Nowadays, the development or improvement of soft actuation mechanisms is a crucial topic for the achievement of dexterous manipulation using. Then, a primary target of research is the design of actuation and driving devices. Consequently, in this paper, we introduce a soft driving epicyclical mechanism that mimics human muscle behavior and fulfills motion requirements to achieve grasping gestures using a robotic finger. The prototype is experimentally assessed, and results show that our approach has enough performance for the implementation in grasping tasks. Furthermore, we introduce the basis for a new soft epicyclical mechanism merger with shape memory alloys to allow active stiffness control of the mechanism.