BCF locomotion is typically described as a wave motion with an increasing amplitude. According to travelling waves of BCF locomotion, a combinatory design of 4 bar linkage is proposed. In this study, 6 conditions are established through the following three aspects: links oscillation (condition 1 and 2), points motion (condition 3 and 4), and body undulation (condition 5 and 6). By calculating equations contained within six conditions, a design of the 1-DOF planar linkage for undulatory deformation is available. For example, 20 bar linkage of 10-joint robotic fish (anguilliform), 16 bar linkage of 8-joint robotic fish (sub-carangiform), 14 bar linkage of 7-joint robotic fish (carangiform), and 10 bar linkage of 5-joint robotic fish (thunniform) are designed with existing biological data. The proposed design is verified by a virtual prototype of the thunniform mechanism. The results demonstrate that the prototype generates travelling waves with high precision.
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