several results from other, recently published, papers. Whenever we use such a result we give a concise summary and references. Moreover, we provide algorithmic descriptions so that a reader of this paper will be able to construct linkages for drawing an arbitrary rational space curve. We continue this article with a formulation of the main theorem and an overview of its proof in . In we provide a concise introduction to dual quaternions and motion polynomials. The proof of our main theorem is done in . It is subdivided into several steps: Construction of a minimal motion to the given rational curve, factorization of this motion, and subsequent linkage construction by means of “Bennett flips”. In we present several examples to illustrate important points of our construction. In the concluding we discuss our result and ideas. We mentioned implementation issues and outline possible extension and application.

Main theorem and overview of proof  {#sec:overview}
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Our main result in this paper is a statement about linkages and bounded rational curves in three-space. A rational curve is a curve admitting a parametric equation of the shape $X = x_0^{-1}(x_1,x_2,x_3)$ with polynomials $x_0,x_1,x_2,x_3 \in {\mathbb{R}}[t]$ and $x_0 \neq 0$. It is no restriction 