Most of the engineering problems can be easily solved by using biomimetic designs. Biomimetic is the process of imitating live animals to create new designs. For example, by mimicking the movements of a fish or snake, it is possible to transfer the desired swimming or crawling movements to a robot. This research is based on an amphibious robot where the propulsion system is imitated by a cuttlefish. In this study, to obtain the required sine wave motion for the cuttlefish's fin, crank-rocker mechanisms are used. Additionally, a circular slot mechanism was used to move these crank-rocker mechanism up and down as in the cuttlefish fins. Since the cuttlefish has two symmetrical wings, these crank-rocker and circular slot mechanisms are repeated symmetrically on both sides. Two separate servo motors (one on the right and one on the left) were used to control the angular position of the crankshafts in circular slots. These servo motors allow the fins to move up and down while the robot is in the water. They also serve to hold the wings at a fixed angle in terrestrial mode. In similar applied robotic researches, dozens of servo motors are used to obtain the required sine motion. This study proposes a propulsion system that can be operate with simple crank-rocker and circular slot mechanisms, instead of using too many servo motors that are expensive and constitutes control complexity. In this study, a design methodology is proposed for this new propulsion system. Various conditions have been considered in the design procedure. In the design criteria section, the required force and velocity, the capacity to overcome obstacles and the motion requirements has been considered for an amphibious robot. Furthermore, the requirements of a continuous movement for oscillating motion have been also considered. As a result of this study, minimum crank number and crank angles were obtained for the undulating motion. It has been also considered the necessary continuous balance condition, in order to make motion on land without tumbling. The calculation of the part lengths that meets the design criteria is described in the mechanism synthesis section.