A three-dimensional article making apparatus includes a build material dispenser positioned adjacent a platform for ejecting a plurality of droplets of build material; and dispenser positioners for relatively positioning the dispenser in five degrees of freedom with respect to the platform. Accordingly, the dispenser may be rotated and flipped to permit construction of a cantilevered portion of an article without requiring support material. The dispenser positioners include a Z-direction positioner for positioning the dispenser vertically relative to the platform, an X-Y positioner for positioning the dispenser in an X-Y planar direction relative to the platform, a flip angle positioner for rotatably positioning the dispenser relative to a generally horizontal axis, and a phi angle positioner for rotatably positioning the dispenser relative to a generally vertical axis. A processor is operatively connected to the dispenser and the dispenser positioners for advancing the dispenser along a predetermined path of travel while operating or firing the dispenser to construct the three-dimensional article in successive layers or portions based upon the article defining data. Method aspects of the invention are also disclosed.