In the Pokemon game one of the swimmer enemies describes himself as locker und gelenk. But what does it mean?
Locker, I've already found in a dictionary.
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"Gelenk" may be rather rare and I would guess the person translating the game just took whatever the dictionary was suggesting without double checking.
The opposite however, "ungelenk", is commonly used both as an adverb or an adjective.
Since "ungelenk" (clumsy, clumsily moving) is not the same as "ungelenkig" (not very limber), I perceive the same difference for "gelenk" vs. "gelenkig", the latter being "limber" and the former being "agile".
Like others have already said, gelenk is synonymous with gelenkig ‘flexible, agile’ and the former is falling out of use. They are not used for different functions, e.g. adverb and adjective.
Some adjectives require the transparent word class suffix +ig in compounds, e.g. neu+ig+keit, others do not appear without it, e.g. ewig, artig. Of these, some have a tendency to incorporate that morpheme into their base form, too, e.g. gelenk+ig, whereas it’s wrong for others like *neu+ig. The reasons for this change may be manifold, from phonologic constraints to semantic disambiguation.
“Transparent” above means that words from other classes do not end in -ig (where i is not part of a diphthong ei). Prominent counter-examples are nouns Essig, Honig, Käfig, König, Pfennig and Reisig (but this list is pretty much complete) and names of all kinds like Leipzig, Grundig, Herbig, Ludwig. Let’s assume, numerals like vier+zig were adjectives. There are also about 100 verbs that end in +ig+en and therefore could have an inflective, imperative or schwa-apocopic form with -ig at the end; they’re usually derivates of adjectives or nouns, and most also include a prefix like be+, er+ or ver+.
“Adjective” is used in a loose sense above, because it may include adverbs and pronouns, cf. wenig+ and einig+. So +ig is restricted to words that can inflect in a common way: differentiated by gender.
I think you meant "Gelenkig" because you can not use the word "Gelenk" to describe someone (at least in common language).
It means that you can move the parts of your body very well. The actual translation is "agile" or "supple"