Singularity Analysis and Representation of the General Gough-Stewart Platform
- 1 March 2000
- journal article
- other
- Published by SAGE Publications in The International Journal of Robotics Research
- Vol. 19 (3), 271-288
- https://doi.org/10.1177/02783640022066860
Abstract
In this paper, the singularity loci of the Gough-Stewart platform are studied and a graphical representation of these loci in the manipulator’s workspace is obtained. The algorithm presented is based on analytical expressions of the determinant of the Jacobian matrix, using two different approaches, namely, linear decomposition and cofactor expansion. The first approach is used to assess the effect of the architecture parameters on the nature of the singularity loci, while the second approach leads to a significant reduction of the computational complexity of the determinant. It is shown that, for a given orientation of the platform, the singularity locus in the Cartesian space is represented by a polynomial of degree three. Moreover, this polynomial equation is applied to several simplified Gough-Stewart architectures and it is shown that the expression is reduced when the base of the mechanism is coplanar and for other special geometries. A comparison with the results obtained using Grassmann geometry is then presented, which illustrates the advantages of using one single compact equation for the singularity loci. The generalization of Fichter’s singular configuration is also developed, and several observations are then made. Finally, a brief discussion on the architecture singularities is presented and a graphical representation of the singularity loci in the Cartesian workspace of the manipulator is obtained. Two examples clearly illustrate the usefulness of the results for the analysis and design of parallel manipulators.Keywords
This publication has 15 references indexed in Scilit:
- An Explanation of Never-Special Assembly Changing Motions for 3–3 Parallel ManipulatorsThe International Journal of Robotics Research, 1999
- The quartic singularity surfaces of planar platforms in the Clifford algebra of the projective planeMechanism and Machine Theory, 1998
- The Octahedral Manipulator: Geometry and MobilityThe International Journal of Robotics Research, 1998
- Kinematische und statische analyse eines ebenen parallelen manipulators mit dem freiheitsgrad zwei: Kinematic and static analysis of a planar two-degree-of-freedom parallel manipulatorMechanism and Machine Theory, 1996
- Simulation and computer‐aided kinematic design of three‐degree‐of‐freedom spherical parallel manipulatorsJournal of Robotic Systems, 1995
- On the quadratic nature of the singularity curves of planar three-degree-of-freedom parallel manipulatorsMechanism and Machine Theory, 1995
- Etude et representation des lieux de singularite des manipulateurs parallelles spheriques a trois degres de liberte avec actionneurs prismatiquesMechanism and Machine Theory, 1994
- Determination of the Workspace of 6-DOF Parallel ManipulatorsJournal of Mechanical Design, 1990
- A Stewart Platform- Based Manipulator: General Theory and Practical ConstructionThe International Journal of Robotics Research, 1986
- Structural Kinematics of In-Parallel-Actuated Robot-ArmsJournal of Mechanical Design, 1983