Unidirectional rotation of the gear in the bath of non-interacting ABPs. (A) Time sequence of $\omega$ ($F_{\text{a}}=8$, $D_{\text{r}}=0.001$ and $\varphi =0.15$). (B) Time sequences of accumulative angles $∆\theta$ for $F_{\text{a}}=$4, 6, 8, 10, 12, from bottom to top ($D_{\text{r}}=0.001$ and $\varphi =0.15$). (C) Averaged angular speed as a function of propelling strength $F_{\text{a}}$. Colored symbols are simulation data and lines are fittings by Eq. (4). Colors represent $\varphi =0.10$ (black), $\varphi =0.15$ (red), and $\varphi =0.20$ (blue); symbols represent $D_{\text{r}}=0.001$ (squares), $D_{\text{r}}=0.003$ (circles), and $D_{\text{r}}=0.005$ (triangles). (D) Long-time averaged flow field of non-interacting ABPs in the gear frame of reference corresponding to the situation in (A).