An injection unit for an injection molding machine includes a cylindrical body rotatably supported in a housing interior for rotational coupling with a plasticizing screw. The cylindrical body is fixed to rotate with the plasticizing screw about an injection axis. A gear train in the housing includes a central gear mounted about, and fixed to rotate with, the cylindrical body, the central gear having an uppermost extent vertically above the injection axis and opposed first and second lateral extents on horizontally opposed sides of the injection axis. A rotary drive for powering rotation of the plasticizing screw includes a first motor having a first motor shaft rotatable about a first motor axis, the first motor axis parallel to the injection axis, the first motor axis at a first elevation below the uppermost extent of the central gear, and laterally outboard of the first lateral extent of the central gear.