What purpose did "the chair" fulfill?

Major spoilers ahead.

The website https://www.dark.netflix.io/ implies that the chair was a prototype of "the machine". But to me that does not make much sense.
The Chair was mainly build by Noah (with the help of Helge). They killed several children (why children?) with it until ultimately it worked and sends Helges younger self back home.
Noah was working under Adams instructions if I remember correctly and should all the time have had access to other means of traveling. In fact 2 of the children they used where kidnapped from 2019 (with the cave passage).

Jonas and his friends where stranded in 1888. There he/they tried to build a machine. Ultimately they succeeded. Before they succeeded they could not send Noah to do the experiments. And their results seem not to be based on the chair experiments. The only sequence of events that would make sense to me is as follows : Noah was also stuck but in 1986. He could use the cave, but not to get back to 18XX. He tries to construct the machine (the chair) to be able to leave 1986. He also has to send Helge back in time. So he did the experiments. When he succeeded, he uses the chair to travel back to 18XX to Jonas, giving him the results of the experiment which helps Jonas to get his time machine (sphere) working.

But as far as I remember there is no connection like this shown in the series. And also if the later machine was bound to the 33 year steps, why the chair shouldn’t and how got Noah back to 18XX then?