Quadrilaterals

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Quadrilaterals One pair of parallel sides Trapezium Two pairs Two pairs of equal of equal parallel adjacent sides sides Kite Parallelogram Four sides equal Four right angles Rhombus Rectangle Four right angles Four equal sides Square Legend Quadrilaterals A, B, C, D are angles a, b, c, d are side lengths B All sides in one plane Not all sides in one plane b Skew a C Planar c A D No crossed sides d Two crossed Note that all properties are sides Simple inherited along the arrows All angles < 180° Complex One angle > 180° Arrow Antiparallelogram (Self-intersecting) Concave (aka Dart/Chevron) Convex Two pairs of Two pairs of opposite equal adjacent equal sides sides Opposite angles sum to 180° Opposite side One pair Equal One pair lengths have Perpendicular of parallel diagonals of opposite equal sums diagonals sides equal sides Tangential Watt Cyclic Ex-tangential Orthodiagonal A + C = B + D = 180° (Inscriptible) a + c = b + d 2 2 2 2 Trapezium Equidiagonal a + c = b + d quadrilateral a + c = b + d A + B = C + D = 180° One pair of Opposite side lengths parallel ides Non-equal Two pairs of equal have equal sums opposite adjacent sides sides parallel Two One pair of Non-parallel Two pairs A second adjacent parallel sides Opposite of equal sides equal (if circle r=∞) pair of parallel right sides Opposite adjacent sides angles equal sum angles sides equal sum Right-angled Isosceles Kite Tangential Parallelogram Bicentric (‘Rhomboid’ if adjacent trapezium trapezium sides are unequal) trapezium Two Four sides Four Four sides Four right Four Four right One pair of opposite equal sides equal angles right angles opposite right equal angles equal sides angles Opposite side Third lengths have equal sums side equal Four right angles Right kite Rhombus Quadric Rectangle 3-sides-equal Isosceles (‘Oblong’ if adjacent trapezium tangential sides are unequal) Four right angles Four Four equal equal sides Four right angles sides Four equal sides Square Equilic 60° .

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Habilitation Thesis
HABILITATION THESIS FLEXIBLE OCTAHEDRA IN THE PROJECTIVE EXTENSION OF THE EUCLIDEAN 3-SPACE AND THEIR APPLICATION Die vorliegende Habilitationsschrift wurde ausgeführt zum Zweck der Erlangung der Lehrbefugnis für das Fach GEOMETRIE eingereicht an der Technischen Universität Wien Fakultät für Mathematik und Geoinformation von Mag.rer.nat. Dr.techn. Georg NAWRATIL 7. Jänner 2011 Danksagung Mein Dank gebührt O.Univ.Prof. Dr. Hellmuth Stachel, der während meiner bisherigen wis- senschaftlichen Tätigkeit stets Zeit für die Beantwortung von Fragen und die Diskussion von Problemen fand. Seine dabei vermittelte geometrische und kinematische Sicht der Dinge, haben meine Denkweise nachhaltig geprägt. Weiters geschätzt habe ich seinen mir stets anvertrauten Gestaltungsfreiraum in Bezug auf Forschung sowie Lehre. Bei dieser Gelegenheit möchte ich mich auch bei all jenen Kollegen der Abteilung für Differential- geometrie und Geometrische Strukturen sowie jenen der Abteilung für Geometrische Model- lierung und Industrielle Geometrie des Instituts für Diskrete Mathematik und Geometrie der TU Wien bedanken, die maßgeblich zur Schaffung einer angenehmen Arbeitsatmosphäre beigetragen haben. Der größte Dank richtet sich jedoch an meine Eltern sowie an meine Freundin Petra, die mich während der Entstehungszeit dieser Habilitationsschrift in allen Belangen tatkräftig unterstützt haben. I Contents 1 Introduction 1 1.1 Application and future research . ....... 3 1.2 References...................................... 4 2 Composition of spherical four-bar-mechanisms (with H. Stachel) 5 2.1 Introduction.................................... 5 2.2 Transmission by a spherical four-bar linkage . ........... 6 2.3 Composition of two spherical four-bar linkages . ........... 9 2.4 Conclusions..................................... 12 2.5 References.....................................
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Flexible Octahedra in the Projective Extension of the Euclidean 3-Space
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SZAKDOLGOZAT Probabilistic Formulation of the Hadwiger
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Nguyen Duc Thang
Nguyen Duc Thang 2700 ANIMATED MECHANICAL MECHANISMS With Images, Brief explanations and YouTube links Part 3 Mechanisms of specific purposes Renewed on 31 October 2017 1 This document is divided into 4 parts. Part 1: Transmission of continuous rotation Part 2: Other kinds of motion transmission Part 3: Mechanisms of specific purposes Part 4: Mechanisms for various industries Autodesk Inventor is used to create all videos in this document. They are available on YouTube channel “thang010146”. To bring as many as possible existing mechanical mechanisms into this document is author’s desire. However it is obstructed by author’s ability and Inventor’s capacity. Therefore from this document may be absent such mechanisms that are of complicated structure or include flexible and fluid links. This document is periodically renewed because the video building is continuous as long as possible. The renewed time is shown on the first page. This document may be helpful for people, who - have to deal with mechanical mechanisms everyday - see mechanical mechanisms as a hobby Any criticism or suggestion is highly appreciated with the author’s hope to make this document more useful. Author’s information: Name: Nguyen Duc Thang Birth year: 1946 Birth place: Hue city, Vietnam Residence place: Hanoi, Vietnam Education: - Mechanical engineer, 1969, Hanoi University of Technology, Vietnam - Doctor of Engineering, 1984, Kosice University of Technology, Slovakia Job history: - Designer of small mechanical engineering enterprises in Hanoi. - Retirement in 2002. Contact Email: [email protected] 2 Table of Contents 11. Brakes .......................................................................................................................... 4 12. Safety clutches ............................................................................................................ 9 13. Mechanisms for indexing, positioning and interlocking .......................................
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References to Additional Literature
References to Additional Literature 1. Angeles J (1982) Spatial kinematic chains, analysis, synthesis, optimisation. Springer, New York 2. Angeles J (1988) Rational kinematics. Springer Tracts in Natural Philosophy 34, New York 3. Angeles J, Hommel G, Kovács P (1993) Computational kinematics. Kluwer, Dordrecht 4. Angeles J (2003) Fundamentals of robotic mechanical systems: Theory, methods and algorithms. 2nd ed. Springer, New York 5. Artobolevski I I (1986) Mechanisms in modern engineering design. v.1–3, Mir, Moscow 6. Beggs J S (1966) Advanced mechanism. Macmillan, New York 7. Beggs J S (1983) Kinematics. Springer, Berlin, Heidelberg, New York 8. Beyer R (1931) Technische Kinematik. Barth, Leipzig 9. Beyer R (1953) Kinematische Getriebesynthese. Springer, Berlin (Engl. trans. Kuenzel H (1963) The kinematic synthesis of linkages. Chapman and Hall, London) 10. Beyer R (1963) Technische Raumkinematik. Springer, Berlin 11. Bogolyubov A N (1967) Razvitie problem mekhaniki mashin (Bibliografiya) [Develop- ment of problems of mechanics in machines (Bibliography)], Naukova Dumka, Kiev 12. Crelier L (1911) Systèmes cinématiques. Gauthier-Villars, Paris 13. de Groot J (Ed.) (1970) Bibliography on kinematics. v.1,2. Eindhoven Univ. of Techn. 14. Dizio˘glu B (1965,1967) Getriebelehre v.1: Grundlagen, v.2: Massbestimmung. Vieweg, Braunschweig 15. Dresig H, Naake S, Rockhausen L (1994) Vollständiger und harmonischer Ausgleich ebener Mechanismen. Fortschritt-Berichte VDI, Reihe 18, 155,71 pp. Düsseldorf 16. Dresig H, Schönherr J, Peisach E E (2000) Typ- und Masssynthese von ebenen Kop- pelgetrieben mit höheren Gliedergruppen. Abschlussbericht DFG-Forschungsvorhaben Dr234/7-2, Bonn 17. Giering O, Hoschek J (eds.) (1994) Geometrie und ihre Anwendungen.
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Combinatorics of Bricard's Octahedra Arxiv:2004.01236V1 [Math.MG] 2
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Radially Expandable Ring-Like Structure with Antiparallelogram Loops
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Latex Template for an EUCOMES 2010 Paper
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On a Special R on a Special Rectangular Problem
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