This paper reports on a linear actuation mechanism in the form of a parallel-crank mechanism (i.e., double-crank mechanism) articulated with two dielectric elastomer actuators working in parallel that are fabricated as a minimum energy structure. This structure is established by stretching a dielectric elastomer (DE) film (VHB4910) over a polyethylene terephthalate (PET) frame so that the energy released from the stretched DE film is stored in the frame as bending energy. The mechanism can output a translational motion under a driving voltage applied between two electrodes of the DE film. We have proposed visco-elastic models for the DE film and the frame of the actuator so that the mechanical properties of the actuator can more accurately be incorporated into the mechanism model. The proposed model accurately predicts the experimental frequency response of the mechanism at different voltages. In addition, an inversion-based feedforward controller was successfully implemented in order to further validate the proposed model for sensorless position control of the actuators and the parallel-crank mechanism articulated with these actuators.