Dielectric elastomers (DEs) consist of highly compliant electrostatic transducers which can be operated as actuators, by converting an applied high voltage into motion, and as sensors, since capacitive changes can be related to displacement information. Due to large achievable deformation (on the order of 100%) and high flexibility, DEs appear as highly suitable for the design of soft robotic systems. An important requirement for robotic systems is the possibility of generating a multi degree-of-freedom (MDOF) actuation. By means of DE technology, a controllable motion along several directions can be made possible by combining different membrane actuators in protagonist-antagonist configurations, as well as by designing electrode patterns which allow independent activation of different sections of a single membrane. However, despite several concepts of DE soft robots have been presented in the recent literature, up to date there is still a lack of systematic studies targeted at optimizing the design of the system. To properly understand how different parameters influence the complex motion of DE soft robots, this paper presents an experimental study on how geometry scaling affects the performance of a specific MDOF actuator configuration. The system under investigation consists of two cone DE membranes rigidly connected along the outer diameter, and pre-compressed out-of-plane against each other via a rigid spacer. The electrodes of both membranes are partitioned in four sections that can be activated separately, thus allowing the desired MDOF actuation feature. Different prototypes are assembled and tested to study the influence of the inner radius as well as the length of the rigid spacer on the achievable motion range. For the first experimental study presented here, we focus our analysis on a single actuation variable, i.e., the rotation of the rigid spacer about a fixed axis. A physics-based model is then developed and validated based on the collected experimental measurements. A model-based investigation is subsequently performed, with the aim of studying the influence of the regarded parameters on the rotation angle. Finally, based on the results of the performed study, a model-based optimization of the prototype geometry is performed.