Stewart Platform - Static Analysis
Table of Contents
1 Coupling
What causes the coupling from \(F_i\) to \(X_i\) ?
\begin{tikzpicture} \node[block] (Jt) at (0, 0) {$J^{-T}$}; \node[block, right= of Jt] (G) {$G$}; \node[block, right= of G] (J) {$J^{-1}$}; \draw[->] ($(Jt.west)+(-0.8, 0)$) -- (Jt.west) node[above left]{$F_i$}; \draw[->] (Jt.east) -- (G.west) node[above left]{$\tau_i$}; \draw[->] (G.east) -- (J.west) node[above left]{$q_i$}; \draw[->] (J.east) -- ++(0.8, 0) node[above left]{$X_i$}; \end{tikzpicture}
Figure 1: Block diagram to control an hexapod
There is no coupling from \(F_i\) to \(X_j\) if \(J^{-1} G J^{-T}\) is diagonal.
If \(G\) is diagonal (cubic configuration), then \(J^{-1} G J^{-T} = G J^{-1} J^{-T} = G (J^{T} J)^{-1} = G K^{-1}\)
Thus, the system is uncoupled if \(G\) and \(K\) are diagonal.