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Solid holed torus knot oscillators

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Abstract

In this paper we develop oscillators whose outputs are solid holed torus knots in real three-dimensional space. Here solid holed knots are closed trajectories on the solid holed torus where the solid holed torus is formed by three perpendicular circles revolved around one another. An electronic circuit is presented that can generate any desired solid holed torus knot.

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References

  1. S. Moran,The Mathematical Theory of Knots and Braids, An Introduction, Mathematical Studies 82, North Holland, Amsterdam, 1983.

    Google Scholar 

  2. R. W. Newcomb, Design of a Torus Knot Oscillator,Proceedings of the 27th Mid-West Symposium on Circuits and Systems, Morgantown, WV, June 1984, vol. 1, pp. 344–347.

    Google Scholar 

  3. R. Parris, A Three-Dimensional System with Knotted Trajectories,American Mathematical Monthly, vol. 84, no. 6, June–July 1977, pp. 468–469.

    Google Scholar 

  4. R. Rassai, Theory and Electronic Circuit Design of Multi-Torus Knot Oscillators, Ph.D. Dissertation, University of Maryland, December 1985.

  5. H. Seifert and W. Threlfoll,A Textbook of Topology, Academic Press, New York, 1980.

    Google Scholar 

  6. M. Waite and C. L. Morgan,Graphics Primer for the IBM PC, McGraw-Hill, Berkeley, CA, 1983, pp. 468–469.

    Google Scholar 

  7. R. Rassai and R. W. Newcomb, Van der Pol Realization of Torus Knot Oscillators,IEEE Transactions on Circuits and Systems, vol. 35, no. 2, February 1988, pp. 215–220.

    Google Scholar 

  8. D. M. Malcolm, Jr.,Robotics, An Introduction, second edition, PWS-Kent, Boston, MA, 1988.

    Google Scholar 

  9. J. J. Craig,Introduction to Robotics, Mechanics and Control, Addison-Wesley, Reading, MA, 1986, pp. 40–52.

    Google Scholar 

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Authors and Affiliations

  1. Microsystems Laboratory, Electrical Engineering Department, University of Maryland, 20742, College Park, Maryland, USA

    Rassa Rassai, George Syrmos & Robert W. Newcomb

Authors
  1. Rassa Rassai
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  2. George Syrmos
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  3. Robert W. Newcomb
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Additional information

Research supported by NSF Grant MIP 87-19886.

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Rassai, R., Syrmos, G. & Newcomb, R.W. Solid holed torus knot oscillators. Circuits Systems and Signal Process 9, 135–145 (1990). https://doi.org/10.1007/BF01236447

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  • DOI: https://doi.org/10.1007/BF01236447

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