Nortons did and made about 6000 of them. Based on a pre-war Baughan design originally used for sidecar trials, it had no differential. Those sold off post-war had the dogs cut off because they just go straight on with swd engaged on tarmac.
The trials heritage is clearly visible in this shot. Plenty of possibility for the 'monkey' to get his weight over the chair wheel.
The picture is taken from a Pathe film and shows 4th Royal Northumberland Fusiliers training at Fontaine in March 1940. They went on to take part in the Arras counter-attack. To quote Blaxland in 'Destination Dunkirk' - "The left or inner column had meanwhile reached Dainville, which stands on a spur overlooking Arras. Y Company 4th RNF came into action here, making what would appear to be the first and only attack ever launched by British Motorcyclists. Having surrounded the village, the company commander, Major Clarke, attacked with a platoon dismounted, supported by a troop of tanks. Forty miscellaneous prisoners were taken and the village was won."
They were also used in some roles in North Africa but a number of later contracts were amended to an "A.A. box" (A commercial box sidecar with an angled front) and were used for traffic control etc.
There is a lot more information on Rob van den Brink's WD Norton website.
http://www.wdnorton.nl/Specification%20BIG4.htm