type of non–trivial[^1] motions, where all points have spherical paths. Moreover it is well known (cf. page 324–325 of [@bottroth]) that this motion–type is a composition of a rotation about a fixed axis and a translation parallel to this axis. Without loss of generality we can assume that this axis is the $z$–axis. We can take any number of points $p_1, \ldots, p_n$ as platform anchor points, and the centers $P_1, \ldots, P_n$ of the spheres containing their paths as base anchor points. For $n \geq 6$ and generic choice of $p_1, \ldots, p_n$, we will get an $n$–pod with mobility $1$. If we project the points $p_i$ and $P_i$ onto the $xy$–plane, then the resulting points $\pi_z(p_i)$ and $\pi_z(P_i)$ are coupled by an inversion $\iota$ followed by a rotation $\rho$ and therefore the condition (i) is fulfilled.

Based on this example we also want to show that the condition (i) is not sufficient for the existence of a self-motion. To do so, we add an extra leg $(p_{n+1}, P_{n+1})$ where $P_{n+1}$ is not the center of the sphere holding the path of $p_{n+1}$, but another point with the same $xy$–coordinates. Then the hypothesis of (i) in Result 1 is 