"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.
pad n.
1550s, "bundle of straw to lie on," a word of obscure origin (perhaps a merger of several separate words), possibly from or related to Low German or obsolete Flemish pad "sole of the foot," which is perhaps from PIE *pent- "to tread, go" (see find (v.)), but see path (n.).
Sense of "soft cushion" is from 1560s, originally a soft saddle. Generalized sense of "something soft" is from c. 1700. Meaning "cushion-like part on the sole of an animal foot" in English is from 1790. The sense of "a number of sheets fastened or glued together at the edge" (in writing-pad, drawing-pad, etc.) is from 1865.
Sense of "takeoff or landing place for a helicopter or missile" is from 1949; the notion is of something to prevent friction or jarring. The word persisted in underworld slang from early 18c. in the sense "sleeping place," and this was popularized again c. 1959, originally in beatnik speech (later hippie slang) in its original English sense of "place to sleep temporarily," also "a room to use drugs."