Abstract: A method for universally fixturing a tire bead loosening tool to a variety of standard off-road vehicle wheel rim configurations or designs and a radially and axially adjustable mounting apparatus for performing the method including a hook extending outwardly from a frame of the tool for interlocking with a tool mounting flange of the rim and an adapter carried by the tool for supporting the tool when mounted to the rim. The adapter has a first portion which is immovably affixed to or integral with a forward face of the tool frame, a second trunnion portion depends from the first adapter portion and a third swivel portion is pivotally carried by a pair of gudgeon arms of the trunnion. Each adapter portion has one or more threaded holes for threadably receiving a desired number of pressure bolts for supporting the tool when mounted. In use, the rim is surveyed and the adapter portion which provides the most stable tool support for such rim type is selected.