Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-24T01:13:50.111Z Has data issue: false hasContentIssue false
  • English
  • Français

Feasibility studies of kinematics problems in the case of a class of redundant manipulators

Published online by Cambridge University Press:  09 March 2009

Shinobu Sasaki
Shinobu Sasaki
Affiliation:
Reactor Engineering, Japan Atomic Energy Research Institute, Tokai-muraNaka-gunIbaraki-ken319-11 (Japan)
Get access Rights & Permissions [Opens in a new window]

Summary

Lately, there have been numerous applications of computer algebra to special functions used in the various field of science and engineering. In this paper, we consider an efficient algorithm which generates velocity Jacobians for any class of general serial link manipulators in a compact form throughout the effective use of frame transformations. Compared with conventional techniques, a marked improvement of that capability is found in computer algebra applications to one class of a seven-joint manipulator. Together with finding of explicit solutions for joint rates, closed form arm solutions for the desired position of the hand are presented by relating the rotational motion of the elbow to a geometry problem.

Keywords

KinematicsRedundant manipulatorComputer algebraSeven-joint robotVelocity Jacobian
Type
Articles
Information
Robotica , Volume 13 , Issue 3 , May 1995 , pp. 233 - 241
Copyright
Copyright © Cambridge University Press 1995

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.Whiteney, D. E., “The Mathematics of Coordinated Control of Prosthetic Arms and Manipulators” Trans. ASME J. Dynamic Syst. Measurement and Control 94(4), 303–309 (1972).CrossRefGoogle Scholar
2.Paul, R. P., Robot Manipulators; Mathematics, Programming and Control (The MIT Press, , Cambridge, MASS, 1981).Google Scholar
3.Orin, D. E. and Schrader, W. W., “Efficient Computation of the Jacobian for Robot Manipulators” Int. J. Robotics Res., 3(4), 66–75 (1984).CrossRefGoogle Scholar
4.Vukobratović, M. and Kircanski, M., “Kinematics and Trajectory Synthesis of Manipulation Robots” In: Scientific Fundamentals of Robotics 3 (Springer Verlag, Berlin, 1986).Google Scholar
5.Klein, C. A. and Huang, C. H., “Review of Pseudo-Inverse Control for Use with Kinematically Redundant Manipulators” IEEE Trans. Syst. Man Cybern. SMC-13(13), 245–250 (1983).CrossRefGoogle Scholar
6.Wampler, C. W. II, “Manipulator Inverse Kinematic Solutions Based on Vector Formulations and Damped Least-Squares Methods” IEEE Trans. Syst. Man Cybern. SMC-16(1), 93–101 (1986).CrossRefGoogle Scholar
7.Yoshikawa, T., “Manipulability of Robotic Mechanisms” Int. J. Robotics 4(2), 3–9 (1985).CrossRefGoogle Scholar
8.Burdick, J. W., “On the Inverse Kinematics of Redundant Manipulators: Characterization of the Self-Motion Manifolds” IEEE Int. Conf. Robotics and Automation(1989) pp. 264–270.Google Scholar
9.Lee, C. S. G. and Ziegler, M., “A Geometric Approach in Solving the Inverse Kinematics of PUMA Robot” Proc. of the 13th Int. Symp. on Ind. Robots,Chicago, 16–1/16–18 (1983) pp. 16/1–16/18.Google Scholar
10.Duffy, J., Analysis of Mechanisms and Robot Manipulators (Edward Arnold, London, 1980).Google Scholar
11.Sasaki, S., “On Numerical Techniques for Kinematics Problem of General Serial-Link Robot Manipulator” Robotica 12, Part 4, 309–322 (1994).CrossRefGoogle Scholar
12.Hearn, A. C., REDUCE User's Manual, version 3.4 (Rand Publication CP78 (7/91), 1991).Google Scholar
13.Davenport, J. H., Siret, Y. and Tournier, E., Computer Algebra; Systems and Algorithms for Algebraic Computation (Academic Press, San Diego, 1993).Google Scholar
14.Nakano, E., “Mechanism and Control of Multi-jointed Manipulators” J. Soc. Instrument and Control Eng. 15(8), 637–644 (1976).Google Scholar