Beautiful Techno-Art & Invention: Circular Adding Machines, 1850-1900 - featuring technical illustrations from US patents for various rotary adding machines. I haven't looked into the background, but patents aren't proof of technical feasibility, and quite possibly many of these devices didn't make it to the stage of practical use. However the W Lang adding machine (pictured above) certainly was feasible, because I have one of exactly this type.
This British-sold "Addometer" works on a straightforward principle; you use a metal stylus to turn a dial to add and subtract, and overflow cascades to the adjacent dial. A slide lever clears everything to zero. (see YouTube demo - I can't show you the workings, as the casing is riveted shut, but the Vintage Calculators Web Museum Addometer page has pictures). These multi-spindle adders were a popular, robust and successful design; they recur in 19th / early 20th century patents, with no clear attribution trail, and continued in use right through to the end of the mechanical calculator era.
This particular one - dating I think from the 1920s-30s - is both technologically and conceptually obsolete: it adds Sterling currency - pounds, shillings, pence, and farthings. As the front logo says, it's US-made (by the Reliable Typewriter and Adding Machine Co., Chicago, Illinois) but the brass logo on the edge has been milled out, and the device rebadged to "Taylor's 74, Chancery Lane, London": a firm that historically sold typewriters and other office equipment.
I'm mildly puzzled that I don't remember any such devices from my childhood. My mother worked in various offices as a secretary, and took me there sometimes when I was on school holidays (this would be very early 1960s). I don't remember seeing anything but typewriters and duplicating machines. Were these calculating devices so expensive, or so cumbersome, that they weren't widely used?