Coordinates for mechanisms configuration spaces

  • Avner Friedman
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 67)

Abstract

A mechanism is a collection of rigid bodies (e.g., bars) connected by movable joints. Typically, one body is fixed (ground). Figure 10.1 shows a 4-bar mechanism. The bars, of length i, are jointed in a way that allows them to rotate freely about their joints. The bar \(\overline {DO}\) is fixed. As the angle θ between l and 0 varies the position of the joint A will vary on the circle with center O and radius l, and the position B must vary in such a way that the distance from the new position of B to the new position of A and to D remain, respectively. 2 and 3. Clearly, not all values of θ are feasible.

Keywords

Configuration Space Rigid Motion Spherical Joint Coordinate Chart Branch Order 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    H.Y. Lee and C.g. Liang, Displacement analysis of the general spatial 7-link 7R mechanism, Mechanics and Machine Theory, 23 (1988), 219–226.CrossRefGoogle Scholar
  2. [2]
    B. Roth et.al, On the design of computer controlled manipulators, in First CISM—IFT. MM Symposium on Theory and Practice of Robots and Manipulators, Vol. 1, pp. 93–113, Udine (1974).Google Scholar
  3. [3]
    J. Duffy and C. Crane, A displacement analysis of the general spatial 7-link 7 R mechanisms, Mechanism and Machine Theory, 15 (1980), 153–169.CrossRefGoogle Scholar
  4. [4]
    B. Morton and M. Elgersma, Coordinates for mechanism configuration spaces, Honeywell Technology Center, February, 1994, Minneapolis, Minnesota.Google Scholar
  5. [5]
    J. Duffy, Analysis of Mechanisms and Robot Manipulators, Edward Arnold Publishers, London and John Wiley & Sons, New York (1980).Google Scholar
  6. [6]
    Modern Kinematics: Development in the Last Forty Years, Arthur G. Erdman editor, John Wiley & Sons, New York (1993).Google Scholar
  7. [7]
    W.P. Thurston and J.R. Weeks, The mathematics of three-dimensional manifolds, Scientific American, pp. 108–120, July 1984.Google Scholar
  8. [8]
    B. Morton and M. Elgersma, A Computational algorithm for 7R spatial mechanism, Submitted to J. of Robotic Systems, June, 1993.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1995

Authors and Affiliations

  • Avner Friedman
    • 1
  1. 1.Institute for Mathematics and its ApplicationsUniversity of MinnesotaMinneapolisUSA

Personalised recommendations