I am looking for rubber bands that are not too elastic.
I remember with LEGO there were rubber bands used as a belt between rotating pieces:
They weren't the usual rubber bands that you can stretch much more:
Do you know what is their name?
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O-rings are typically made from a firmer rubber than a rubber band. They will stretch but not as much. They come in all sizes, so you're going to have a shopping quest ahead of you, but "O-ring" is probably the best search term for you.
The lego parts were small drive belts. They're used in other applications such as record players. Similar parts are available (e.g. from CPC or Maplin in the UK, Amazon or eBay everywhere).