Thin foldable origami mechanisms allow reconfiguration of normally complex structures with a large volumetric change, low cost and versatility; however, there is rarely a systematic way to make them autonomously actuated due to the lack of low-profile actuators. The required actuation contradicts engineering design parameters between actuation range, actuation speed and back-drivability. This paper presents a novel approach to a fast and controllable folding by embedding the actuation system in a nominally flat platform. The design, fabrication and modelling of an electromagnetic actuation system are reported; a 1.7 mm thick single degree-of-freedom (DoF) foldable parallel structure reaching an elevation of 13 mm has been used as a proof-of-concept for the proposed methodology. We also report on the extensive test results that validate the mechanical model in terms of the loaded and unloaded speed, the blocked force, and the range of actuation.