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.
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References
Bottema’s kinematical papers
Over bewegingen der elliptische ruimte, waarbij alle krommen congruente vlakke krommen beschrijven, Nederlandsche Akademie van Wetenschappen, Afdeling Natuurkunde, 53, 1944, 25–30.
De bijzondere bewegingen van Darboux in de elliptische ruimte, Nederlandsche Akademie van Wetenschappen, Afdeling Natuurkunde, 53, 1944, 58–65.
Eine Bemerkung über die Koppelkurve, Nieuw Archief voor Wiskunde, 22, 1944, 9–14.
On Cardan positions for the plane motion of a rigid body, Proceedings Koninklijke Nederlandsche Akademie van Wetenschappen, 52, 1949, 643–651.
Over de kinematische afbeelding volgens Beth en haar toepassing op de centrale drijfstangbeweging, Euclides, 25, 1949/50, 253–256.
Enige Stellingen uit de kinematica, Simon Stevin, 227, 1950, 106–114.
Recent work on kinematics, Applied Mechanics Review, 6, 1953, 25–40.
On Alt’s special three-bar sextic, Proceedings Koninklijke Nederlandsche Akademie van Wetenschappen, A57, 1954, 498–504.
Zur Kinematik des Rollgleitens, Archiv der Mathematik, 6, 1954, 25–28.
Zur Kinematik des Schleifkurvengetriebes, Öst. Akad. Wiss. Math. Naturw. Kl. Anzeiger, 1956, 109–111.
On Staude’s motion in five-dimensional space, Proceedings Koninklijke Nederlandsche Akademie van Wetenschappen, A57, 1957, 248–253.
Die Bahnkurven eines merkwürdigen Zwölfstabgetriebes, Öst. Ing. Arch., 14, 1960, 218–222.
Zur Kinematik der Schlittenbewegung, Monatshefte Math. 64, 1960, 226–232.
Koppelkrommen met twee undulatiepunten, De Ingenieur 73, 49W, 1961, 188–189.
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.
Ein Problem der affinen Kinematik, Proceedings Koninklijke Nederlandse Akademie van Wetenschappen, 67, 1964, 290–300.
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.
Acceleration axes in spherical kinematics, Trans. ASME, Journal Engineering Industry, 2, 1965, 150–154.
On Ball’s curve, Journal of Mechanisms, 1, 1966, 3–8.
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.
On Staude’s motion in four-dimensional space, Nieuw Archief voor Wiskunde, 14(3), 1966c, 1–6.
Flexible hexagons, Proceedings Koninklijke Nederlandse Akademie van Wetenschappen, 70, 1967, 151–155.
On some loci in plane instantaneous kinematics, Journal of Mechanisms, 2, 1967a, 141–146.
Getriebe mit zwei Wälzkurvenpaaren, Forsch. Geb. Ing. Wes., 34, 1968, 149–150.
On displacements of a rigid body, Commun. Phys. Math. Soc. Sci. Fennica, 33, 1968, 1–3.
With F. Freudenstein and T. Koetsier, Finite conic section Burmester theory, Journal of Mechanisms, 4, 1969, 359–373.
On some loci of lines in plane kinematics, Journal of Mechanisms, 5, 1970, 541–548.
Een scheve stangenvierzijde, Euclides, 45, 1969/70, 267–269.
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.
Instantaneous kinematics for spatial two-parameter motion, Proceedings Koninklijke Nederlandsche Akademie van Wetenschappen, B74, 1971a, 53–62.
The motion of the skew four bar, Journal of Mechanisms, 6, 1971b, 69–79.
Characteristic properties of symmetric plane motion, Proceedings Koninklijke Nederlandsche Akademie van Wetenschappen, B75, 1972, 145–151.
On a set of displacements in space, Trans. ASME, Ser. B. Journal of Engineering for Industry, 95, 1973, 451–454.
Beweging langs een lemniscaat, Euclides. 49, 1973/74, 150–154.
Cardan motion in elliptic geometry, Canadian Journal of Mathematics, 27(1), 1975, 37–43.
On the instantaneous binormals to the paths of points in a moving body, Mechanism and Machine Theory, 10, 1975, 11–15.
The λ-pairs of curves for a cycloidal motion, Mechanism and Machine Theory, 10, 1975, 189–195.
Line envelope coupler curves of hinged four-bars, Teor. Mashin. Mech. Moscow, 1976, 156–161 [in Russian].
With G.R. Veldkamp, On cage-plane motion, Trans. ASME, Ser. B Journal of Engineering for Industry, 99, 1977, 662–664.
Eine spezielle ebene Affinbewegung, Anz. Math. Naturw. Klasse Öst. Akad. Wiss., 7, 1978, 168–172.
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.
With G.R. Veldkamp, Zweigliedrige äquiforme ebene Bewegungen, Proceedings Koninklijke Nederlandsche Akademie van Wetenschappen, B84(l), 1980, 21–26.
A plane motion with a stationary pole, Bul. Inst. Politeh. Iasi, 26, 1980, 3–4.
Secondary centers of curvature for the pointpaths of a planar motion, Mechanism and Machine Theory, 16, 1981, 147–151.
On the upward motion of a double cone on an inclined plane, Elemente der Mathematik, 36, 1981, 121–126.
With E.J.F. Primrose, A quadratric transformation in plane kinematics, Simon Stevin, 55, 1981, 197–203.
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.
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.
Other references
H.J.E. Beth, Kinematica in het platte vlak, Gorinchem, 1949.
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.
O. Bottema, De elementaire meetkunde van het platte vlak, P. Noordhoff N.V, Groningen, Batavia, 1938.
O. Bottema and Bernard Roth, Theoretical Kinematics, North Holland Publishing Company, Amsterdam/New York/Oxford, 1979.
N. Dergiades and R. Van Lamoen, Rectangles attached to the side of a triangle, Forum Geom., 3, 2003, 145–159.
M. Husty, On the kinematic constraint surfaces of general three-legged planar robot platforms, Mechanism and Machine Theory, 38, 2003, 379–394.
H.J. Kamphuis, Application of spherical instantaneous kinematics to the spherical slider-crank mechanism, Journal of Mechanism, 4, 1969, 43–56.
G.R. Veldkamp, Curvature Theory in Plane Kinematics, J.B. Wolters Groningen, 1963.
G.R. Veldkamp, Kinematica, Scheltema & Holkema, Amsterdam, 1970.
G.R. Veldkamp. Canonical systems and instantaneous invariants in spatial kinematics, Journal of Mechanisms, 2, 1976, 329–388.
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).
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.)
Sashalmi, É. and Hoffmann, M., Generalizations of Bottema’s theorem on pedal points, Annales mathematicae et informaticae, 31, 2004, 25–31.
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Koetsier, T. (2007). Oene Bottema (1901–1992). In: Ceccarelli, M. (eds) Distinguished Figures in Mechanism and Machine Science. History of Mechanism and Machine Science, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6366-4_3
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