Dual-Number Methods in Kinematics, Statics and Dynamics
eBook - ePub

Dual-Number Methods in Kinematics, Statics and Dynamics

  1. 240 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

Dual-Number Methods in Kinematics, Statics and Dynamics

About this book

This well-organized book uses 3x3 coordinate-transformation matrices and 3-element vectors with dual-number elements to analyze the mechanics of mechanism, robots, and other mechanical systems. Dual-Number Methods in Kinematics, Statics and Dynamics serves as a text for a course using dual-number methods as well as a manual for the reader to develop his or her abilities for the design of machinery or evaluation of mechanical systems. In addition to the explanatory text and derivations, the author includes numerous examples and exercises to enable the reader to gain insight and perfect skills.

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Yes, you can access Dual-Number Methods in Kinematics, Statics and Dynamics by Ian Fischer in PDF and/or ePUB format, as well as other popular books in Technology & Engineering & Civil Engineering. We have over one million books available in our catalogue for you to explore.

Chapter 1 - Definitions

The Dual Number

The concept of the dual number was introduced by Clifford during 1873 and the name was given by Study in 1903.
The dual number ε is defined such that
ε≠0(1)
ε2=0(2)
A dual number, which perhaps should be called a “duplex” number in analogy with complex numbers, is written as
a^=a+εa0(3)
where symbol a represents the primary (or real) part of duplex (or dual) number â and symbol a0 represents the dual component of duplex (or dual) number â.
In the mathematics of dual numbers, addition is defined as
a^+b^=(a+b)+ε(a0+b0)(4)
Multiplication is defined as
a^b^=(a+εa0)(b+εb0)(5)
=ab+ε(ab0+a0b)(6)
Division is handled in a manner similar to the division of complex numbers
a^b^=a+εa0b+εb0(7)
=a+εa0b+εb0b−εb0b−εb0(8)
=ab+εa0b−ab0b2(9)
Division by a pure dual number is not defined.
Raising a dual number to a power is
a^n=(a+εa0)n(10)
=an+εna0an−1(11)
Thus the square root of a dual number is
a^=a+εa02a(12)
The Taylor series expansion of a function of a dual number is
f(a^)=f(a+εa0)(13)
=f(a)+εa0df(a)da(14)
All formal operations of dual number are the same algebra followed by...

Table of contents

  1. Cover Page
  2. Half title
  3. Title Page
  4. Copyright Page
  5. Preface
  6. Dedication Page
  7. Table of Content
  8. Chapter 1 Definitions
  9. Chapter 2 Coordinate Transformation
  10. Chapter 3 Matrix Modeling of Joints and Links
  11. Chapter 4 Displacement Analysis
  12. Chapter 5 Velocity Analysis
  13. Chapter 6 Static Analysis
  14. Chapter 7 Dynamic Analysis
  15. Chapter 8 Dual-Number Programming
  16. Bibliography
  17. Index