Let's start with the original sentence.
A variety of self-sustained motion mechanisms in nature can be classified into just two groups: motion based on propulsion or on ratchet principles.
The first "duplicate" that you point out is "motion mechanisms". Let's move the words around a bit, though.
A variety of mechanisms for self-sustained motion in nature can be classified into just two groups: motion based on propulsion or on ratchet principles.
Mechanism isn't duplicating "motion"; it was part of a compound noun that I split up for illustration.
While it is encouraged to use different synonyms to avoid using the same word multiple times in the same sentence, a technical subject like this has a harsher treatment of synonyms. (Anybody else remember the "Canary Trap" from Tom Clancy's books?) While "motion" and "movement" are synonyms to the layperson, they are not in physics.
The only remaining qualm remains with the list following the colon. I would probably rewrite it as follows.
A variety of self-sustained motion mechanisms in nature can be classified into just two groups: motion based on propulsion and motion based on ratchet principles.
The original sentence was attempting to be too compact and resulted in a sentence that nearly needs two passes before you understand it. Technical writing is slow reading to begin with; we should aim to make it readable the first time through.