....listed and described the rotating wheel etc varieties.

There are many "variants" of RA Badges,as with most other Cap & Other Badges,mostly due to Manufacturers differences,however as LB rightly states the most commonly found{& eagerly sought after} variant is the "Moving Wheel" Royal Regiment of Artillery Badge,which to all intents & purposes is identical to the normal badge but has an additional "free moving" wheel superimposed over the struck wheel on the badge,it can be found on O/Rs Brass badges,including HAC;{The one illustrated above in previous post is a "Moving wheel" HAC Badge} & Officers K/D Bronze {See below},as well as current issue anodised aluminium badges.

another variant ,not so commonly found[Also illiustrated] is the "non voided" wheel,where in the spirit of economy {of labour as opposed to material} the sections between the Spokes of the Wheel & Crown was left "Unvoided" & just for luck I am posting a Manufacturer's variant{possibly Canadian?},which is quite distinctly different from the norm,having a much "Fatter" appearance {especially the "Gun" & different lettering,noticeably on the word "UBIQUE"

A selection of Variant RA/RFA/RGA/RHA Badges;~

Source: Royal Field Artillery-Cap Badge