is, a spatial quadrilateral with equal opposite edge lengths. displays an abstract representation and a 3D model of a Bennett linkage. The joint axes $\ell_1$ and $\ell_4$ are attached to the fixed link while $\ell_2$ and $\ell_3$ belong to the moving link. Two things about Bennett linkages are important to us:

-   Bennett linkage constitute the only type of spatial four-bar linkages with one degree of freedom and

-   their configuration curve consists of only one component.

[img/bennett]{} (14,45)[$\ell_1$]{} (16,19)[$\ell_2$]{} (38,3)[$\ell_3$]{} (49,36)[$\ell_4$]{} (58,45)[$\ell_1$]{} (61,19)[$\ell_2$]{} (85,3)[$\ell_3$]{} (94,36)[$\ell_4$]{}

Here is our main result:

\[th:1\] For every bounded rational curve of degree $d$ and circularity $c$ in three space, there exists a spatial revolute linkage with one degree of freedom with at most $3d-4c+2$ links and $\frac{9}{2}d-6c+1$ joints such that the trajectory of one point attached to the moving link is precisely the given rational curve.

Before we embark on a proof of this theorem (which will consume large parts of this paper), we would like to make a few remarks:

-   The theorem talks about *bounded* rational curves. This is necessary because all trajectories of a linkage with only revolute joints are bounded. It is, however, admissible that the rational curve parameterizes 