How about a picture of a modern version? The item in the upper right corner of the lower set of pictures. The difference is that the center post appears fixed and the pulley and slide move together. On your piece the pulley and ratchet move, but the result is the same, a pulley to apply tension to a belt to keep it taut.
http://www.york-ind.com/index.htm?gclid=CNTX8o6A3qACFV455wodjTfREA
Anything using a belt of rope or leather generally needs a way to keep the belt taut. Considering the date of 1877 it probably would have been a machine operated by human power. I'm thinking household equipment because of it's size. It's probably not robust enough for farm or industrial machinery, but could have been used on lighter household equipment. Check some patent drawings for sewing machines, spinning and carding machines, these all needed high speed belts to operate, thus needing tensioner pulleys.
Musketeer