Mechanical Self-Assembly of a Strain-Engineered Flexible Layer: Wrinkling, Rolling, and Twisting
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Engineering Curves – I
Engineering Curves – I 1. Classification 2. Conic sections - explanation 3. Common Definition 4. Ellipse – ( six methods of construction) 5. Parabola – ( Three methods of construction) 6. Hyperbola – ( Three methods of construction ) 7. Methods of drawing Tangents & Normals ( four cases) Engineering Curves – II 1. Classification 2. Definitions 3. Involutes - (five cases) 4. Cycloid 5. Trochoids – (Superior and Inferior) 6. Epic cycloid and Hypo - cycloid 7. Spiral (Two cases) 8. Helix – on cylinder & on cone 9. Methods of drawing Tangents and Normals (Three cases) ENGINEERING CURVES Part- I {Conic Sections} ELLIPSE PARABOLA HYPERBOLA 1.Concentric Circle Method 1.Rectangle Method 1.Rectangular Hyperbola (coordinates given) 2.Rectangle Method 2 Method of Tangents ( Triangle Method) 2 Rectangular Hyperbola 3.Oblong Method (P-V diagram - Equation given) 3.Basic Locus Method 4.Arcs of Circle Method (Directrix – focus) 3.Basic Locus Method (Directrix – focus) 5.Rhombus Metho 6.Basic Locus Method Methods of Drawing (Directrix – focus) Tangents & Normals To These Curves. CONIC SECTIONS ELLIPSE, PARABOLA AND HYPERBOLA ARE CALLED CONIC SECTIONS BECAUSE THESE CURVES APPEAR ON THE SURFACE OF A CONE WHEN IT IS CUT BY SOME TYPICAL CUTTING PLANES. OBSERVE ILLUSTRATIONS GIVEN BELOW.. Ellipse Section Plane Section Plane Hyperbola Through Generators Parallel to Axis. Section Plane Parallel to end generator. COMMON DEFINATION OF ELLIPSE, PARABOLA & HYPERBOLA: These are the loci of points moving in a plane such that the ratio of it’s distances from a fixed point And a fixed line always remains constant. The Ratio is called ECCENTRICITY. (E) A) For Ellipse E<1 B) For Parabola E=1 C) For Hyperbola E>1 Refer Problem nos. -
A Characterization of Helical Polynomial Curves of Any Degree
A CHARACTERIZATION OF HELICAL POLYNOMIAL CURVES OF ANY DEGREE J. MONTERDE Abstract. We give a full characterization of helical polynomial curves of any degree and a simple way to construct them. Existing results about Hermite interpolation are revisited. A simple method to select the best quintic interpolant among all possible solutions is suggested. 1. Introduction The notion of helical polynomial curves, i.e, polynomial curves which made a constant angle with a ¯xed line in space, have been studied by di®erent authors. Let us cite the papers [5, 6, 7] where the main results about the cubical and quintic cases are stablished. In [5] the authors gives a necessary condition a polynomial curve must satisfy in order to be a helix. The condition is expressed in terms of its hodograph, i.e., its derivative. If a polynomial curve, ®, is a helix then its hodograph, ®0, must be Pythagorean, i.e., jj®0jj2 is a perfect square of a polynomial. Moreover, this condition is su±cient in the cubical case: all PH cubical curves are helices. In the same paper it is also stated that not only ®0 must be Pythagorean, but also ®0^®00. Following the same ideas, in [1] it is proved that both conditions are su±cient in the quintic case. Unfortunately, this characterization is no longer true for higher degrees. It is possible to construct examples of polynomial curves of degree 7 verifying both conditions but being not a helix. The aim of this paper is just to show how a simple geometric trick can clarify the proofs of some previous results and to simplify the needed compu- tations to solve some related problems as for instance, the Hermite problem using helical polynomial curves. -
Flexible Fluidic Actuators for Soft Robotic Applications
University of Wollongong Research Online University of Wollongong Thesis Collection 2017+ University of Wollongong Thesis Collections 2019 Flexible Fluidic Actuators for Soft Robotic Applications Weiping Hu Follow this and additional works at: https://ro.uow.edu.au/theses1 University of Wollongong Copyright Warning You may print or download ONE copy of this document for the purpose of your own research or study. The University does not authorise you to copy, communicate or otherwise make available electronically to any other person any copyright material contained on this site. You are reminded of the following: This work is copyright. Apart from any use permitted under the Copyright Act 1968, no part of this work may be reproduced by any process, nor may any other exclusive right be exercised, without the permission of the author. Copyright owners are entitled to take legal action against persons who infringe their copyright. A reproduction of material that is protected by copyright may be a copyright infringement. A court may impose penalties and award damages in relation to offences and infringements relating to copyright material. Higher penalties may apply, and higher damages may be awarded, for offences and infringements involving the conversion of material into digital or electronic form. Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong. Research Online is the open access institutional repository for the University of -
Linguistic Presentation of Objects
Zygmunt Ryznar dr emeritus Cracow Poland [email protected] Linguistic presentation of objects (types,structures,relations) Abstract Paper presents phrases for object specification in terms of structure, relations and dynamics. An applied notation provides a very concise (less words more contents) description of object. Keywords object relations, role, object type, object dynamics, geometric presentation Introduction This paper is based on OSL (Object Specification Language) [3] dedicated to present the various structures of objects, their relations and dynamics (events, actions and processes). Jay W.Forrester author of fundamental work "Industrial Dynamics”[4] considers the importance of relations: “the structure of interconnections and the interactions are often far more important than the parts of system”. Notation <!...> comment < > container of (phrase,name...) ≡> link to something external (outside of definition)) <def > </def> start-end of definition <spec> </spec> start-end of specification <beg> <end> start-end of section [..] or {..} 1 list of assigned keywords :[ or :{ structure ^<name> optional item (..) list of items xxxx(..) name of list = value assignment @ mark of special attribute,feature,property @dark unknown, to obtain, to discover :: belongs to : equivalent name (e.g.shortname) # number of |name| executive/operational object ppppXxxx name of item Xxxx with prefix ‘pppp ‘ XXXX basic object UUUU.xxxx xxxx object belonged to UUUU object class & / conjunctions ‘and’ ‘or’ 1 If using Latex editor we suggest [..] brackets -
Helical Curves and Double Pythagorean Hodographs
Helical polynomial curves and “double” Pythagorean-hodograph curves Rida T. Farouki Department of Mechanical & Aeronautical Engineering, University of California, Davis — synopsis — • introduction: properties of Pythagorean-hodograph curves • computing rotation-minimizing frames on spatial PH curves • helical polynomial space curves — are always PH curves • standard quaternion representation for spatial PH curves • “double” Pythagorean hodograph structure — requires both |r0(t)| and |r0(t) × r00(t)| to be polynomials in t • Hermite interpolation problem: selection of free parameters Pythagorean-hodograph (PH) curves r(ξ) = PH curve ⇐⇒ coordinate components of r0(ξ) comprise a “Pythagorean n-tuple of polynomials” in Rn PH curves incorporate special algebraic structures in their hodographs (complex number & quaternion models for planar & spatial PH curves) • rational offset curves rd(ξ) = r(ξ) + d n(ξ) Z ξ • polynomial arc-length function s(ξ) = |r0(ξ)| dξ 0 Z 1 • closed-form evaluation of energy integral E = κ2 ds 0 • real-time CNC interpolators, rotation-minimizing frames, etc. helical polynomial space curves several equivalent characterizations of helical curves • tangent t maintains constant inclination ψ with fixed vector a • a · t = cos ψ, where ψ = pitch angle and a = axis vector of helix • fixed curvature/torsion ratio, κ/τ = tan ψ (Theorem of Lancret) • curve has a circular tangent indicatrix on the unit sphere (small circle for space curve, great circle for planar curve) • (r(2) × r(3)) · r(4) ≡ 0 — where r(k) = kth arc–length derivative -
The Close-Packed Triple Helix As a Possible New Structural Motif for Collagen
The close-packed triple helix as a possible new structural motif for collagen Jakob Bohr∗ and Kasper Olseny Department of Physics, Technical University of Denmark Building 307 Fysikvej, DK-2800 Lyngby, Denmark Abstract The one-dimensional problem of selecting the triple helix with the highest volume fraction is solved and hence the condition for a helix to be close-packed is obtained. The close-packed triple helix is ◦ shown to have a pitch angle of vCP = 43:3 . Contrary to the conventional notion, we suggest that close packing form the underlying principle behind the structure of collagen, and the implications of this suggestion are considered. Further, it is shown that the unique zero-twist structure with no strain- twist coupling is practically identical to the close-packed triple helix. Some of the difficulties for the current understanding of the structure of collagen are reviewed: The ambiguity in assigning crystal structures for collagen-like peptides, and the failure to satisfactorily calculate circular dichroism spectra. Further, the proposed new geometrical structure for collagen is better packed than both the 10=3 and the 7=2 structure. A feature of the suggested collagen structure is the existence of a central channel with negatively charged walls. We find support for this structural feature in some of the early x-ray diffraction data of collagen. The central channel of the structure suggests the possibility of a one-dimensional proton lattice. This geometry can explain the observed magic angle effect seen in NMR studies of collagen. The central channel also offers the possibility of ion transport and may cast new light on various biological and physical phenomena, including biomineralization. -
Structural Insight Into Marburg Virus Nucleoprotein-RNA Complex Formation
bioRxiv preprint doi: https://doi.org/10.1101/2021.07.13.452116; this version posted July 13, 2021. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. 1 Structural insight into Marburg virus nucleoprotein-RNA complex formation 2 3 Yoko Fujita-Fujiharu1,2,3, Yukihiko Sugita1,2,4, Yuki Takamatsu1,#, Kazuya Houri1,2,3, Manabu 4 Igarashi5, Yukiko Muramoto1,2,3, Masahiro Nakano1,2,3, Yugo Tsunoda1, Stephan Becker6,7, 5 Takeshi Noda1,2,3* 6 7 1 Laboratory of Ultrastructural Virology, Institute for Frontier Life and Medical Sciences, 8 Kyoto University, 53 Shogoin Kawahara-cho, Sakyo-ku, Kyoto 606-8507, Japan 9 2 Laboratory of Ultrastructural Virology, Graduate School of Biostudies, Kyoto University, 53 10 Shogoin Kawahara-cho, Sakyo-ku, Kyoto 606-8507, Japan 11 3 CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332- 12 0012, Japan 13 4 Hakubi Center for Advanced Research, Kyoto University, Kyoto, Japan. 14 5 Division of Epidemiology, International Institute for Zoonosis Control, Hokkaido University, 15 Sapporo 001-0020, Japan 16 6 Institute of Virology, University of Marburg, 35043 Marburg, Germany. 17 7 German Center for Infection Research (DZIF), Marburg-Gießen-Langen Site, University of 18 Marburg, 35043 Marburg, Germany. 19 20 # present address: Department of Virology I, National Institute of Infectious Diseases, Gakuen 21 4-7-1, Musashimurayama-city, Tokyo 208-0011, Japan 22 *correspondence to: [email protected] 23 24 bioRxiv preprint doi: https://doi.org/10.1101/2021.07.13.452116; this version posted July 13, 2021. -
Α/Β Coiled Coils 2 3 Marcus D
1 α/β Coiled Coils 2 3 Marcus D. Hartmann, Claudia T. Mendler†, Jens Bassler, Ioanna Karamichali, Oswin 4 Ridderbusch‡, Andrei N. Lupas* and Birte Hernandez Alvarez* 5 6 Department of Protein Evolution, Max Planck Institute for Developmental Biology, 72076 7 Tübingen, Germany 8 † present address: Nuklearmedizinische Klinik und Poliklinik, Klinikum rechts der Isar, 9 Technische Universität München, Munich, Germany 10 ‡ present address: Vossius & Partner, Siebertstraße 3, 81675 Munich, Germany 11 12 13 14 * correspondence to A. N. Lupas or B. Hernandez Alvarez: 15 Department of Protein Evolution 16 Max-Planck-Institute for Developmental Biology 17 Spemannstr. 35 18 D-72076 Tübingen 19 Germany 20 Tel. –49 7071 601 356 21 Fax –49 7071 601 349 22 [email protected], [email protected] 23 1 24 Abstract 25 Coiled coils are the best-understood protein fold, as their backbone structure can uniquely be 26 described by parametric equations. This level of understanding has allowed their manipulation 27 in unprecedented detail. They do not seem a likely source of surprises, yet we describe here 28 the unexpected formation of a new type of fiber by the simple insertion of two or six residues 29 into the underlying heptad repeat of a parallel, trimeric coiled coil. These insertions strain the 30 supercoil to the breaking point, causing the local formation of short β-strands, which move the 31 path of the chain by 120° around the trimer axis. The result is an α/β coiled coil, which retains 32 only one backbone hydrogen bond per repeat unit from the parent coiled coil. -
An Experimental Investigation of Helical Gear Efficiency
AN EXPERIMENTAL INVESTIGATION OF HELICAL GEAR EFFICIENCY A Thesis Presented in Partial Fulfillment of the Requirements for The Degree of Master of Science in the Graduate School of the Ohio State University By Aarthy Vaidyanathan, B. Tech. * * * * * The Ohio State University 2009 Masters Examination Committee: Dr. Ahmet Kahraman Approved by Dr. Donald R Houser Advisor Graduate Program in Mechanical Engineering ABSTRACT In this study, a test methodology for measuring load-dependent (mechanical) and load- independent power losses of helical gear pairs is developed. A high-speed four-square type test machine is adapted for this purpose. Several sets of helical gears having varying module, pressure angle and helix angle are procured, and their power losses under jet- lubricated conditions are measured at various speed and torque levels. The experimental results are compared to a helical gear mechanical power loss model from a companion study to assess the accuracy of the power loss predictions. The validated model is then used to perform parameter sensitivity studies to quantify the impact of various key gear design parameters on mechanical power losses and to demonstrate the trade off that must take place to arrive at a gear design that is balanced in all essential aspects including noise, durability (bending and contact) and power loss. ii Dedicated to all those before me who had far fewer opportunities, and yet accomplished so much more. iii ACKNOWLEDGMENTS I would like to thank my advisor, Dr. Ahmet Kahraman, who has been instrumental in fostering interest and enthusiasm in all my research endeavors. His encouragement throughout the course of my studies was invaluable, and I look to him for guidance in all my future undertakings. -
Eukaryotic Genome Annotation
Comparative Features of Multicellular Eukaryotic Genomes (2017) (First three statistics from www.ensembl.org; other from original papers) C. elegans A. thaliana D. melanogaster M. musculus H. sapiens Species name Nematode Thale Cress Fruit Fly Mouse Human Size (Mb) 103 136 143 3,482 3,555 # Protein-coding genes 20,362 27,655 13,918 22,598 20,338 (25,498 (13,601 original (30,000 (30,000 original est.) original est.) original est.) est.) Transcripts 58,941 55,157 34,749 131,195 200,310 Gene density (#/kb) 1/5 1/4.5 1/8.8 1/83 1/97 LINE/SINE (%) 0.4 0.5 0.7 27.4 33.6 LTR (%) 0.0 4.8 1.5 9.9 8.6 DNA Elements 5.3 5.1 0.7 0.9 3.1 Total repeats 6.5 10.5 3.1 38.6 46.4 Exons % genome size 27 28.8 24.0 per gene 4.0 5.4 4.1 8.4 8.7 average size (bp) 250 506 Introns % genome size 15.6 average size (bp) 168 Arabidopsis Chromosome Structures Sorghum Whole Genome Details Characterizing the Proteome The Protein World • Sequencing has defined o Many, many proteins • How can we use this data to: o Define genes in new genomes o Look for evolutionarily related genes o Follow evolution of genes ▪ Mixing of domains to create new proteins o Uncover important subsets of genes that ▪ That deep phylogenies • Plants vs. animals • Placental vs. non-placental animals • Monocots vs. dicots plants • Common nomenclature needed o Ensure consistency of interpretations InterPro (http://www.ebi.ac.uk/interpro/) Classification of Protein Families • Intergrated documentation resource for protein super families, families, domains and functional sites o Mitchell AL, Attwood TK, Babbitt PC, et al. -
STACK: a Toolkit for Analysing Β-Helix Proteins
STACK: a toolkit for analysing ¯-helix proteins Master of Science Thesis (20 points) Salvatore Cappadona, Lars Diestelhorst Abstract ¯-helix proteins contain a solenoid fold consisting of repeated coils forming parallel ¯-sheets. Our goal is to formalise the intuitive notion of a ¯-helix in an objective algorithm. Our approach is based on first identifying residues stacks — linear spatial arrangements of residues with similar conformations — and then combining these elementary patterns to form ¯-coils and ¯-helices. Our algorithm has been implemented within STACK, a toolkit for analyzing ¯-helix proteins. STACK distinguishes aromatic, aliphatic and amidic stacks such as the asparagine ladder. Geometrical features are computed and stored in a relational database. These features include the axis of the ¯-helix, the stacks, the cross-sectional shape, the area of the coils and related packing information. An interface between STACK and a molecular visualisation program enables structural features to be highlighted automatically. i Contents 1 Introduction 1 2 Biological Background 2 2.1 Basic Concepts of Protein Structure ....................... 2 2.2 Secondary Structure ................................ 2 2.3 The ¯-Helix Fold .................................. 3 3 Parallel ¯-Helices 6 3.1 Introduction ..................................... 6 3.2 Nomenclature .................................... 6 3.2.1 Parallel ¯-Helix and its ¯-Sheets ..................... 6 3.2.2 Stacks ................................... 8 3.2.3 Coils ..................................... 8 3.2.4 The Core Region .............................. 8 3.3 Description of Known Structures ......................... 8 3.3.1 Helix Handedness .............................. 8 3.3.2 Right-Handed Parallel ¯-Helices ..................... 13 3.3.3 Left-Handed Parallel ¯-Helices ...................... 19 3.4 Amyloidosis .................................... 20 4 The STACK Toolkit 24 4.1 Identification of Structural Elements ....................... 24 4.1.1 Stacks ................................... -
Stapled Peptides—A Useful Improvement for Peptide-Based Drugs
molecules Review Stapled Peptides—A Useful Improvement for Peptide-Based Drugs Mattia Moiola, Misal G. Memeo and Paolo Quadrelli * Department of Chemistry, University of Pavia, Viale Taramelli 12, 27100 Pavia, Italy; [email protected] (M.M.); [email protected] (M.G.M.) * Correspondence: [email protected]; Tel.: +39-0382-987315 Received: 30 July 2019; Accepted: 1 October 2019; Published: 10 October 2019 Abstract: Peptide-based drugs, despite being relegated as niche pharmaceuticals for years, are now capturing more and more attention from the scientific community. The main problem for these kinds of pharmacological compounds was the low degree of cellular uptake, which relegates the application of peptide-drugs to extracellular targets. In recent years, many new techniques have been developed in order to bypass the intrinsic problem of this kind of pharmaceuticals. One of these features is the use of stapled peptides. Stapled peptides consist of peptide chains that bring an external brace that force the peptide structure into an a-helical one. The cross-link is obtained by the linkage of the side chains of opportune-modified amino acids posed at the right distance inside the peptide chain. In this account, we report the main stapling methodologies currently employed or under development and the synthetic pathways involved in the amino acid modifications. Moreover, we report the results of two comparative studies upon different kinds of stapled-peptides, evaluating the properties given from each typology of staple to the target peptide and discussing the best choices for the use of this feature in peptide-drug synthesis. Keywords: stapled peptide; structurally constrained peptide; cellular uptake; helicity; peptide drugs 1.