A positioning system for positioning an engine component for attachment to an engine of an aircraft, comprising: a pair of spaced-apart upright supports (144, 146) configured to be mounted to a base on opposite sides of a component bay region of the base; a lift frame including a frame crossbeam and a pair of cambered trusses having respective apexes, the trusses being secured at their apexes at spaced-apart positions to the frame crossbeam, and having distal ends configured to be secured at spaced-apart positions to the engine component; a crossbeam support on which the frame crossbeam is supported for rotation relative to the crossbeam support; wherein the crossbeam support is supported and configured for relative movement along the pair of upright supports (144, 146); a lift mechanism configured to move the crossbeam support along at least one upright support of the pair of upright supports (144, 146); a rotational drive (68, 168) configured to rotate the frame crossbeam relative to the crossbeam support; a laser assembly configured to support a first laser and a second laser at a known distance apart along a reference line, the laser assembly being configured to be positioned relative to the engine component with the reference line oriented vertically, the first and second lasers being individually adjustable in a respective plane including the reference line to align a respective laser beam of each of the first and second lasers with a target position on the aircraft associated with the aircraft engine, with the laser assembly providing a first indication representative of a first angle of the laser beam of the first laser relative to the reference line and a second indication representative of a second angle of the laser beam of the second laser relative to the reference line; and a system controller configured to (a) control operation of the rotational drive (68, 168) to rotate the frame crossbeam relative to the crossbeam support to rotationally position the engine component secured to the lift frame, (b) determine a vertical distance between the engine component and the target position on the aircraft based at least in part on the first and second angles and the known distance, and (c) control operation of the lift mechanism to move the crossbeam support along the at least one upright support (144, 146) in a direction that reduces the vertical distance between the engine component and the engine. a pair of spaced-apart upright supports (144, 146) configured to be mounted to a base on opposite sides of a component bay region of the base; a lift frame including a frame crossbeam and a pair of cambered trusses having respective apexes, the trusses being secured at their apexes at spaced-apart positions to the frame crossbeam, and having distal ends configured to be secured at spaced-apart positions to the engine component; a crossbeam support on which the frame crossbeam is supported for rotation relative to the crossbeam support; wherein the crossbeam support is supported and configured for relative movement along the pair of upright supports (144, 146); a lift mechanism configured to move the crossbeam support along at least one upright support of the pair of upright supports (144, 146); a rotational drive (68, 168) configured to rotate the frame crossbeam relative to the crossbeam support; a laser assembly configured to support a first laser and a second laser at a known distance apart along a reference line, the laser assembly being configured to be positioned relative to the engine component with the reference line oriented vertically, the first and second lasers being individually adjustable in a respective plane including the reference line to align a respective laser beam of each of the first and second lasers with a target position on the aircraft associated with the aircraft engine, with the laser assembly providing a first indication representative of a first angle of the laser beam of the first laser relative to the reference line and a second indication representative of a second angle of the laser beam of the second laser relative to the reference line; and a system controller configured to (a) control operation of the rotational drive (68, 168) to rotate the frame crossbeam relative to the crossbeam support to rotationally position the engine component secured to the lift frame, (b) determine a vertical distance between the engine component and the target position on the aircraft based at least in part on the first and second angles and the known distance, and (c) control operation of the lift mechanism to move the crossbeam support along the at least one upright support (144, 146) in a direction that reduces the vertical distance between the engine component and the engine.