On Stewart Gough manipulators with multidimensional self-motions

By means of bond theory, we study Stewart Gough (SG) platforms with n-dimensional self-motions with n>2. It turns out that only architecturally singular manipulators can possess these self-motions. Based on this result, we present a complete list of all SG platforms, which have n-dimensional self-motions. Therefore this paper also solves the famous Borel Bricard problem for n-dimensional motions. We also give some remarks and a new result on SG platforms with 2-dimensional self-motions; nevertheless a full discussion of this case remains open.