According to old Sears and Eatons catalogues, there was quite a variety of tire shrinkers made in many different styles by many different manufacturers. This one was made by A B Jardine & Co. of Hespeler, Ontario.
The principle of operation was that a blacksmith would heat a small section of the tire in his forge until it was red-hot, then put it in the machine. The grooved cams would grasp the tire and pressure applied to the extending arm (lower right in these pix) would pull the two halves of the machine, which are hinged at the top, together, shrinking the heated section of the tire slightly.
This procedure was often necessary as constant contact with the road surface tended to expand and stretch the tire, making for a loose fit on the wheel. Sufficiently loose, the tire would simply fall off the wheel - not a good thing...
This tire stretcher is displayed at Pandosy Mission, fittingly, on the outside wall of the blacksmith shop.
A demonstration of a similar machine in operation can be viewed on
You Tube