Well, my daughter and Vita had asked about this piece of kit, which has been gracing my garages since about 1962. At that time I was the proud owner of an Ariel Square Four motorcycle with a large family sidecar. Indeed, I owned two in quick succession.
You can see the pinions at "A" and "C" in the drawing above. I used the aforementioned tool to successfully remove these. When the engine was reassembled I put the puller carefully away "for next time" and never used it again. It is till awaiting reuse after over 60 years! Incidentally, over the years, as I have lifted cylinder heads off motorcycles, I have always preserved the old gaskets as memories - I found the old Square Four ones.
I loved those Square Fours. At that time (apart from the too expensive Vincents) they were the only 1000cc motorcycles and were ideal for dragging a large family "chair". They managed, easily, a wife and 3 small children and were only eventually replaced by a Morris Traveller car for family comfort.
My daughter remembered my affection for them and once, as a "thank you" present she bought me a painting of one, which still graces the bedroom wall.