Sleeveless errand
A sleeveless errand is a fruitless quest or a pointless exercise and dates from at least the 14th century. In those days, sleeveless meant futile or inadequate and no one is quite sure why, unless a sleeveless garment was somehow inadequate. A sleeveless errand appears in John Heywood Proverbs (1546) when it was already a well-known expression. Shakespeare uses it in Troilus and Cressida (c.1601) Act V, Scene IV, “the dissembling drab of a sleeveless errand.”