*(s)keng-

The core idea of this root was:

crooked, angled

And it was also used for the idea of having a limp.

The branch around Schenkel is based on the fact that legs of humans and animals are bent, crooked or at least we can bend them at the knee.
The branch around schenken (to give a present) started out with the idea of holding a jug at an angle to pour your friend wine or beer  – a meaning that is still alive.
And from there, it broadened toward the more general sense of giving presents.

The only English member I could find in the sources was shank, which clearly is direct counterpart of the German Schenkel.