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Three-dimensional Functions of Independent Random Variables

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Error Analysis with Applications in Engineering

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 169))

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Abstract

Chapter 8 is devoted to three-dimensional functions of independent random variables along with applications to an analysis of a positioning accuracy of robot manipulators. Procedure of determining polyhedrons of the positioning accuracy in such cases when tolerance limits of the positioning accuracy of particular joints of the manipulator are given, is described. When the positioning accuracy of joints is random according to a normal distribution then the procedure of determining of ellipsoids of probability concentration is described. Examples of application illustrate how to proceed.

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References

  1. Kotulski, Z., Szczepiński, W.: On two methods of determining the ellipses and ellipsoids of the positioning accuracy of robot manipulators. Ing. Arch. (Arch. Appl. Mech.) 63(1), 25–41 (1993)

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  2. Szczepiński, W.: Theory of polyhedron of positioning accuracy of manipulators. Mech. Mach. Theory 26(7), 697–709 (1991)

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  3. Szczepiński, W.: Introduction to the Calculus of Tolerance Limits in Mechanical Engineering. Polish Scientific Editors, Warsaw (1993) (in Polish)

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  4. Szczepiński, W., Wesołowski, Z.: On determining positioning accuracy of robot manipulators. Bull. Acad. Pol. Sci., Sér. Sci. Tech. 42, 177–186 (1994)

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Authors and Affiliations

  1. PAN Warszawa, Inst. Fundamental Technological Research, ul. Pawińskiego 5B, 02-106, Warsaw, Poland

    Zbigniew Kotulski & Wojciech Szczepiński

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  1. Zbigniew Kotulski
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  2. Wojciech Szczepiński
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Correspondence to Zbigniew Kotulski .

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Kotulski, Z., Szczepiński, W. (2010). Three-dimensional Functions of Independent Random Variables. In: Error Analysis with Applications in Engineering. Solid Mechanics and Its Applications, vol 169. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3570-7_8

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  • DOI: https://doi.org/10.1007/978-90-481-3570-7_8

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-3571-4

  • Online ISBN: 978-90-481-3570-7

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