some necessary conditions for the mobility of $n$–pods. Eventually we consider the case of $n$–pods with high mobility (namely with strictly more than one degree of freedom) and we also provide necessary conditions on the geometry of these devices.

From the kinematic point of view this paper contains the following main results (see Corollary \[corollary:mob1\] and Theorem \[theorem:mobility\_two\]):

[**Result 1**]{}

*If an $n$–pod is mobile, then one of the following conditions holds:*

-   There exists at least one pair of orthogonal projections $\pi_L$ and $\pi_R$ such that the projections of the platform points $p_1, \ldots, p_n$ by $\pi_L$ and of the base points $P_1, \ldots, P_n$ by $\pi_R$ differ by an inversion or a similarity.

-   There exists $m \leq n$ such that $p_1, \ldots, p_m$ are collinear and $P_{m+1}, \ldots, P_n$ are collinear, up to permutation of indices.

In the following we only give one example for each of the two cases of Result 1, as a full listing of all examples known in the literature is beyond the scope of this paper (for some of them, see for example [@GeissSchreyer], [@Karger] and [@KargerHusty]).

It was proven by Bricard (cf. Chapter VI of [@bricard]) that there is exactly one 