"pliant, flexible," 1560s, of uncertain origin, possibly from limb (n.1) on notion of supple boughs of a tree [Barnhart], or from limp (adj.) "flaccid" [Skeat], or somehow from Middle English lymer "shaft of a cart" (see limber (n.)), but the late appearance of the -b- in that word argues against it. Related: Limberness. Dryden used limber-ham (see ham (n.1) in the "joint" sense) as a name for a character "perswaded by what is last said to him, and changing next word."
"detachable forepart of a field-gun carriage," 1620s, alteration of Middle English lymer (early 15c.), earlier lymon (c. 1400), probably from Old French limon "shaft," a word perhaps of Celtic origin, or possibly from Germanic and related to limb (n.1). Compare related Spanish limon "shaft," leman "helmsman."
The nautical limber "hole cut in floor timbers to allow water to drain" (1620s), however, appears to be unrelated; perhaps from French lumière "hole, perforation," literally "light."