Stewart varieties: a direct algebraic model for Stewart platforms
- 1 October 1990
- journal article
- Published by Association for Computing Machinery (ACM) in ACM SIGSAM Bulletin
- Vol. 24 (4) , 42-59
- https://doi.org/10.1145/101108.101113
Abstract
We present a new approach to modelling a triangular Stewart platform, which we regard as defining an octahedron. The lines joining the unlinked articulation points correspond to the diagonals of the octahedron. Using a classical determinant identity, we show that the squares on the diagonals satisfy a rather special system of non-linear algebraic equations. A set of bounded solutions (the "Stewart variety") easily yields the coordinates of a platform. In fact, each solution gives two platforms, which are symmetric with respect to the base plane. Using Newton's method, we give an effective algorithm to calculate the Stewart variety and the corresponding platform coordinates. We conclude with the algorithm at work on two examples.Keywords
This publication has 1 reference indexed in Scilit:
- A Platform with Six Degrees of FreedomProceedings of the Institution of Mechanical Engineers, 1965