Idiom: Round the bend
OED definition: Mad
Example: I’ll go round the bend if I have to look after the kids all day
An alternative suggestion is that traditional Victorian mental institutions used to have long, tree-lined driveways leading up to the main building. However, in order to distinguish a mental hospital from the large stately homes of the period, the driveway curved at the end rather than led directly to the front door. This had the added advantage of hiding the buildings so that they could not be seen from the road. Therefore if you were mad, you would have to go round the bend of the driveway in order to get the hospital.
There is, however, one entry in the Oxford English Dictionary of Sea Slang from 1929, which suggests that the phrase is ‘an old navel term for anyone who is mad’. There is very little other evidence to support this idea, though.