first straight line linkages, Kempe’s theorem must have been a true surprise to his contemporary kinematicians. Throughout the 20th century, it was considered a milestone result.

Kempe’s constructive proof can be used to actually compute a linkage that draws a planar algebraic curve. However, it was clear from the beginning that this construction is of no practical relevance. It requires an excessive number of links and joints, even for curves of low degree. Nowadays, an asymptotic bound of $O(d^n)$ for the number of links necessary to draw an algebraic curve of degree $d$ in an ambient space of dimension $n$ is known [@abbott08]. Nonetheless, drawing an ellipse with a Kempe linkage already requires hundreds of links [@kobel08]. A wealth of more practical examples for algebraic curve generation can be found in the monograph [@artobolevskii64]. However, the constructions there are rather specific to certain classes of curves and, more importantly, use mechanical constraints different from rigid links and revolute joints.

Kempe’s Theorem talks about algebraic curves and it is natural to ask for simplifications in case of rational curves. This was done recently in [@gallet15] where the authors constructed scissor-like linkages to draw rational planar curves. Their construction is based on 