Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T09:18:27.605Z Has data issue: false hasContentIssue false
  • English
  • Français

Special configurations of robot-arms via screw theory

Published online by Cambridge University Press:  09 March 2009

K. H. Hunt
K. H. Hunt
Affiliation:
Department of Mechanical Engineering, Monash University, Clayton, Victoria 3168, (Australia)
Get access Rights & Permissions [Opens in a new window]

Abstract

SUMMARY

The Jacobian of serial robot-arms is examined, and the matrix of cofactors of a singular Jacobian is presented as a means of explaining the physical nature of special configurations. Because the columns of both these matrices are screw coordinates, screw theory is central to proper understanding. ‘Realistic’ robot-arms are seen to behave in ways that can be explained not by particularizing from a general formulation but rather by carefully interpreting the relevant special screw systems from the outset. Higher singularities (with more than one freedom-loss) are then touched upon.

Type
Articles
Information
Robotica , Volume 4 , Issue 3 , July 1986 , pp. 171 - 179
Copyright
Copyright © Cambridge University Press 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Hunt, K.H., Kinematic geometry of mechanisms (Clarendon Press, Oxford, 1978).Google Scholar
2.Gorla, B., “Influence of the control on the structure of a manipulator from a kinematic point of view” Proc. 4th Symposium on Theory and Practice of Robots and Manipulators, Poland (1981) pp. 30–46.Google Scholar
3.Waldron, K.J., Wang, S-L. and Bolin, S.J., “A study of the Jacobian matrix of serial manipulators” ASME Paper No. 84-DET-33 (1984), to be published by ASME In: J. Mechanisms, Transmissions, and Automation in Design.Google Scholar
4.Sugimoto, K., Duffy, J. and Hunt, K.H., “Special configurations of spatial mechanisms and robot arms” Mechanism and Machine Theory 17, 119–32 (1982).CrossRefGoogle Scholar
5.Hartenberg, R.S. and Denavit, J., Kinematic Synthesis of Linkages (McGraw-Hill, New York, 1964).Google Scholar
6.Paul, R.P., Robot manipulators: mathematics, programming, and control (The MIT Press, Cambridge, Massachusetts, 1981).Google Scholar
7.Duffy, J., Analysis of Mechanisms and Robot Manipulators (Arnold, London, 1980).Google Scholar
8.Beni, G. and Hackwood, S. (editors), Recent Advances in Robotics (Wiley, New York, 1985), Chapter 5 “A vector analysis of robot manipulators” by Lipkin, H. and Duffy, J., pp. 175–239.Google Scholar
9.Woo, L. and Freudenstein, F., “Application of line geometry to theoretical kinematics and the kinematic analysis of mechanical systems” J. Mechanisms 5, 417–60 (1970).CrossRefGoogle Scholar
10.Ball, R.S., The Theory of Screws (Cambridge University Press, England, 1900).Google Scholar
11.Hohn, R.E., Elementary Matrix Algebra (Macmillan, New York, 1958).Google Scholar