Various embodiments include methods adapted to displace turbomachine components from a location within a turbomachine. In some embodiments, a method of displacing a turbine bucket from a turbomachine wheel slot using a displacement apparatus, includes: detachably engaging an engagement arm of the displacement apparatus to the turbine bucket, the engagement arm attached to a linear actuator coupled to a body of the displacement apparatus, and the engagement arm adapted to be actuated in a first axial direction by the linear actuator; contacting the turbomachine wheel with at least two contacting portions of the body of the displacement apparatus; and displacing the turbine bucket from a position within a slot of the turbomachine wheel in the first axial direction by linearly actuating the engagement arm with the linear actuator.