# Periodic motion mechanism
## Periodic motion gear
* Time : $t$
* Teeth : $T$

$$t_A\frac{T_B}{T_A} = t_B$$
## Geneva drive
<div style="text-align: center;">
<img src="https://static.sdcpublications.com/multimedia/978-1-58503-767-4/files/krb/geneva%20wheel.JPG" alt="image"width="200">
</div>

>https://static.sdcpublications.com/multimedia/978-1-58503-767-4/files/krb/krb_gen_page3.htm
* Number of separators : $N > 4$
### Transmission angle
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<img src="https://hackmd.io/_uploads/H1IVLSoPll.png" alt="image"width="350">
</div>

* transmission angle : $\theta_\text{on}$
* Non-transmission angle : $\theta_\text{off}$
$$\frac{2\pi}{2N} = \theta$$

$$\theta_\text{on} = 2(\frac\pi2-\theta) = \pi-\frac{2\pi}N = \pi(1-\frac2N)$$

$$\theta_\text{off} = 2\pi-\pi(1-\frac2N)$$

$$= \pi(2-(1-\frac2N)) =\pi(1+\frac2N)$$
### Transmission time
* transmission time : $t_\text{on}$
* Non-transmission time : $t_\text{off}$
$$t_\text{on} : \theta_\text{off} = \pi(1-\frac2N) : \pi(1+\frac2N)$$

$$\omega = \frac t{2\pi}$$

$$t_\text{on} = \frac t{2\pi}(\pi(1-\frac2N)) = \frac t2-\frac tN$$

$$t_\text{off} = \frac t{2\pi}(\pi(1+\frac2N)) = \frac t2+\frac tN$$