Electrostatic soft actuators are widely employed in soft machines due to their fast response, low energy consumption and noise, high energy density, and ease of control. This paper presents an electrostatic flexi-limbed actuation building block based on the dielectrophoretic liquid zipping concept. We establish a model to describe its performance using the theory of large deformation of beams and the energy analysis method. The effectiveness and accuracy of the proposed mathematical model were validated through experiments. Using this model, we investigated the influence of various design parameters on the actuator's static actuation performance. Additionally, we experimentally analyzed the actuator's output force under static voltage and its dynamic behavior under alternating excitation. Furthermore, we evaluated the actuator's locomotion performance in a soft inchworm-like robot by integrating it with a unidirectional wheel assembly. This research provides exploratory experience and new ideas for the design and application of further electro-ribbon actuators.