The unique motion styles of flagella and cilia (i.e., planar/helical waveform propulsion of flagella and twodimensional (2D)/three-dimensional (3D) asymmetric ciliary beating), play a key role in many biological activities and inspire lots of bionic designs, especially miniature robotic systems. However, quite different to the fact in nature that microorganisms can evolve diverse motions from the homologous bio-structure (9 + 2 axoneme structure), current bionics can still not find an effective engineering solution to achieve such wisdom. Herein, by investigating the inner structure of flagella/cilia and their intrinsic driven mechanisms, we derive a unified physical model to describe the microtubules' bending and the constructed external motions. Then, we propose a three-channel based tubular actuation concept and correspondingly fabricate an actuator via a rod-embedded casting process. By sequencing the actuation of each channel, our design can not only reproduce the diverse 2D/3D flagellar/ciliary motility in nature, but also extrapolate a variety of symmetry-breaking ciliary beating modes for effective propulsion at low Reynolds number. This study deepens our understanding of the propulsion mechanism of microorganisms and provides new inspirations for the design of biomimetic systems, which may find significant applications in a wide spectrum of engineering fields.