# A Design Method for Multijoint Explosive-Proof Manipulators by Two Motors
## 2 Materials and Methods
### Motion Theory of the Manipulator
#### 2.2.2 Power Switching among Joints  
The SJPM and SJPS of every joint's PSU are organized by belts (shown in Figure 10); the SJC is driven by SJPM and they are shown in detail in Figure 13a (the same as \(SPP_{1}\)-\(SPP_{3}\) in Figure 12). They are driven by the switch motor synchronously and their work areas are evenly distributed on the circumference (shown in Figure 14). In Figure 13, \(SJC_{1}\)-\(SJC_{3}\) rotate around a circle and \(SPF_{1}\)-\(SPF_{3}\) will push the \(SJC_{1}\)-\(SJC_{3}\) only once per circle. Figure 13f is the status of the PSU in Figure 11a.  
Figure 12: (**a**) The status of power pulleys before the \(Joint_{2}\) is driven to rotate. (**b**) The status of power pulleys after the \(Joint_{2}\) is driven to rotate. (**b**) is the phase difference of the \(P_{3}\) after the \(Joint_{2}\) is rotated \(\delta_{1}\) relative to (**a**). \(r_{1}\)–\(r_{3}\) are the radii of the \(SPP_{1}\)–\(SPP_{3}\). \(P_{1}\)–\(P_{3}\) are the mark points of \(SPP_{1}\)–\(SPP_{3}\). The (**a**)–2 and (**b**)–2 is the phase relationship of \(P_{1}\)–\(P_{3}\).  
Figure 13: The phase relations of work areas of 3 cams which are driven to rotate clockwise by the switch motor. \(PA_{1}\)–\(PA_{3}\) are cam work areas of \(SJC_{1}\)–\(SJC_{3}\). \(F_{1}\)–\(F_{2}\) are the contact points between the SJC and SJF of \(Joint_{1}\)–\(Joint_{3}\). The right sub-sub-figure of every sub-figure is the current phase of cams’ work areas. (**a**) The initial status of \(SJC_{1}\)–\(SJC_{3}\). (**b**) \(SJC_{1}\)–\(SJC_{3}\) rotate 30 deg synchronously relative to (**a**). (**c**) \(SJC_{1}\)–\(SJC_{3}\) rotate 30 deg  
If the \(Joint_{2}\) is driven, the difference will also occur between the SJC and SJF without any measures. Figure 15 shows the influence of the differences (\(\delta_{3}\)) in the phase of \(SJC_{3}\) when the \(Joint_{2}\) is driven to rotate for \(\delta_{1}\). The phase relationship among the cams of PSUs is changed, and leads to the manipulator driving two joints (\(Joint_{1}\) and \(Joint_{3}\)) at the same time (shown in Figure 15). It will result in the manipulator being out of control.  
Therefore, a pair of clutches (Part 3 and Part 4 in Figure 1) are adopted to separate the rotation between SJPM and SJPS when the \(Joint_{2}\) is driven (shown in Figure 16). If the \(Joint_{2}\) is in switched on status (Figure 11a), its SJPS will be driven to rotate by the \(Arm_{2}\) and the phase difference will occur between SJPM and SJPS. When the \(Joint_{2}\) finishes rotating, the phase of every SJC is unchanged because the SJPM separates from SJPS. Finally, the phase difference occurred only on the two clutches; the initial phase among \(SPC_{1}\)-\(SPC_{3}\) and \(SJC_{1}\)-\(SJC_{3}\) is maintained. So, the other two joints are not influenced by the motion of the current joint. If the manipulator continues switching power among joints, then the switch motor will rotate the SJPM to return along the original road and SJPS will be together with SJPM as before (the separating motion has been presented in Section 2.1.2). As a result, the phases of all the cams in every joint's PSU can maintain their initial relations in this way (compare Figure 16a-(2) with Figure 16b-(2)).  
Figure 15: The phase difference for the \(SJC_{3}\) after the \(Joint_{2}\) is rotated \(\delta_{1}\). (**a**) The iniational status of three joints. (**b**) The work areas of the \(Joint_{1}\) and \(Joint_{3}\) will be driven at the same time. The work areas of the \(Joint_{1}\) and \(Joint_{3}\) overlap. If the switch motor driving the cams makes the \(PA_{1}\) contact the \(F_{1}\), then \(PA_{3}\) may contact the \(F_{3}\) at the same time. So the \(Joint_{1}\) and \(Joint_{3}\) will be driven at the same time.