On the Self-Mobility of Point-Symmetric Hexapods

Abstract

In this article, we study necessary and sufficient conditions for the self-mobility of point symmetric hexapods (PSHs). Specifically, we investigate orthogonal PSHs and equiform PSHs. For the latter ones, we can show that they can have non-translational self-motions only if they are architecturally singular or congruent. In the case of congruency, we are even able to classify all types of existing self-motions. Finally, we determine a new set of PSHs, which have so-called generalized Dietmaier self-motions. We close the paper with some comments on the self-mobility of hexapods with global/local symmetries.

Hexapods with Plane-Symmetric Self-Motions

“…Assumptions on the geometry of the platform and base; e.g., (a) linear mapping between platform and base [16][17][18][19][20][21][22], (b) symmetry properties of platform and base [20][21][22][23][24], (c) special topology (e.g., octahedral structure [25]), or a combination of these assumptions (e.g., [20-22]) 2.…”