Error Analysis with Applications in Engineering

  • Zbigniew A. Kotulski
  • Wojciech Szczepinski

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

Table of contents

  1. Front Matter
    Pages I-IX
  2. Zbigniew Kotulski, Wojciech Szczepiński
    Pages 1-13
  3. Zbigniew Kotulski, Wojciech Szczepiński
    Pages 15-47
  4. Zbigniew Kotulski, Wojciech Szczepiński
    Pages 49-90
  5. Zbigniew Kotulski, Wojciech Szczepiński
    Pages 91-105
  6. Zbigniew Kotulski, Wojciech Szczepiński
    Pages 107-147
  7. Zbigniew Kotulski, Wojciech Szczepiński
    Pages 149-173
  8. Zbigniew Kotulski, Wojciech Szczepiński
    Pages 175-187
  9. Zbigniew Kotulski, Wojciech Szczepiński
    Pages 189-209
  10. Zbigniew Kotulski, Wojciech Szczepiński
    Pages 211-230
  11. Zbigniew Kotulski, Wojciech Szczepiński
    Pages 231-246
  12. Back Matter
    Pages 247-270

About this book

Introduction

This book presents, in the simplest possible manner, those branches of error analysis which find direct applications in solving various problems in engineering.

Chapters I, II, III, and IV contain a presentation of the fundamentals of error calculus: basic characteristics of error distributions, histograms and their various applications, basic continuous distributions of errors and functions of independent random variables. In Chapter V, two-dimensional distributions of errors are discussed with applications. Fundamentals of the theory of two-dimensional continuous independent and dependent random variables are also discussed in that chapter. Then the methods of determination of the ellipses of probability concentration for the two-dimensional continuous normal distribution are given. Chapter VI deals with two-dimensional vectorial functions of independent random variables along with practical applications to the analysis of the positioning accuracy of mechanisms with two-dimensional movements. The procedure of determination of ellipses of probability concentration is also described. In Chapter VII, three-dimensional distributions of errors are considered, while Chapter VIII deals with the three-dimensional vectorial functions of independent random variables. The theory is illustrated by examples of the analysis of the positioning accuracy of robot manipulators. The examples of determining the ellipsoids of probability concentration are presented. Chapter IX contains error analysis-inspired problems that are described by implicit equations and Chapter X presents useful definitions and facts of probability theory for future readings.

This book has been written for readers whose main interests are applications of error calculus in various problems of engineering.

In all ten chapters much attention is paid to the practical significance of error analysis.

Keywords

Analysis Regression Transformation ellipsoids error analysis linear regression mechanics mechatronics robot manipulators

Authors and affiliations

  • Zbigniew A. Kotulski
    • 1
  • Wojciech Szczepinski
    • 2
  1. 1.Inst. Fundamental PAN WarszawaWarszawaPoland
  2. 2.Inst. Fundamental PAN WarszawaWarszawaPoland

Bibliographic information

  • DOI https://doi.org/10.1007/978-90-481-3570-7
  • Copyright Information Springer Science+Business Media B.V. 2010
  • Publisher Name Springer, Dordrecht
  • eBook Packages Engineering
  • Print ISBN 978-90-481-3569-1
  • Online ISBN 978-90-481-3570-7
  • Series Print ISSN 0925-0042
  • About this book