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Please look at the photographs shown in the description. There is also a file called Asembly_reference.step, which shows the assembled plotter, so you can see it from whichever angle you wish. There are also further indications in the "Thing details".
Instead of the solenoid, you could use a servo motor. Check the posted "makes". One shows a servo being used instead of the solenoid.
Good luck with your build and do not hesitate to ask further questions.