Welcome to Cleveland, spaceman! This was a training device from what was the Lewis Research Center and is now the John H. Glenn Research Center in Cleveland, Ohio.
It was located inside the Altitude Wind Tunnel and looks capable of doing some totally gnarly maneuvers. The MASTIF was designed to replicate an out-of-control tumbling spacecraft over which the pilot needed to regain control.
The picture, NASA Photo C-1959-52233, appeared in a chapter called “Between Human and Machine” in the 2006 publication Critical Issues in the History of Spaceflight. I found it in the archive.org NASA Technical Reports Server.