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Oene Bottema (1901–1992)

  • Teun Koetsier
Part of the History of Mechanism and Machine Science book series (HMMS, volume 1)

Abstract

Oene Bottema was a 20th century Dutch mathematician working in geometry. In the third quarter of the 20th century, the great majority of mathematicians had turned away from classical geometry. At the same time kinematics continued to play an important role in mechanical engineering. The engineers needed a man like Bottema who applied his encyclopedic knowledge of 19th century geometry with 20th century precision to many kinematical problems. He wrote almost 50 papers on kinematics. Most of them contain original contributions. He invented the method of instantaneous invariants in instantaneous kinematics. With Bernard Roth he wrote the influential survey Theoretical Kinematics, North Holland, Amsterdam, 1979.

Keywords

Machine Theory Elliptic Motion Coupler Curve Harmonic Ratio Apply Mechanics Review 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

Bottema’s kinematical papers

  1. Over bewegingen der elliptische ruimte, waarbij alle krommen congruente vlakke krommen beschrijven, Nederlandsche Akademie van Wetenschappen, Afdeling Natuurkunde, 53, 1944, 25–30.Google Scholar
  2. De bijzondere bewegingen van Darboux in de elliptische ruimte, Nederlandsche Akademie van Wetenschappen, Afdeling Natuurkunde, 53, 1944, 58–65.Google Scholar
  3. Eine Bemerkung über die Koppelkurve, Nieuw Archief voor Wiskunde, 22, 1944, 9–14.Google Scholar
  4. On Cardan positions for the plane motion of a rigid body, Proceedings Koninklijke Nederlandsche Akademie van Wetenschappen, 52, 1949, 643–651.Google Scholar
  5. Over de kinematische afbeelding volgens Beth en haar toepassing op de centrale drijfstangbeweging, Euclides, 25, 1949/50, 253–256.Google Scholar
  6. Enige Stellingen uit de kinematica, Simon Stevin, 227, 1950, 106–114.Google Scholar
  7. Recent work on kinematics, Applied Mechanics Review, 6, 1953, 25–40.Google Scholar
  8. On Alt’s special three-bar sextic, Proceedings Koninklijke Nederlandsche Akademie van Wetenschappen, A57, 1954, 498–504.Google Scholar
  9. Zur Kinematik des Rollgleitens, Archiv der Mathematik, 6, 1954, 25–28.Google Scholar
  10. Zur Kinematik des Schleifkurvengetriebes, Öst. Akad. Wiss. Math. Naturw. Kl. Anzeiger, 1956, 109–111.Google Scholar
  11. On Staude’s motion in five-dimensional space, Proceedings Koninklijke Nederlandsche Akademie van Wetenschappen, A57, 1957, 248–253.Google Scholar
  12. Die Bahnkurven eines merkwürdigen Zwölfstabgetriebes, Öst. Ing. Arch., 14, 1960, 218–222.Google Scholar
  13. Zur Kinematik der Schlittenbewegung, Monatshefte Math. 64, 1960, 226–232.Google Scholar
  14. Koppelkrommen met twee undulatiepunten, De Ingenieur 73, 49W, 1961, 188–189.Google Scholar
  15. Some remarks on theoretical kinematics. I. On instantaneous invariants; II. On the application of elliptic functions in kinematics, in Proceedings of an International Conference for Teachers of Mechanisms, Yale University, New Haven, Hamden, Conn., 1961a, pp. 159–167.Google Scholar
  16. Ein Problem der affinen Kinematik, Proceedings Koninklijke Nederlandse Akademie van Wetenschappen, 67, 1964, 290–300.Google Scholar
  17. On the determination of the Burmester points for the five positions of a moving plane, Proceedings Koninklijke Nederlandse Akademie van Wetenschappen, A67, 1964, 310–318.Google Scholar
  18. Acceleration axes in spherical kinematics, Trans. ASME, Journal Engineering Industry, 2, 1965, 150–154.Google Scholar
  19. On Ball’s curve, Journal of Mechanisms, 1, 1966, 3–8.Google Scholar
  20. With F. Freudenstein, Kinematics and the theory of mechanisms, Applied Mechanics Review, 19, 1966, 285–289. Also in Applied Mechanics Surveys, Washington, Spartan, 1966b, 85–92.Google Scholar
  21. On Staude’s motion in four-dimensional space, Nieuw Archief voor Wiskunde, 14(3), 1966c, 1–6.Google Scholar
  22. Flexible hexagons, Proceedings Koninklijke Nederlandse Akademie van Wetenschappen, 70, 1967, 151–155.Google Scholar
  23. On some loci in plane instantaneous kinematics, Journal of Mechanisms, 2, 1967a, 141–146.Google Scholar
  24. Getriebe mit zwei Wälzkurvenpaaren, Forsch. Geb. Ing. Wes., 34, 1968, 149–150.Google Scholar
  25. On displacements of a rigid body, Commun. Phys. Math. Soc. Sci. Fennica, 33, 1968, 1–3.Google Scholar
  26. With F. Freudenstein and T. Koetsier, Finite conic section Burmester theory, Journal of Mechanisms, 4, 1969, 359–373.CrossRefGoogle Scholar
  27. On some loci of lines in plane kinematics, Journal of Mechanisms, 5, 1970, 541–548.Google Scholar
  28. Een scheve stangenvierzijde, Euclides, 45, 1969/70, 267–269.Google Scholar
  29. With T. Koetsier and B. Roth, On the smallest circle determined by three positions of a rigid body, Trans. ASME, Ser. B. Journal of Engineering for Industry, 93, 1971, 328–333.Google Scholar
  30. Instantaneous kinematics for spatial two-parameter motion, Proceedings Koninklijke Nederlandsche Akademie van Wetenschappen, B74, 1971a, 53–62.Google Scholar
  31. The motion of the skew four bar, Journal of Mechanisms, 6, 1971b, 69–79.Google Scholar
  32. Characteristic properties of symmetric plane motion, Proceedings Koninklijke Nederlandsche Akademie van Wetenschappen, B75, 1972, 145–151.Google Scholar
  33. On a set of displacements in space, Trans. ASME, Ser. B. Journal of Engineering for Industry, 95, 1973, 451–454.Google Scholar
  34. Beweging langs een lemniscaat, Euclides. 49, 1973/74, 150–154.Google Scholar
  35. Cardan motion in elliptic geometry, Canadian Journal of Mathematics, 27(1), 1975, 37–43.Google Scholar
  36. On the instantaneous binormals to the paths of points in a moving body, Mechanism and Machine Theory, 10, 1975, 11–15.Google Scholar
  37. The λ-pairs of curves for a cycloidal motion, Mechanism and Machine Theory, 10, 1975, 189–195.Google Scholar
  38. Line envelope coupler curves of hinged four-bars, Teor. Mashin. Mech. Moscow, 1976, 156–161 [in Russian].Google Scholar
  39. With G.R. Veldkamp, On cage-plane motion, Trans. ASME, Ser. B Journal of Engineering for Industry, 99, 1977, 662–664.Google Scholar
  40. Eine spezielle ebene Affinbewegung, Anz. Math. Naturw. Klasse Öst. Akad. Wiss., 7, 1978, 168–172.Google Scholar
  41. With G.R. Veldkamp, Instantane projektive und affine Kinematik, Sber. Öst. Akad. Wiss. Math-naturwiss. Klasse Abt. II, 188, Bd. 1 bis 3. Heft, 1979, 119–141.Google Scholar
  42. With G.R. Veldkamp, Zweigliedrige äquiforme ebene Bewegungen, Proceedings Koninklijke Nederlandsche Akademie van Wetenschappen, B84(l), 1980, 21–26.Google Scholar
  43. A plane motion with a stationary pole, Bul. Inst. Politeh. Iasi, 26, 1980, 3–4.Google Scholar
  44. Secondary centers of curvature for the pointpaths of a planar motion, Mechanism and Machine Theory, 16, 1981, 147–151.Google Scholar
  45. On the upward motion of a double cone on an inclined plane, Elemente der Mathematik, 36, 1981, 121–126.Google Scholar
  46. With E.J.F. Primrose, A quadratric transformation in plane kinematics, Simon Stevin, 55, 1981, 197–203.Google Scholar
  47. With Y. Chen and B. Roth, Rational rotation functions and the special points of rational algebraic motions in the plane, Mechanism and Machine Theory, 17, 1982, 335–348.CrossRefGoogle Scholar
  48. Comments on ‘Axodes for the four-revolute spherical mechanism’ by R.S. Sodhi and T.E. Shoup, Mechanism and Machine Theory, 17, 1982, 173–178, Letter to the Editor, Mechanism and Machine Theory, 20, 1985, 239-242.CrossRefGoogle Scholar

Other references

  1. H.J.E. Beth, Kinematica in het platte vlak, Gorinchem, 1949.Google Scholar
  2. O. Bottema, Het invoeren van coördinaten in de projectieve meetkunde, Koninklijke Academie van Wetenschappen te Amsterdam, Verslag van de gewone vergadering der afdeeling Natuurkunde, XXXVII, No. 7, 1928, 1–10.Google Scholar
  3. O. Bottema, De elementaire meetkunde van het platte vlak, P. Noordhoff N.V, Groningen, Batavia, 1938.Google Scholar
  4. O. Bottema and Bernard Roth, Theoretical Kinematics, North Holland Publishing Company, Amsterdam/New York/Oxford, 1979.zbMATHGoogle Scholar
  5. N. Dergiades and R. Van Lamoen, Rectangles attached to the side of a triangle, Forum Geom., 3, 2003, 145–159.zbMATHGoogle Scholar
  6. M. Husty, On the kinematic constraint surfaces of general three-legged planar robot platforms, Mechanism and Machine Theory, 38, 2003, 379–394.zbMATHCrossRefGoogle Scholar
  7. H.J. Kamphuis, Application of spherical instantaneous kinematics to the spherical slider-crank mechanism, Journal of Mechanism, 4, 1969, 43–56.CrossRefGoogle Scholar
  8. G.R. Veldkamp, Curvature Theory in Plane Kinematics, J.B. Wolters Groningen, 1963.Google Scholar
  9. G.R. Veldkamp, Kinematica, Scheltema & Holkema, Amsterdam, 1970.Google Scholar
  10. G.R. Veldkamp. Canonical systems and instantaneous invariants in spatial kinematics, Journal of Mechanisms, 2, 1976, 329–388.Google Scholar
  11. G.R. Veldkamp, The instantaneous motion of a line in a t-position. Mechanism and Machine Theory 18, 1983, 439–444. G.R. Veldkamp, Oene Bottema: A biographical sketch, Mechanism and Machine Theory, 21, 1986, 447–449 (with a short list of Bottema’s publications).CrossRefGoogle Scholar
  12. G.R. Veldkamp, Oene Bottema: A biographical sketch, Nieuw Archief voor Wiskunde, 4e serie, deel 5, nr. 3, 1987, 249–276. (This is a slightly corrected version of Veldkamp, (1986). The paper is accompanied by a complete list of publications.)Google Scholar
  13. Sashalmi, É. and Hoffmann, M., Generalizations of Bottema’s theorem on pedal points, Annales mathematicae et informaticae, 31, 2004, 25–31.zbMATHGoogle Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  • Teun Koetsier
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceVrije UniversiteitAmsterdamThe Netherlands

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