A remarkable set of Schönflies-singular planar Stewart Gough platforms (Q631049)

A Stewart-Gough-platform (SGP) is called Schönflies-singular if the platform is singular for all poses of the moving plate stemming from the transformations of a Schönflies group \(X(a)\) with the fixed direction \(a\). The author works out analytic and geometric conditions for these interesting SGPs and delivers a complete list of possible types: The fixed or the moving plate of anchor points have to lie in a plane orthogonal to the fixed direction \(a\) of the corresponding Schönflies group \(X(a)\). Further on, the author studies self-motions of these special singular platforms. He shows that in all cases such self-motions possess a quadratic singular set.