# A Design Method for Multijoint Explosive-Proof Manipulators by Two Motors
## 2 Materials and Methods
### Power Switch Unit
#### 2.1.3 Cams Design Method
\begin{cases}s_{1}=h_{1}(\frac{\theta}{\theta_{1}}-\frac{1}{\pi}\sin(\pi \frac{\theta}{\theta_{1}})),&\theta\in(0,\theta_{1})\\ s_{2}=h_{1}+(h-h_{1}-h_{2})\frac{\theta-\theta_{1}}{\theta_{2}-\theta_{1}},& \theta\in(\theta_{1},\theta_{2})\\ s_{3}=h-h_{2}(\frac{\theta_{3}-\theta}{\theta_{3}-\theta_{2}}-\frac{1}{\pi} \sin(\pi\frac{\theta_{3}-\theta}{\theta_{3}-\theta_{2}})),&\theta\in(\theta_{ 2},\theta_{3})\\ s_{4}=h,&\theta\in(\theta_{3},\theta_{4})\\ s_{5}=h-h_{2}(\frac{\theta-\theta_{4}}{\theta_{5}-\theta_{4}}-\frac{1}{\pi} \sin(\pi\frac{\theta-\theta_{4}}{\theta_{5}-\theta_{4}})),&\theta\in(\theta_{ 4},\theta_{5})\\ s_{6}=h-h_{2}-(h-h_{1}-h_{2})\frac{\theta-\theta_{5}}{\theta_{6}-\theta_{5}},& \theta\in(\theta_{5},\theta_{6})\\ s_{7}=h_{1}(\frac{\theta_{7}-\theta}{\theta_{7}-\theta_{6}}-\frac{1}{\pi} \sin(\pi\frac{\theta_{7}-\theta}{\theta_{7}-\theta_{6}})),&\theta\in(\theta_{ 6},\theta_{7})\\ s_{8}=0,&\theta\in(\theta_{7},\pi)\end{cases}  \tag{1}\]  
Equation (2) and Figure 7 give the velocity of the SPF and SJC when they are pushed from 0 mm to 3 mm by SPC and SJF. In the equation, \(v\) represents the linear velocity of the SPC and SJF along their axis directions. \(v_{1}\)-\(v_{9}\) represent the linear velocity of the SPC and SJF in the eight segments along their axis directions. \(r\) represents the working radius of the cam. \(\omega\) represents the angular velocity of the cam. \[v=\begin{cases}v_{1}=h_{1}\tau\omega\frac{1}{\theta_{1}}(1-\cos(\pi\frac{ \theta}{\theta_{1}})),&\theta\in(0,\theta_{1})\\ v_{2}=\frac{1}{\theta_{2}-\theta_{1}}r\omega(h-h_{1}-h_{2}),&\theta\in(\theta_{ 1},\theta_{2})\\ v_{3}=h_{2}\frac{r\omega}{\theta_{3}-\theta_{2}}(1+\cos(\pi\frac{\theta_{3}- \theta}{\theta_{3}-\theta_{2}})),&\theta\in(\theta_{2},\theta_{3})\\ v_{4}=0,&\theta\in(\theta_{3},\theta_{4})\\ v_{5}=-h_{2}\frac{r\omega}{\theta_{5}-\theta_{4}}(1+\cos(\pi\frac{\theta_{5}- \theta}{\theta_{5}-\theta_{4}})),&\theta\in(\theta_{4},\theta_{5})\\ v_{6}=-\frac{1\[a= \begin{cases}a_{1}=h_{1}\tau\omega^{2}\frac{\pi}{(\theta_{1})^{2}}\sin(\pi(\frac{ \theta}{\theta_{1}}))),&\theta\in(0,\theta_{1})\\ a_{2}=0,&\theta\in(\theta_{1},\theta_{2})\\ a_{3}=\frac{h_{2}\tau\omega^{2}}{(\theta_{3}-\theta_{2})^{2}},&\theta\in( \theta_{2},\theta_{3})\\ a_{4}=0,&\theta\in(\theta_{3},\theta_{4})\\ a_{5}=-\frac{h_{2}\tau\omega^{2}}{(\theta_{5}-\theta_{4})^{2}},&\theta\in( \theta_{4},\theta_{5})\\ a_{6}=0,&\theta\in(\theta_{5},\theta_{6})\\ a_{7}=-h_{1}\tau\omega^{2}\frac{\pi}{(\theta_{7}-\theta_{6})^{2}}\sin(\pi( \frac{\theta-\theta_{6}}{\theta_{7}-\theta_{6}}))0,&\theta\in(\theta_{6}, \theta_{7})\\ a_{8}=0,&\theta\in(\theta_{7},\pi)\end{cases}  \tag{3}\]  
The \(s_{1}\)-\(s_{3}\)s segments are the motion region, \(s_{1}\) and \(s_{3}\) are the sine law curve, the return region is designed to be the same as the motion region. In Figure 8, the accelerations of SPF and SJC are consistent and smooth without a discontinuity point. This will make the SJPM (Part 6) rotate smoothly without impact when the velocities of SPF and SJC are changed. Equation (4) and Figure 9 give the pressure angle of the cam mechanism. In the equation, \(\alpha\) represents the pressure angle between the cam and its follower. \(\alpha_{1}\)-\(\alpha_{9}\) represent the pressure angle between the cam and its follower in the eight segments. \[\alpha