Abstract: A stylus is supported by an upper coupling member which is supported by a lower coupling member which is supported by a probe which is movably supported by a rail of a coordinate positioning machine. The coupling members are held together by a permanent magnet, and their relative positioning is established by first and second sets of positioning elements provided on the first and second coupling members respectively. The sets of positioning elements are mutually engagable in a plurality of angular orientations about the axis of the coupling to provide a plurality of angularly indexed positions at which the lower coupling member has stable and repeatable positions relative to the upper coupling member. The coupling is carried to the indexing dock where a carrier engages the lower coupling member, and the lower coupling member is released from the upper coupling member by energizing an electromagnet which repels the coupling members apart.