  This paper deals with the old and classical problem of determining necessary
conditions for the overconstrained mobility of some mechanical device. In
particular, we show that the mobility of pentapods/hexapods implies either a
collinearity condition on the anchor points, or a geometric condition on the
normal projections of base and platform points. The method is based on a
specific compactification of the group of direct isometries of $\mathbb{R}^3$.
