In his 1637 Géométrie Descartes introduced a general method to adopt algebra in geometrical problem solving. Such a method was still based on geometric constructions, and curves were introduced as traces of ideal machines. Differently from Descartes' idea of limiting geometry to algebraic curves, in the second half of the 17th century, mathematicians looked for an appropriate geometrical legitimation to introduce non-algebraic curves. A general problem that originated a wide class of transcendental curves was the inverse tangent problem: new curves were introduced given the properties that their tangents have to satisfy. Suitable ideal and also real machines have been designed and realized to solve this class of problems. The aim of this paper is to propose an original machine that, by the solution of inverse tangent problems, traces both conics and some tran-scendental curves obtained as oblique trajectories of confocal conics. For such a machine we also provide the 3D printable model: in this way we wish to allow a widespread of this kind of machines between mathematical enthusiasts but also for laboratory activities in teaching mathematics.