The romanlocks site mentioned above is thorough, and shows the extensive variety of roman locks.
The type under discussion by the OP was commonly known as the ‘chinese padlock’; archaeologists more commonly now use the term ‘expanding barb’ or barrel padlock (although barrel is far from the only form, it is more common in northern Europe). They spread west from China from 1millenium BC along trade routes, along north and south of the Mediterranean and thence throughout the roman empire. Roman models were copied by the Vikings, and died out in Britain 17C.
Some viking models were iron, others were cast bronze, keys mostly lost-wax castings. Barrel and shackle with springs can come completely apart and tended to become separated, then discarded.
Arabic ones usually covered in verbal engraving; Indian and Chinese ones often in animal shapes. There are masses of modern ones going cheap on eBay, mainly from China. They were in normal use until the 1960’s, and still common in more remote parts of Asia. They make pretty souvenirs for tourists, and have been exported on chinese furniture.
There is a detailed description with good diagrams in PITT-RIVERS ‘On the development and distribution of primitive locks and keys’ Chatto & Windus 1883 which is probably available from Google Books.
