. These mechanisms are called hybrid planar-spherical 7R, hybrid spherical-spherical 7R, and hybrid planar-planar 6RIP DM mechanisms. Their discontinuous mobility is explained employing the Lie group algebraic properties of the displacement set. Moreover, the same given spatial arrangement of joints can be linked in two ways constituting two distinct chains, which have a quite different mobility. One chain has two global degrees of freedom (d.o.f.), which disobey the general Grubler-Kutzbach mobility criterion. The other chain exhibits a singular pose, which is a bifurcation towards two distinct working modes of mobility with one d.o.f. Then the set of relative motions between any two specific links is not manifold but consists of the union of displacement one-dimensional manifolds. In general, when two or more subgroups are involved in a closed-loop chain, the discontinuous mobility can happen by changing the order of the kinematic pair linking.
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Yang, Shuo, Bin Wu, Xiucheng Liu, Mingzhi Li, Heying Wang, and Cunfu He. "Piezoelectric Impact Energy Harvester Based on the Composite Spherical Particle Chain for Self-Powered Sensors." Sensors 21, no. 9 (2021): 3151. http://dx.doi.org/10.3390/s21093151.

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In this study, a novel piezoelectric energy harvester (PEH) based on the array composite spherical particle chain was constructed and explored in detail through simulation and experimental verification. The power test of the PEH based on array composite particle chains in the self-powered system was realized. Firstly, the model of PEH based on the composite spherical particle chain was constructed to theoretically realize the collection, transformation, and storage of impact energy, and the advantages of a composite particle chain in the field of piezoelectric energy harvesting were verified. Secondly, an experimental system was established to test the performance of the PEH, including the stability of the system under a continuous impact load, the power adjustment under different resistances, and the influence of the number of particle chains on the energy harvesting efficiency. Finally, a self-powered supply system was established with the PEH composed of three composite particle chains to realize the power supply of the microelectronic components. This paper presents a method of collecting impact energy based on particle chain structure, and lays an experimental foundation for the application of a composite particle chain in the field of piezoelectric energy harvesting.
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Korpinar, Talat. "Geometric magnetic phase for timelike spherical optical ferromagnetic model." International Journal of Geometric Methods in Modern Physics 18, no. 07 (2021): 2150099. http://dx.doi.org/10.1142/s0219887821500997.

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In this paper, we give some constructions for the applications of optical magnetic Heisenberg spherical ferromagnetic chain of T - timelike magnetic particle by spherical de Sitter frame in de Sitter space. This aim may be concluded by well-known de Sitter frame or a new alternative spherical frame with an optical magnetic spherical Heisenberg ferromagnetic chain. Moreover, we achieve total magnetic phases of T - timelike magnetic particle evolutions. Finally, we obtain some numerical modeling of optical magnetic spherical Heisenberg ferromagnetic flows.
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Pavlenko, Sophia A., Daniil E. Larin, and Elena N. Govorun. "Self-assembly of hydrophobic–amphiphilic diblock copolymers in solution." Journal of Physics: Condensed Matter 34, no. 12 (2022): 125001. http://dx.doi.org/10.1088/1361-648x/ac462c.

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Abstract Thermoresponsive polymers are usually characterized by a locally amphiphilic chain structure and their self-assembly in solution is controlled, in particular, by the surface activity of the monomer units or side chains. We theoretically study the condensed state of a single diblock copolymer molecule consisting of a hydrophobic block and amphiphilic block with hydrophobic groups in the backbone and pendant polar groups. The equilibrium parameters of the polymer globules of different shapes are determined using the mean-field approach to determine the most favorable structure. Morphological diagrams of condensed macromolecules are presented depending on the chain length, amphiphilic block fraction, interaction parameters, and pendant volume and length. The diagrams are compared with those of a copolymer molecule with the same fraction of amphiphilic monomer units which are regularly distributed along the chain. The diblock copolymer molecule is found to form a single spherical or flattened particle, with the core from the hydrophobic block, or a granular micelle consisting of spherical or nearly spherical particles, in agreement with the experimental data in the literature. The optimal chain parameters for self-assembly into a stable single core–shell particle are predicted.
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Jackson, George, and Keith E. Gubbins. "Mixtures of associating spherical and chain molecules." Pure and Applied Chemistry 61, no. 6 (1989): 1021–26. http://dx.doi.org/10.1351/pac198961061021.

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Procházka, Karel, and Zuzana Limpouchová. "Tethered Chains in Concave Volumes. A Monte Carlo Study." Collection of Czechoslovak Chemical Communications 59, no. 10 (1994): 2166–89. http://dx.doi.org/10.1135/cccc19942166.

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Monte Carlo study of tethered chain conformations in spherical cavities was performed in a relatively broad range of average segment densities (i.e. numbers of tethered chains with increasing length in the sphere). Simulations were performed on a tetrahedral lattice using (i) an equilibrated self-avoiding walk for systems containing a single tethered chain with increasing length, and (ii) a simultaneous self-avoiding walk of many tethered chains in the spherical cavity together with equilibration of the system which was performed by a modified algorithm similar to that of Siepmann and Frenkel. Only a geometric excluded volume effect of segments was considered (i.e. the prohibition principle of a double occupancy of one lattice site by two different segments). Various distribution functions (e.g. distribution of the end-to-end and the end-to-gravity center distances and their orientations with respect either to the radial direction, or to the direction of the first-to-second segment connection, etc.) were calculated and the effect of increasing average segment density in the sphere on conformational characteristics of individual chains was studied. It was found that conformational and orientational properties of relatively short tethered chains are only little affected by increasing segment density (i.e. by the number of chains in the spherical cavity), whereas arrangements of long tethered chains are significantly influenced by the density of the system.
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Li, Wanyue, and Xinyue Yu. "An integrated T-spherical fuzzy GLDS method for evaluating resiliency in the food supply chain." Computer and Decision Making: An International Journal 2 (March 4, 2025): 482–94. https://doi.org/10.59543/comdem.v2i.13877.

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A resilient food supply chain is vital for maintaining the stability and efficiency of food distribution systems. This study introduces a novel approach that integrates a T-spherical fuzzy set with the Group Linear Distance System (GLDS) method to evaluate resiliency in the food supply chain. The T-spherical fuzzy set is utilized to handle the food supply chain’s uncertainties and vagueness in assessing resiliency factors, such as farmers, processors, wholesalers, supermarkets, and small retailers. The TSF-GLDS method is integrated with the PWA operator and using entropy measurement, the significance weights of these factors are determined and the resiliency index is calculated. The approach provides a comprehensive and reliable tool for decision-makers to assess and enhance the resiliency of food supply chains. This article verifies the constructed method’s validity and practicality through examples. The results demonstrate its ability to quantitatively measure the degree of resiliency and provide insights for optimizing food supply chain operations. To summarize, this integrated approach contributes to the better understanding and managing resiliency in food supply chains, ultimately leading to more robust and reliable systems.
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Gonzalez-Tovar, Enrique, and Marcelo Lozada-Cassou. "The spherical double layer: a hypernetted chain mean spherical approximation calculation for a model spherical colloid particle." Journal of Physical Chemistry 93, no. 9 (1989): 3761–68. http://dx.doi.org/10.1021/j100346a076.

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Singh, Himanshi, Debes Ray, Joachim Kohlbrecher, and Vinod K. Aswal. "Interaction of nanoparticles with non-spherical micelles and bilayers." Journal of Applied Physics 131, no. 15 (2022): 154701. http://dx.doi.org/10.1063/5.0084795.

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Interaction of different-sized anionic silica nanoparticles with non-spherical micelles and bilayers of non-ionic surfactant C12E10 has been studied by small-angle neutron scattering (SANS). The non-ionic surfactant C12E10 in aqueous solution self-assembles to form core–shell spherical micelles. Different means (temperature, salts, and alcohols) have been examined to induce the structural transition of micelles from spherical to non-spherical and bilayer formation. The dehydration from micellar shell leads to such transition in the cases of increasing temperature and selective salt (e.g., KF). On the other hand, for alcohols, spherical to non-spherical micellar transition or bilayer formation arises for long-chain length alcohols CnOH ( n > 5) because of the mixed micelles formation of alcohol with surfactant. From the different ways to alter the micellar morphology, transitions obtained by alcohols were found to be the best suited for nanoparticle–surfactant solution as they do not influence the interactions between nanoparticle and surfactant and among nanoparticles. It is found that the shorter chain length alcohols (CnOH, n ≤ 5) interact with nanoparticles via the adsorption of individual micelles while the non-spherical micelles and bilayers of surfactant formed in the presence of long-chain length alcohols rearrange themselves to attach onto the nanoparticles. SANS with an advantage of contrast variation (contrast matching silica nanoparticles with solvent) provides the evidence of bilayer formation around nanoparticles. The concentration effect of long-chain length alcohol on micelle morphology and subsequently on the nanoparticle–surfactant system is also examined. It is found that the adsorption of surfactant bilayer structures is prominent in the case of larger particle size due to flattened curvature.
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Chu, Chia-Cheng, and Pai-Yi Hsiao. "Expansion of Single Chains Released from a Spherical Cavity." Polymers 15, no. 1 (2022): 198. http://dx.doi.org/10.3390/polym15010198.

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A two-stage model is developed to explain the phenomena of chain expansion, released from a confining cavity. In the first stage, the chain is assumed to expand as a sphere, while in the second stage it expands like a coil. The kinetic equations for the variation of chain size are derived in the two stages by balancing the rate of the free energy change with the rate of the energy dissipation. Langevin dynamics simulations are then performed to examine the theory. We find that the expansion process is dominated by the second stage and the evolution of chain size follows, mainly, the predicted curve for coil expansion, which depends on the chain length and is not sensitive to the confining volume fraction. It permits to define the expansion time for the process. Further study reveals that the chain does undergo a spherical expansion in the first stage with the characteristic time much shorter than the one for the second stage. As a consequence, the first-stage variation of chain size can be regarded as an add-on to the principal curve of expansion designated by the second stage. The scaling behaviors and the associated scaling exponents are analyzed in details. The simulation results well support the theory.
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Dissertations / Theses on the topic "Spherical chain"

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BOUDH-HIR, MOHAMED ESSALAH. "Contribution a l'etude theorique de la structure et de la thermodynamique d'un fluide polaire au voisinage d'une surface." Paris 6, 1987. http://www.theses.fr/1987PA066040.

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Le profil position-orientation donne par les approximations type msa, lhnc. . . Est identique a celui des spheres dures. Il est montre que, meme dans ce cas, il existe des orientations privilegiees. Loin de la surface, seul le potentiel image classique subsiste. Au voisinage de celle-ci, le resultat est plus complique et ne peut etre prevu par la theorie classique. Il est montre aussi qu'un potentiel anisotrope faible ( equiv. A kt) suffit pour produire des effets observables sur le plan experimental. Deux approximations ont ete comparees: blip et l'inegalite de gibbs-bogolioubov. Enfin, etude des fonctions de correlation de paire: il est montre que, sur la surface et loin de celle-ci, ces fonctions sont decrites par les potentiels direct et image. Dans la region intermediaire, la solution est plus compliquee
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Ezhova, Anna [Verfasser]. "Specific interactions of Ag+ ions with linear polyacrylate chains and spherical polyacrylate brushes and Ag nanoparticle formation therein / Anna Ezhova." Paderborn : Universitätsbibliothek, 2015. http://d-nb.info/1073944875/34.

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Winder, Brian Geoffrey. "Achieving Complex Motion with Fundamental Components for Lamina Emergent Mechanisms." Diss., CLICK HERE for online access, 2008. http://contentdm.lib.byu.edu/ETD/image/etd2279.pdf.

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Abdul-Sater, Kassim [Verfasser], Tim C. [Akademischer Betreuer] [Gutachter] Lüth, Burkhard [Gutachter] Corves, and Johann [Gutachter] Hartl. "Task-Based, Computer-Aided Kinematic Design of Spherically Constrained Kinematic Chains / Kassim Abdul-Sater. Betreuer: Tim C. Lüth. Gutachter: Tim C. Lüth ; Burkhard Corves ; Johann Hartl." München : Universitätsbibliothek der TU München, 2016. http://d-nb.info/1104368331/34.

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Abdul-Sater, Kassim Verfasser], Tim C. [Akademischer Betreuer] [Lüth, Burkhard [Gutachter] Corves, and Johann [Gutachter] Hartl. "Task-Based, Computer-Aided Kinematic Design of Spherically Constrained Kinematic Chains / Kassim Abdul-Sater. Betreuer: Tim C. Lüth. Gutachter: Tim C. Lüth ; Burkhard Corves ; Johann Hartl." München : Universitätsbibliothek der TU München, 2016. http://nbn-resolving.de/urn:nbn:de:bvb:91-diss-20160125-1271521-1-1.

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Zhang, Wuyang. "Conformation of 2-fold Anisotropic Molecules Confined on a Spherical Surface." Thesis, 2012. http://hdl.handle.net/10012/6581.

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Anisotropic molecules confined on a spherical or other curved surface can display coupled positional and orientational orderings, which make possible applications in physics, chemistry, biology, and material science. Therefore, controlling the order of such system has attracted much attention recently. Several distinct conformations of rod-like or chain-like molecules confined on a spherical surface have been predicted, including states such as tennis-ball, rectangle, and cut-and-rotate splay. These conformations have four +1/2 defects and are suggested to dominate over the splay conformation that has two +1 defects. For the purpose of investigating the conformations of 2-fold anisotropic molecules confined on the spherical surface, the author of this thesis utilizes the Onsager model to study the system of rigid rods and conducts Monte Carlo simulations on the bead-bond model to research the system of semiflexible polymer chains. At low surface coverage density, no particular pattern of the molecules would form. However, coupled positional and orientational ordering begins to emerge beyond a transition density. On the basis of the numerical solutions of the Onsager model of rigid rods, the splay conformation is shown to be the only stable state. On the other hand, Monte Carlo simulations on a polymer system indicate that the ordered state always accompanies the tennis-ball symmetry. With comparison to the continuous isotropic-nematic transition of a fluid of hard rods embedded in a flat two-dimensional space, the disorder-order transition for both the system of rigid rods and the system of polymer chains confined on the spherical surface has first-order phase-transition characteristics.
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Kureba, Chamunorwa Oscar. "Fine structure of the isoscalar giant quadrupole resonance and 2+ level densities in spherical to deformed nuclei across the isotope chain 142,144,146,148,150,Nd using the (p,p’) reaction." Thesis, 2014. http://hdl.handle.net/10539/15066.

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A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, May 23, 2014.<br>A systematic experimental investigation was performed of the phenomenon of fine structure, with emphasis on the region of the Isoscalar Giant Quadrupole Resonance (ISGQR), in nuclei across stable even-even neodymium isotopes. The 200 MeV proton beams were delivered by the Separated Sector Cyclotron (SSC) facility of iThemba Laboratory for Accelerator Based Sciences (iThemba LABS). Measurements were made using the state-of-the-art K = 600 magnetic spectrometer, where unique high energy-resolution ( E ≈ 42 − 48 keV FWHM) proton inelastic scattering results were obtained on 142Nd, 144Nd, 146Nd, 148Nd and 150Nd targets. All measurements were taken at θLab = 8◦, where the cross-section of the ISGQR is at a maximum. An additional measurement was also made for the 142Nd at θLab = 7◦. Nuclei with mass number A ≈ 150 and neutron number N ≈ 90 are of special interest since they occupy that region of the nuclide chart wherein the onset of permanent prolate deformation occurs. The stable neodymium (Z = 60) isotopes have been chosen in the present study in order to investigate the effects accompanying the onset of deformation on the excitation energy spectra in the ISGQR region (9 ≤ Ex ≤ 15 MeV). The neodymium isotopes extend from the semi-magic N = 82 nucleus (142Nd) to the permanently deformed N = 90 (150Nd) nucleus. In order to emphasize the ISGQR in the measured excitation energy spectra, a Discrete Wavelet Transform (DWT) background subtraction was carried out. This model independent method for background determination decomposes the spectrum into various approximations and details through the application of high pass and low pass filters. A comparison of the resonance widths extracted shows a systematic broadening of the ISGQR (􀀀 = 3.220 MeV to 5.100 MeV), moving from spherical 142Nd to highly deformed 150Nd nuclei as has already been observed for the Isovector Giant Dipole Resonance (IVGDR) excited by γ-capture. Even though it is known that the IVGDR spectacularly splits and shows a double bump for the deformed 150Nd, no obvious splitting of the ISGQR was observed. In order to investigate the fine structure of the ISGQR, a theoretical microscopic calculation termed the Quasiparticle-Phonon Model (QPM) was applied to predict excitation energy spectra for 142−146Nd targets. These calculations were based on the one- plus two-phonon configuration. Characteristic energy scales were extracted for the resonance region using the Continuous Wavelet Transform (CWT) technique, on both experimental data and theoretical predictions. Comparison of the resulting characteristic energy scales suggests the coupling to low-lying collective vibrations as the dominant contributor to the ISGQR decay width. Level densities of 2+ states were extracted through the application of a fluctuation analysis technique, for full spectra from the ground state upwards in all five Nd targets. Comparisons are made with theoretical predictions from the Back Shifted Fermi Gas, Hartree-Fock-BCS and Hartree-Fock-Bogoluibov models. While there is generally an excellent agreement between experimental level densities and theoretical predictions from the ground state up to less than 10 MeV excitation, there is a marked disagreement beyond 10 MeV in all target nuclei. Comparison of the experimental results for the Nd isotope chain shows a clear systematic trend in which the onset of this disagreement occurs at lower and lower excitation energies, moving from low to high mass. For the spherical 142Nd nucleus the deviation occurs at about 9 MeV while in the case of the deformed 150Nd this occurs much earlier at about 4 MeV, all limited to a maximum of 103 MeV−1 by the energy resolution of the present experiment. Additionally, measurements of elastic scattering and inelastic excitation of lowlying collective states in 144−150Nd has also been possible. Excitation energy spectra in all targets predominantly exhibited various 2+ states, owing to the “spin-filter” effects. A single strong 3− 1 state, together with a weak 4+ 1 state were observed in each target nucleus. Angular distributions were obtained for the various ground and excited states by applying the optical model of elastic scattering and Distorted Wave Born Approximation (DWBA) of inelastic scattering. Deformation lengths δL were obtained for most of the states and these were in good agreement with previously obtained results from the literature.
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Tolety, Anurag Bharadwaj. "Geometric Design of Spherical Serial Chains with Curvature Constraints in the Environment." Thesis, 2011. http://hdl.handle.net/1969.1/ETD-TAMU-2011-08-9736.

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This research builds up on recent results in planar kinematic synthesis with contact direction and curvature constraints on the workpiece. The synthesis of spherical serial chains is considered to guide a rigid body, such that it does not violate normal direction and curvature constraints imposed by contact with objects in the environment. These constraints are transformed into conditions on the velocity and acceleration of points in the moving body to obtain synthesis equations which can be solved by algebraic elimination. Trajectory interpolation formulas yield the movement of the chain with the desired contact properties in each of the task positions. Example shows the application of the developed theory to the failure recovery of a robot manipulator.
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Chang, Tao Yuan, and 張道源. "The Study and Design of Two Degree of Freedom Spherical Platform - Using Chair as an Example." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/d43k48.

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Book chapters on the topic "Spherical chain"

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Parvari Rad, Farid, Rocco Vertechy, Giovanni Berselli, and Vincenzo Parenti-Castelli. "Compliant Serial 3R Chain with Spherical Flexures." In Advances in Robot Kinematics 2016. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56802-7_2.

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Ohkita, Masaaki, Heizo Tokutaka, Makoto Ohki, Matashige Oyabu, and Kikuo Fujimura. "Classification of Chain-Link and Other Data with Spherical SOM." In Advances in Intelligent Systems and Computing. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-35230-0_4.

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Green, Peter F., Hyunjoon Oh, Pinar Akcora, and Sanat K. Kumar. "Structure and Dynamics of Polymer Nanocomposites Involving Chain-Grafted Spherical Nanoparticles." In Dynamics of Soft Matter. Springer US, 2011. http://dx.doi.org/10.1007/978-1-4614-0727-0_13.

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Parvari Rad, Farid, Giovanni Berselli, Rocco Vertechy, and Vincenzo Parenti-Castelli. "Stiffness Analysis of a Fully Compliant Spherical Chain with Two Degrees of Freedom." In Advances in Robot Kinematics. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06698-1_29.

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Khairy, Khaled, Emmanuel Reynaud, and Ernst Stelzer. "Detection of Deformable Objects in 3D Images Using Markov-Chain Monte Carlo and Spherical Harmonics." In Medical Image Computing and Computer-Assisted Intervention – MICCAI 2008. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-85990-1_129.

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Donyatalab, Yaser, and Fariba Farid. "Spherical Fuzzy Linear Assignment with Objective Weighting Concept in the Sustainable Supply Chain of Aviation Fuel." In Intelligent and Fuzzy Techniques for Emerging Conditions and Digital Transformation. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-85577-2_90.

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Nguyen, Phi-Hung, Thu-Hien Tran, and Lan-Anh Thi Nguyen. "Overcoming Barriers: A Multi-level Spherical Fuzzy MCDM Approach to Digital Transformation in Vietnam’s Agricultural Supply Chain." In Lecture Notes in Networks and Systems. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-67192-0_45.

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Tran, Thu-Hien, Phi-Hung Nguyen, and Lan-Anh Thi Nguyen. "Strategic Insights into Post-harvest Losses: A Spherical Fuzzy Delphi-DEMATEL Investigation of the Vietnamese Agricultural Supply Chain." In Lecture Notes in Networks and Systems. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-67192-0_42.

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McCarthy, J. Michael, and Gim Song Soh. "Algebraic Synthesis of Spherical Chains." In Interdisciplinary Applied Mathematics. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-7892-9_9.

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Lekkerkerker, Henk N. W., Remco Tuinier, and Mark Vis. "Phase Separation and Long-Lived Metastable States in Colloid–Polymer Mixtures." In Colloids and the Depletion Interaction. Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-52131-7_4.

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AbstractWhen a dispersion containing spherical colloids is mixed with a polymer solution two kinds of instabilities can occur, as depicted in Fig. 4.1: (1) bridging flocculation caused by adsorbing polymer chains or (2) unmixing driven by the depletion force.
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Conference papers on the topic "Spherical chain"

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Abdul-Sater, Kassim, Franz Irlinger, and Tim C. Lueth. "Three-Position Synthesis of Spherically Constrained Planar 3R Chains." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47365.

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This paper presents a dimensional finite position synthesis procedure for a 8-bar linkage, that we call the spherically constrained planar 3R chain. The procedure aims at using the well-developed constraint-based synthesis equations of spherical RR chains in order to constrain a planar serial 3R guiding chain, synthesized before for a maximum number of three task poses. This maximum number of task positions results from the specific linkage topology, which requires to select specific axes of spherical RR chains. However, three-position synthesis allows it to apply a specific version of the dyad triangle equation of planar RR chains to the problem. A particular assumption forces that this version of the dyad triangle equation becomes nothing but the synthesis equation of a planar 3R chain, which is easily solved for the three prescribed task poses. An example is provided showing a synthesized spherically constrained planar 3R chain reaching three prescribed planar poses.
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Soh, Gim Song, and J. Michael McCarthy. "Five Position Synthesis of Spherical (6, 7) Linkages." In ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/detc2008-49889.

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This paper presents a geometric synthesis procedure for spherical (6, 7) linkages, often known as spherical six-bar linkages, based on adding two spherical RR constraints to a spherical 3R serial chain. The design can use the spherical 3R chain to shape the movement of the linkage and identify a set of task positions that shape the trajectory of the end-effector. We use five task positions to completely specify the two RR chains that constrain the system to one degree-of-freedom. This procedure yields spherical versions of the various topologies for the planar Watt and Stephenson six-bar linkages. We find that for any design problem we obtain at a minimum of two design candidates for the Watt-type linkage, and as many as 185 different design for all of the topologies obtained by constraining the spherical 3R chain. Wampler’s method for the analysis of spherical loops is used to analyze these linkages. An example design is presented in detail.
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Purwar, Anurag, Jun Wu, Aditya Gupta, and Q. Jeffrey Ge. "A Visual, Interactive Approach to Synthesis of Spherical 6R Closed Chains for Rational Motions via Constraint Manifold Modification." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28874.

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In this paper, we present an interactive, visual design approach for the dimensional synthesis of spherical 6R closed chains for a given rational motion using constraint manifold modification. This work is an extension of our previous work on the dimensional synthesis of planar 6R closed chains using the aforementioned approach. The theoretical underpinning of this work is based on representation of spherical displacements by quaternions and the kinematic mapping approach. In this way, motion of the coupler of a spherical 6R chain motion maps to a rational curve and the kinematic constraints of a spherical 6R closed chain map to hyper-dimensional algebraic surfaces in the image space of spherical displacements. Thus, the problem of determining dimensional parameters of the chain is reduced to finding the surface parameters that satisfy the geometry of the curve. This, in turn, resolves into satisfying the kinematic constraints of the chain. We provide designers an interactive, user friendly graphical tool that allows them to visually contain the image curve by simple geometric manipulation of the size, orientation, and the location of the constraint surfaces. This simple and straightforward design process lends designers an understanding of the mechanism design methodology.
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Lee, Chung-Ching, and Jacques M. Herve´. "Three Novel Discontinuously Movable Spatial 7-Link Mechanisms." In ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/detc2006-99386.

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Three kinds of new discontinuously movable (DM) spatial 7-link mechanisms named hybrid planar-spherical 7R, hybrid spherical-spherical 7R, and hybrid planar-planar 6R1P DM mechanisms are synthesized by combining planar and spherical 4R trivial chains. Their discontinuous mobility is explained using the Lie group algebraic properties of the displacement set. In addition, the same given spatial arrangement of joints can be linked in two ways thus constituting two distinct chains with a quite different mobility. One chain has two global degrees of freedom (dofs), which disobey the general Grubler-Kutzbach mobility criterion. The other chain exhibits a singular pose, which is a bifurcation towards two distinct working modes of one-dof mobility. As a result, the set of relative motions between any two specific links is not a manifold but consists of the union of displacement 1-dimensional manifolds.
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5

Dooley, J. R., and J. M. McCarthy. "Dynamics of Open and Closed Chain Spherical Mechanisms Using Quaternion Coordinates." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0376.

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Abstract This paper presents a general technique for deriving the equations of motion for any open or closed chain spherical mechanism. The technique uses quaternion coordinates to represent the position of each rigid body in the mechanism. Thus, if there are n moving bodies in the chain, there are 4n generalized coordinates in the equations of motion. The use of quaternion coordinates results in standardized quadratic constraint relations representing the hinged connections between bodies in the mechanism. These constraint equations augment the equations of motion. This technique has two important features. First, it is specifically adapted to spherical mechanisms and presents all positions as rotations. Second, the quadratic form of the constraint equations simplifies the computation of velocities and accelerations compatible with the constraints. As an example the equations of motion for a closed six bar spherical chain are derived.
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Purwar, Anurag, Zhe Jin, and Q. J. Ge. "Rational Motion Interpolation Under Kinematic Constraints of Spherical 6R Closed Chains." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35727.

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The work reported in this paper brings together the kinematics of spherical closed chains and the recently developed freeform rational motions to study the problem of synthesizing rational interpolating motions under the kinematic constraints of spherical 6R closed chains. The results presented in this paper are extension of our previous work on the synthesis of piecewise rational spherical motions for spherical open chains. The kinematic constraints under consideration are workspace related constraints that limit the position of the links of spherical closed chains in the Cartesian space. Quaternions are used to represent spherical displacements. The problem of synthesizing smooth piecewise rational motions is converted into that of designing smooth piecewise rational curves in the space of quaternions. The kinematic constraints are transformed into geometric constraints for the design of quaternion curves. An iterative algorithm for constrained motion interpolation is presented that detects the violation of the kinematic constraints by searching for those extreme points of the quaternion curve that do not satisfy the constraints. Such extreme points are modified so that the constraints are satisfied and the resulting new points are added to the ordered set of the initial positions to be interpolated. An example is presented to show how this algorithm produces smooth spherical rational spline motions that satisfy the kinematic constraints of a spherical 6R closed chain. The algorithm can also be used for the synthesis of rational interpolating motions that approximate the kinematic constraints of spherical 5R and 4R closed chains within a user-defined tolerance.
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Sonawale, Kaustubh H., Alex Arredondo, and J. Michael McCarthy. "Computer Aided Design of Useful Spherical Watt I Six-Bar Linkages." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13454.

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This paper presents a software system for the kinematic synthesis of useful spherical Watt I six-bar linkages that can guide a body through five task positions. The design procedure begins with the specification of a spherical 3R open chain that reaches five specified task positions. The six-bar linkage is designed by constraining the 3R spherical chain to the topology of a Watt I spherical six-bar linkage. The CAD software SolidWorks is used to specify the 3R chain and the five spherical task positions. We describe the SolidWorks Add-In MechGen that reads the SolidWorks data and generates candidate linkages. Included in the task specification are tolerance zones that allow random adjustments to the task positions to search for defect-free linkages. An example is provided that demonstrates the five position synthesis of a useful spherical Watt I six-bar linkage.
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Giaier, Kevin S., Andrew P. Murray, and David H. Myszka. "Serial Chains of Spherical Four-Bar Mechanisms to Achieve Design Helices." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34287.

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This paper presents a method for designing serial chains of spherical four-bar mechanisms that can achieve up to five design helices. The chains are comprised of identical copies of the same four-bar mechanism by connecting the coupler of the prior spherical mechanism to the base link of the subsequent spherical mechanism. Although having a degree of freedom per mechanism, the design methodology is based upon identically actuating each mechanism. With these conditions, the kinematic synthesis task of matching periodically spaced points on up to five arbitrary helices may be achieved. Due to the constraints realized via the spherical equivalent of planar Burmester Theory, spherical mechanisms produce at most five prescribed orientations resulting in this maximum. The methodology introduces a companion helix to each design helix along which the intersection locations of each spherical mechanisms axes must lie. As the mechanisms are connected by rigid links, the distance between the intersection locations along the companion helices is a constant. An extension to the coupler matches the points along the design helices. An approach to mechanically reducing the chain of mechanisms to a single degree of freedom is also presented. Finally, an example shows the methodology applied to three design helices.
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Perkins, David A., Michael L. Turner, and Andrew P. Murray. "Static Analysis of Torque and Coupler Driven Spherical Four-Bar Mechanisms With an Applied Load." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35359.

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Spherical four-bar mechanisms are classically designed to be driven via a torque applied to the input link. This paper presents a comparison of the resulting statics associated with this method of actuating a spherical four-bar versus actuating the mechanism with the force applied directly to the coupler. A force may be applied in this fashion via a spherical-prismatic-spherical, or SPS, chain mounted between the ground frame and the coupler with the prismatic joint actuated. The spherical four-bar linkage with the SPS chain connected directly to the coupler defines a spatial analogue to the Stephenson III six-bar mechanism. Moreover, this work builds on previously derived static models of spherical four-bars by considering the additional loading issues associated with links at different radii and the forces that arise from an external load on the coupler.
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Kinra, Vikram K., Benjamin K. Henderson, and Konstantin Maslov. "Elastodynamic Response of a Chain of Particles." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-0887.

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Abstract The reflection of an axially incident plane longitudinal wave from a linear chain of identical spherical inclusions embedded in a viscoelastic matrix is measured. The reflection spectrum is characterized by a sequence of resonances corresponding to the Floquet condition, where an integral number of half-wavelengths in the matrix spans the interparticle distance.
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