A picture of the toy often called a "limber jack" or, in French Canada, a "Ti-Jean" can be seen here. (Or find other pictures by doing a Google search for images.) I bought one many years ago from a street performer in Quebec City – I think mine is more jointed and handsomer than these ones. We still bring him out for special occasions.

My kids used to have a toy like the one described by Turtle Old Man on 18 Sept. – it is quite different. Don't know if it had a proper name, ours was a Henry or something.

I've never heard either toy called a "limber jim" and this isn't really a useful addition to the thread, so I'll go back to just reading again ...