A wire winding machine has a winding wheel that includes a central core having an adjustable outside dimension. A central member and a plurality of outer members are connected with linkages that allow the outside dimension to be adjusted. At least one of the outer members is moveable once a desired amount of wire has been wound so that the wound wire can be removed in an axial direction relative to the winding wheel. In a disclosed example, an end member of the winding wheel cooperates with at least the one outer member to move it into a first position for receiving the wire and releasing it to be moveable a second position for removing the wound wire from the central core of the winding wheel.