Nicolaus Copernicus, as noted, lived well before spirographs.
So, when he said the orbits of Tychonian type which he considered Geocentrism would imply along with observations, were harder to explain than those of a Heliocentric universe, the issue was he had no idea how to describe a spirograph pattern.
Some have imagined he was speaking about physical impossibility, like the "for no reason at all objection" on the video
by CoolHardLogic with the title Testing Geocentrism - Part 1.
A man who was raised basically as a scholastic while becoming a clergyman and who on top of that read Cicero and Plato was hardly likely to be stuck in that kind of objection.
Some have also imagined he wanted to contradict the passages in Scripture that supported Geocentrism - nothing could be further from the truth, without having read Commentariolus or De Revolutionibus Orbium Celestium, I think it is all very technical and sticks to non-Biblical stuff - or he would have been in trouble with the Church as was later the case with Galileo on two occasions, 1616 and 1633 processes.
Also, his solution is not what modern astronomers adopt as such, it has lots of what they consider problems even if Geocentrics do not, and some which Geocentrics would agree on.
He explains parallax is not observed because of the very great distance of the stars, which kind of predicts a parallax if one could only see the stars as if they were closer. However, as his outermost sphere is "stellarum fixarum" and is qualified as "immobilis", the kind of parallax he would have predicted if he had been only told of the telescope is far from that phenomenon which commonly observed by astronomers commonly is by Heliocentrics called parallax. The phenomenon according to which Proxima Centauri and 61 Cygni are different numbers of light years away from us, and Sirius even further, as Heliocentrics interpret it, does not look like what he would have predicted.
It is therefore at the very least doubtful if the phenomenon we are used to call "parallax" is a confirmation of the "parallax" Copernicus and Galileo predicted.
And if a confirmation is doubtful, it is not proving.
Also, with the apparent sizes that he accepted for the stars, without certain corrections later added to these (whether they be really more correct is another problem, basically, the theory is that seen from Earth within athosphere they appear huger because light is diffused around the real central image of the star), the result would be that in order not to show parallax they must be so far away as to be (not only some of them, but each) thousand times larger than the Sun.
L'obiezione più efficace all'universo copernicano era però il problema delle dimensioni delle stelle . Secondo i modelli geocentrici dell'universo, le stelle si trovano poco oltre i pianeti; in questa situazione le loro dimensioni stimate con un semplice calcolo geometrico non risultavano troppo diverse da quelle del Sole. Con la teoria eliocentrica di Copernico le stelle dovevano essere estremamente lontane e quindi, applicando lo stesso sistema di calcolo, risultavano esageratamente grandi, di dimensioni pari a migliaia di volte quelle del Sole.
Note 7 of the Italian wikipedia goes to D. Danielson e C. M. Graney, Processo a Copernico, Le Scienze Marzo 2014. An Italian Science magazine, obviously.
But above all, when he considered that a parallax, if it could only be observed, would prove Heliocentrism, he parted from the idea that all fixed stars are really fixed. This has since been refuted by Halley.