An arm and shoulder exercise machine (20) including a base (22), a vertical rack (32) and resistance means (38) is disclosed herein. Resistance means (38) can be adjusted vertically and pivotally with respect to rack (32) using a unique rack-and-pinion system. A preferred machine (20) also includes an exercise arm (130) which carries a sliding or floating hand grip assembly (142). A preferred machine (20) further includes a pair of pivoting caster assemblies (50), each including a pair of casters (66) and a handle (54). In their raised positions, caster assemblies (50) are above feet (29); when the caster assemblies (50) are in their lowered positions casters (66) are below feet (29), thereby rendering machine (20) transportable.