"joint between the principal bones of the leg," Old English cneo, cneow "knee," from Proto-Germanic *knewa- (source also of Old Norse kne, Old Saxon kneo, Old Frisian kni, Middle Dutch cnie, Dutch knie, Old High German kniu, German Knie, Gothic kniu), from PIE root *genu- (1) "knee; angle." For pronunciation, see kn-.
To be across (someone's) knee in reference to spanking is from 1866. Knee-breeches is from 1827; knee-pants is from 1858. Knee-slapper "funny joke" is from 1955.