Hi Sparker. A VK40 would be a vertical crankshaft 4 hp Tecumseh-Kirby-Lauson engine. I don't know the model - 2.5 and 3.5 hp seem to be the usual. There should be a metal plate on the engine indicating the model and that it was made by James N. Kirby but by some mysterious process (commonly known as a licensing agreement) it is actually a Tecumseh or Lauson engine (same thing of course: Tecumseh bought Lauson and inflicted its brand on the new subsidiary). I'll tell you a trade secret: I pick those small Lauson engines out by glancing at the carburetor, especially the air cleaner. Here is a picture of it from another thread.
[Linked Image]
That strange structure, especially the wire clip, is distinctive.

I've never heard of a self-propelled Turner, the Turner brand came and went a long time ago. There seems to be a screw hole that would once have retained a belt guard.

If it is a standard V belt you can identify the specification by taking two measurements. First, check the width of the groove in the V pulley just below the outer circumference. An A section would be 1/2" wide. If it is 3/8" that is below the ordinary industrial sizes, but is designated as 3 section and is common for automotive purposes. If you run an inch tape measure around the outside of the pulleys you'll find the outside circumference of the belt. The standard part numbers in the belt trade consist of the section followed by the outside circumference, such as A33 (a 33" A section). You can get into the nauseating detail here:
http://www.gates.com/catalogs/file_display.cfm?file=Belt_ID_Chart_bkmrks.pdf&thisPath=gates%5Ccatalogs

If the grooves are V shaped it will originally have had a V belt, but I doubt it will be as big as A section. I wouldn't waste my time trying to track down a second hand 40 year old V belt, it would shatter if you dropped it. I also wouldn't waste my time trying to find a Turner spare part, since the firm has been gone 30 years or so and was socially insignificant when it existed.