Jacob,
Your engine is pretty rough. As Nick suggests, you should, or could try to run it (using an air compressor, not live steam). Before you attempt this however I would at minimum make sure that everything that is supposed to rotate actually does rotate, and everything that is supposed to slide actually does slide. A minor cleaning and oiling of moving parts etc. In addition, it appears as if the valve rod from the eccentric to the vertical link (the part with the 4 holes) is quite bent and bowed. You may have to straighten that up. I attempted to do a patent search on anything resembling this engine without success. Could you share your great grandpas name? This would improve search chances.
If you wish to search for yourself, the search terms "Steam Engine variable valve cutoff" would probably give you the best results, although technically your engine is not variable because it can't be adjusted while running so maybe "steam engine adjustable valve cutoff" would yield better results. I really don't see anything on this engine that would have been patentable unless it was very early 1800's. Engines were quite technically advanced by 1840's and 1850's with governable variable valve cutoff for engine speed control.
Jim in Minnesota.