a bounded portion of an unbounded curve, for example a line segment.

-   Boundedness also implies that $d$ is even and $c$ is an integer so that our bounds on the number of links and joints are integers as well.

-   The linkage of is not unique. In fact, uncountably many linkages exist. Even planar or spherical curves may be drawn by spatial linkages.

-   However, our approach is capable of producing planar linkages for planar curves () and retains the bounds of [@gallet15] for the numbers of links and joints of bounded planar rational curves.

-   Our approach can also produce spherical linkages for spherical curves. For them, the number of links and joints reduces to $d+2$ and $\frac{3}{2}d+1$, respectively ().

-   The linkages can be constructed in such a way, that their configuration curve is free of spurious components. This is however not the case if the linkage is required to be planar or spherical.

Our proof of is constructive and can be translated into algorithms, mostly based on polynomial algebra over the dual quaternions. Our presentation pays attention to these algorithmic approach and gives ample information for actual implementation. The proof consists of several steps. We begin 