Portable slat-and-wire fabric machines having twisters comprising a suitable carrier provided with guides, clamps, or holders for the strand wires, which are eccentrically mounted at one side of and revoluble upon or within a ring or substantially annular guide forming a sort of eccentric strap. The carrier holds the strand wires at one side of the strap center and revolves or turns within it, so as to move the wires in a circular path to the opposite side to cross them. This is repeated to produce the desired number of twists.