# Performance Analysis of Hybrid Kinematic Mechanism for Fusion Reactor Maintenance
## 4 HKM Error Analysis  
Since oil is not allowed in the high-temperature clean environment of the vacuum vessel, hydraulic drive and grease lubrication cannot be used. Therefore, each cylinder in the HKM parallel mechanism is driven by electrical power instead of a hydraulic system, as shown in Figure 8. The lubrication between each joint adopts dry friction lubrication.  
Figure 6: Lifting left outboard BB joint inverse kinematic solution (**a**); displacement inverse kinematic solution (**b**).  
Figure 7: Lifting left inboard BB joint inverse kinematic solution (**a**); displacement inverse kinematic solution (**b**).  
However, the weight of the BB is over 80 tons, thus, during the transportation of the BB, dry friction lubrication will cause a high torque on the spherical joint at one end of the piston, and it will be transferred to the cylinder in reverse. If the rotation between the piston rod and the cylinder is limited, the piston rod may suffer fatigue damage, so it must be allowed to rotate. From the abovementioned limitations, the HKM parallel mechanism spherical joints should be changed to universal joints during the BB lifting remote maintenance, where the rotation requirements of piston will be satisfied by the rotation between the piston and the cylinder, as shown in Figure 8b. The piston is driven by a ball screw, which will produce position error when the piston rotates relative to the cylinder.  
In order to calculate the HKM end-effector position error caused by the piston rotation, an HKM simulation model was built in Adams software. Based on the inverse kinematic solution of the HKM lifting left inboard and outboard BBs obtained in Section 3, the piston rotation angle can be calculated by simulation in Adams, as shown in Figure 9. The results show that the piston rotates during the lifting of both the inboard and outboard BBs. During the lifting of the left outboard BB, piston 3 produces the maximum rotation angle \(\Delta\theta_{3}=0.13\ rad\) at the time of 40 s. During lifting of the left inboard BB, piston 3 produces the maximum rotation angle \(\Delta\theta_{3}=0.19\ rad\) at the time of 55 s. With the HKM of each piston's thread at a pitch of \(p=15\) mm, combined with the angular error \(\Delta\theta_{i}\), the stroke error of each piston can be obtained:  
\[\Delta l_{i}=\frac{\Delta\theta_{i}}{2\pi}p. \tag{31}\]  
Figure 8: HKM prototype (**a**); piston thread drive mechanism (**b**).  
Figure 9: Rotation angle of HKM spherical joint around the link during the left outboard (**a**) and inboard (**b**) BB lifting.  
By adding the obtained \(\Delta l_{i}\) for each piston stroke error to the HKM inverse kinematic solution, the simulated position error of the HKM end-effector is obtained and is shown in Figure 10. The end-effector position error distribution is similar to the piston rotation angle error distribution. During the lifting of the left outboard BB, the end-effector produces a maximum absolute error \(\Delta P=1.5\) mm at the moment of 40 s, and during the lifting of the left inboard BB, the end-effector produces a maximum absolute error \(\Delta P=3.1\) mm at the moment of 55 s. Since the BB height is more than 10 m and the gap between adjacent BBs is only 20 mm, the large position error of the HKM on the \(x\) and \(y\) axes may hit the adjacent BBs to affect the stable motion of the HKM. In addition, the end position error is also influenced by the overall control error, rigid-flexible coupling deformation error, machining error, assembly error, creep error caused by wear, etc., which further causes the risk of collision. Therefore, it is necessary to compensate the end position error of the HKM to improve the operation accuracy.