large grallatorial bird with very long legs, beak, and neck, Old English cran, common Germanic (cognates: Old Saxon krano, Old High German krano, German Kranich, and, with unexplained change of consonant, Old Norse trani, Danish trane), from PIE *gere-no-, suffixed form of root *gere- (2) "to cry hoarsely," also the name of the crane (cognates: Greek geranos, Latin grus, Welsh garan, Lithuanian garnys "heron, stork"). Thus the name is perhaps an echo of its cry in ancient ears.
Misapplied to herons and storks. The gray European crane was "formerly abundant in marshy places in Great Britain, and prized as food" [OED], but was extinct there through much of 20c.
Use for "machine with a long arm for moving weights" is attested from late 13c. (a sense also in equivalent words in German, French, and Greek). The constellation was one of the 11 added to Ptolemy's list in the 1610s by Flemish cartographer Petrus Plancius after Europeans began to explore the Southern Hemisphere.