■ Curriculum Vitae
 ■ Teaching -
    Lehrveranstaltungen
 ■ Lehrbuch Geometrie
 ■ Research Interests
 ■ Selected Publications

















Fine Art Prints-Katalog
Januar 2012


Prof. Dr. Gert Bär

Professor of Geometry / Kinematics


 
  Office Willersbau,   Room B 121
  Zellescher Weg 12-14,   D-01069 Dresden
 
  Phone / Fax / E-mail (+49) ((-0)351) 463 37082 (office)
  (+49) ((-0)351) 463 37579 (secretary, Ms. Sabine Patkos)
(+49) ((-0)351) 463 36027

 
  Postal Address Prof. Dr. Gert Bär
  Institute of Geometry
Dresden University of Technology
D-01062 Dresden
Germany
Institut für Geometrie
Technische Universität Dresden
01062 Dresden

 




  ■ Curriculum Vitae                                                                                                                                              

Plücker conoid
 

1969 degree dissertation in mathematics
1972 degree "Dr.rer nat." at Dresden University of Technology
1975-77 assistant professor at Technical University of Chemnitz
1977-85 assistant professor at Dresden University of Technology
1984 degree "Dr.rer.nat.habil."
1985 associate professor
1992 full professor
2011 professor in retirement
     

  ■ Teaching - Lehrveranstaltungen                                                                                                                        


Animationen in der   Kinematikausbildung  










  AnimationGrundfunktionen  
Mathematica-Notebook,  
kann mit "Shift + linke Maustaste"  
gespeichert werden  

 
  
     

  ■ Lehrbuch Geometrie                                                                                                                                         

Reihe: Mathematik für Ingenieure und Naturwissenschaftler

2., überarbeitete und erweiterte Auflage
223 Seiten

ISBN 3-519-20722-2


more information
 
 



Zykloidenverzahnung nach Ph. de la Hire (1694)
Cycloid gearing

     

  ■ Research Interests                                                                                                                                           

 
 
  • Geometry and its Application 
  • Computer Aided Geometric Design 
  • Computer Graphics and Visualisation 
  • Kinematics and Robotics 
  • Theory of Gearing
     

  ■ Selected Publications                                                                                                                                       

  • BÄR, G. F. :
    Zufall und Absicht in der Kurve - ein Werkzeug der Gestaltung. In:  U. Beyer (Hrsg.): Die Basis der Vielfalt – Geometrie als Grundlage und Anregung des Denkens. Verlag Springer Vieweg 2016, pp. 48-65.
     
  • BÄR, G: F. :
    On Optimizing the Basic Geometry of Hypoid Gears. Mechanism and Machine Theory, Vol.104 (2016), pp. 274–286.
  • BÄR, G. F. :
    Kollisionsfreies Schleifen einer Schraubfläche mit einem Drehkegel. In: C. Leopold (Hrsg.): Über Form und Struktur - Geometrie in Gestaltungsprozessen. Springer 2014.
     
  • BÄR, G. F.; MODLER, K.-H.; EHLIG, J.; LIN, S.:
    Two poses synthesis of spatial linkages using similarity transformation. 13. World Congress in Mechanism and Machine Science, Guanajuato, México, 19-25 June, 2011, Proceedings  A11_464.
  • BÄR, G. F. :
    Invariant planar motion interpolation using positions and poles. Proceedings 14. Int. Conf. on Geometry and Graphics. Aug. 5-9, 2010, Kyoto, Japan.
     
  • BÄR, G. F. :
    Bewegungsentwurf in der Ebene mit vorgeschriebenen Ebenenlagen. Proceedings 6.Tagung der DGFGG, 24.-26.03.2010, Aachen-Kornelimünster.

     
     
    Lagrange-Bewegungsinterpolation Hermite-Bewegungsinterpolation

     
  • BÄR, G. F. :
    Two Synthesis Methods for Non-Circular Cylindrical Gears. JGG , Vol.13 (2009) , No.1, 101-112.

     
     

     
  • BÄR, G. F.; MODLER, K.-H.; et al.:
    General method for the synthesis of geared linkages with non-circular gears. Mechanism and Machine Theory 44 (2009) 726-738.
     
  • BÄR, G. F.:
    Two Synthesis Methods for Non-Circular Gears. Proc. 13th Int. Conf. on Geometry and Graphics, Aug. 4-8, Dresden, 2008.  
     
  • BÄR, G. F.:
    Bildnerische Studien in der Mathematik. Informationsblätter der Geometrie, Jg.26, Heft1, 2008, S. 23-32. 
     
  • BÄR, G.; WEISS, G.:
    Kinematic Analysis of a Pentapod Robot. JGG 10 (2006), 2, 125-134.
     
  • BÄR, G.:
    Bildnerische Experimente mit dem Menger-Schwamm.
    erscheint im Vortragsband zur Tagung "Geometrie, Kunst und Wissenschaft" der DGfGG im März 2006 an der Hochschule für Künste Bremen (Abstract)

     
     
    Scheiben des M4 der Dicke 5 Scheiben des M4 der Dicke 3 Knospung MS4  (Video - load it)

     
  • BÄR, G.:
    Aspects of Geometry and Art. JGG 8 (2004), No.2, 231-241.
     
  • ACHTMANN, J.; BÄR, G.:
    Optimized Bearing Ellipses of Hypoid Gears. ASME J. Mech. Design, Vol.125, No.4, pp.739-745 (2003).

     
     
    For given machine tool settings of a universal hypoid gear generator, the tooth contact patterns are computed for the coast and drive side of a hypoid gear drive. Each contact pattern is replaced by a determined tooth-bearing ellipse. The position, shape, and inclination of each bearing ellipse is calculated. By the help of these data, an influence function is designed that describes the influence of supplemental kinematic flank correction motions (modified motions) on the gear-tooth contact. Examples show the influence of helical motion and modified roll. An evaluation function permits the calculation of modified motions that improve the tooth contact either at coast and drive side simultaneously, or only at one of the sides. For a given pair of start-bearing ellipses at coast and drive side, and for given importance weights to the sides, we describe how modified motions can be computed that best fit a given target pair of bearing ellipses.
    Parameters of bearing ellipses at coast and drive side of the gear

     
  • BÄR, G.:
    Line-geometric Relations at a Point of Contact. Proceedings DSG-CK 2003, 27.02.-1.3.2003, TU Dresden, FR Mathematik, pp. 33-40.
     
  • BÄR, G.:
    Explicit Calculation Methods for Conjugate Profiles. Journal for Geometry and Graphics. Vol.7, No.2, 201-210 (2003)
    (Movies)

     
     
    Wenn Achsabstand, Übersetzungsverhältnis und eine gewünschte Eingriffslinie für eine Stirnradverzahnung vorgeschrieben sind, dann ergeben sich die konjugierten Zahnradprofile als Lösung einer gewöhnlichen Differentialgleichung. Mit diesem Ergebnis können optimale Zahnradprofile für unterschiedliche Anwendungen konstruiert werden, z.B. für Schraubenverdichter oder Vakuumpumpen.

    If the spur-gear centers, the gear ratio, and a line of action are given then conjugate gear profiles are determined by the solution of an ordinary differential equation. This result permits the design of optimized profiles for various mechanical applications e.g. screw-type compressors and vacuum pumps.


    SymmetrischeSchraubenverdichterrotoren
    Symmetrical screw pump rotors

                                
     

    Optimierte asymmetrische Schraubenverdichterrotoren
    Optimized asymetrical screw pump rotors


     
  • VOGEL, O; GRIEWANK, A; BÄR, G.:
    Direct Gear Tooth contact Analysis for Hypoid Bevel Gears. Comput. Methods Appl. Mech. Engrg. 191 (2002) 3965-3982. (ps-file)
     
  • BÄR, G.:
    Zur Optimierung der Grundgeometrie von Hypoidgetrieben. Proc. Tagung Antriebstechnik/Zahnradgetriebe 14./15.09.2000, TU Dresden, S. 372-386
     
  • IOTCHEV, V.; BÄR, G.:
    Berechnungen zur Auswirkung von Zusatzbewegungen auf die Kontaktgeometrie von Hypoidkegelrädern. Preprint IOKOMO-01-00, TU Dresden, 2000 (ps-file)
     
  • BÄR, G.; DÖBBECKE, T.; KUNZMANN, S.:
    Optische Vermessung von Lehrdornen und Gewinden. Proceedings DGZfP-Fachtagung "Optische Formerfassung" Stuttgart, 5.10-6.10.1999, S. 307-312.

     
     
    Zur Ermittlung funktionsbestimmender Parameter von Lehrdornen und Gewinden wurde ein Labormessplatz nach dem Streifenprojektionsprinzip aufgebaut und getestet. Dabei wurden Oberflächenpunkte der Prüflinge optisch erfaßt, ihre Daten zu einem PC übertragen und die jeweiligen funktionsbestimmenden Parameter der Prüflinge durch speziell entwickelte Auswerteprogramme berechnet.


    Lichtschnitte auf einem zylindrischen Lehrdorn


    Approximierte Ellipsenpunkte


     
  • BÄR, G.:
    Zur Auslegungsberechnung von Hypoidgetrieben. Preprint IOKOMO-02-1999, TU Dresden, 1999 (ps-file)
     
  • BÄR, G.; IOTCHEV V.:
    Accurate Tooth Contact Determination for Hypoid Bevel Gears using Automatic Differentiation. 4th World Congress on Gearing and Power Transmission, Paris, March 16-18, 1999, Vol.1, pp. 519-529.

     
     
    For the first time, due to automatic differentiation, tooth contact of meshing hypoid gears is achieved that does not involve any approximation. The path of contact, the contact pattern, reduced contact ellipses, and the transmission error are computable with machine accuracy of the computer. The new model of gear tooth flank generation can predict the occurrence of undercut and compute the undercutted flank geometry for any machine settings. Approaches are given to optimize the contact pattern geometrically.


    Reduced DUPIN-indicatrices along the path of contact on the pinion tooth surface


     
  • BÄR, G.:
    Berührende Schraubflächen mit Schraublinienkanten. Mathematica Pannonica 8/2 (1997), pp. 225-236.

     
     
    The problem is considered to determine a contacting helicoid to a given helicoid where the concerned screw axes are skew. Then, both helicoids contact along a surface stripe. Its surface axes and pitches are calculated. All axes form a PLÜCKER-conoid. Afterwards, an algorithm which determines the dressed or undercutted helicoid generated by a helicoid underlying a screw motion is presented. The generating helicoid may have a helix edge.
    Such a helix edge generally causes a gap in the corresponding line of contact. With a solution of two given equations it is possible to avoid such a gap. Examples illustrate the results.


    Contacting Helical Surfaces with Skew Axes


     
  • BÄR, G.; KORTHALS, T.: 
    3D-Evaluation of Light Intersection Images. Proceedings 3D Analysis and Synthesis '96. Infix, pp. 23-29

     
     
    Electro-optical 3D-measuring systems consisting of a CCD-camera, a grid projection device, and corresponding image processing equipment are well-known and increasingly used in industry. The authors are interested in the problem to predict the accuracy and performance of such a system on the base of single accuracies of its components and the dimension of the measured objects. Here, specifically, the measuring of industrial objects like balls, bevels, and shafts is investigated.
    Such objects can be represented by quadric surfaces. The fact that a light plane of the projector intersects a quadratic surface along a conic is used. Furthermore, all conics of the same measuring capture are projectivly related. These geometric phenomena are used to perform computer simulation of high accuracy measurement of axes, diameters, and angles which are found at the considered objects.


    Capture of measuring points


     
  • BÄR, G.; LIEBSCHNER, B.:
    A General Purpose System of Teaching Geometry. Proceedings of CADEX '96, IEEE Press 1996, pp. 202-206

     
     
    The paper describes the development and application of the software package CoGeo (Computer Geometry) at the Institute of Geometry of the Dresden University of Technology. This software has been developed to support a great variety of tasks in education and research as training in mathematics, geometry and design, general teaching of programming or computer graphics. It is used by different target groups such as students of mechanical and civil engineering, computer science, mathematics, as well as faculty and researchers. The fundamental steps in the design, implementation and application of the system are compatibly presented.

     
  • BÄR, G.: 
    Dressing of Helicoids and Surfaces of Revolution. VDI Berichte Nr. 1230, 1996, pp. 995-1003
     
  • BÄR, G.: 
    Curvatures of the Enveloped Helicoid. Mech. Mach. Theory, Vol. 32, No.1(1997), pp.111-120.

     
     
    Geometric modelling is needed in mechanical engineering to calculate the geometry of worm gears, threads, and similar mechanical elements that can be described by helicoids or surfaces of revolution, and that are to be manufactured by milling, grinding, or whirling. In the past, the tasks of calculating surfaces of revolution (representing a form cutter or grinding wheel) for milling a given helicoid (representing a worm gear), and calculating the enveloped helicoid for a given surface of revolution were solved separately. Here it will be shown that the two results can be achieved by a more general approach.
    Furthermore, in this paper we consider not only the computation of points of interesting curves of enveloped helicoids but also the computation of tangent lines and osculating circles of such curves. Therefore, some results of differential geometry of helicoids are provided. At first, we calculate the normal curvature of an arbitrary plane section through a helicoid that is defined by an arbitrary generating curve. Then this result is specialised to transverse and axial sections. Furthermore, it is shown that the classification of points of the helicoid as elliptic, parabolic, or hyperbolic can be based on a constructive criterion in the transverse section plane. Finally, the example of an elliptical helicoid and its envelope is used to illustrate the theory.

    Axial section of an enveloped helical
    surface along with the evolute.
    (The evolute is the locus of the
    centers of curvature and the
    envelope of the axial section's normals.)

     
  • BÄR, G.; PRIES, M.:
    Analytische Behandlung des Wälzfräsens. Mech. Mach. Theory 28 (1993), No.1, 65-71.
     
  • BÄR, G.: 
    CAD of Worms and Their Machining Tools. Computers & Graphics, Vol. 14 (1990) Nos.3/4, 405-411.
    (more)
     
  • BÄR, G.; LIEBSCHNER, B.:
    Software zum Berechnen und Konstruieren von Schnecken und Gewinden sowie ihrer Werkzeuge. Werkstatt und Betrieb 122 (1989) 4, 289-291.
    (more)
     
  • BÄR, G.: 
    Konstruktion Dupinscher Indikatrizen berührender Schraub-und Drehflächen. Beitr. Algebra und Geometrie 19 (1985) 205-216.
     
  • BÄR, G.: 
    Parametrische Interpolation empirischer Raumkurven. ZAMM 57 (1977) 305-314.


K. Nestler   04/2013