it is of dimension one, we call it a *configuration curve* and say the linkage has *one degree of freedom.* If this is the case, we designate one link as fixed and another as moving. We view the relative displacements of the moving link with respect to the fixed link as a curve in ${\mathrm{SE}(3)}$. The *orbit* or *trajectory* of a point attached to the moving link is the locus of all positions in space when the point is subject to all possible displacements in this curve. A linkage is called *spherical,* if all axes are concurrent and *planar* if they are parallel. The trajectories of spherical linkages are spherical curves and the trajectories of planar linkage are curves in parallel planes. For a more formal definition of (at least planar) linkages we refer to [@gallet15].

Let us illustrate some of these concept at hand of a Bennett linkage [@bennett03; @bennett14; @baker98; @perez04] which will play a crucial role in our linkage construction in . A Bennett linkage is a spatial four-bar linkage with one degree of freedom. Its four axes $\ell_1$, $\ell_2$, $\ell_3$, $\ell_4$ are the perpendiculars to two incoming edges in the vertices of a spatial parallelogram, that 