# Equivalent Dynamic Analysis of a Cable-Driven Snake Arm Maintainer
## 1 Introduction  
A cable-driven snake arm maintainer (SAM) drive unit is generally placed outside of a robot's working space. This placement reduces the number of electronic devices on the entire snake arm, which is highly conducive to remote maintenance tasks in complex and narrow environments, such as nuclear power plants [1, 2, 3]. The China Fusion Engineering Test Reactor (CFETR) is large-scale, international scientific project adopting a remote handing system (RH) for regular monitoring and maintenance [4]. As shown in Figure 1, the SAM is installed at the end of the CFETR multipurpose overload robot (CMOR) and is transported to the inside of the vacuum chamber via a CASK transfer vehicle for reactor maintenance, flaw detection, and dust removal, as well as general monitoring and observation [5]. The SAM has a large enough dexterous operating space and is sufficiently adaptable in a high-radiation environment. It can remove a large amount of dust left by high-temperature plasma bombardment at the base of the divertor during operation of the test reactor. It can also obtain high-quality plasma and improve the operational stability of the test reactor. Traditional industrial robots cannot meet the requirements of narrow, multiobstacle, and high-radiation operations in a vacuum chamber environment. The SAM has a high slenderness ratio, and its redundant degrees of freedom allow for complete streamlining of motion, with strong environmental adaptability and obstacle avoidance ability. Therefore, the application potential for monitoring and maintenance of large, complex equipment in narrow spaces is extensive [6, 7]. There are two main types ofSAM: underactuated (continuum) and rigid hyper-redundant arms. The majority of SAMs are formed in series using several basic joint units (flexible rods, springs, universal joints, etc.) [8; 9; 10]. OC Robotics initially defined a rigid hyper-redundant SAM and designed the snake arm using the principle of bionics before applying it to extreme environments, such as nuclear power plants [11]. [PERSON] et al. [12] introduced a continuous SAM integrated with multilayer flexible plane springs that can realize precise linear movement. The authors of [13; 14] designed a coupled SAM control scheme combining interactive obstacle control and path-following algorithms. The authors of [15; 16] used the exponential integration method to solve the inverse kinematics of a hyper-redundant SAM. SAM has the characteristics of a series-parallel structure, and it is difficult to analyze the dynamics of its motion process. The dynamic equations established by the traditional Newton-Euler method, the Lagrangian method, the Gaussian method, etc., cannot clearly describe the relationship between the motion of each joint of a SAM and the force of the cable [17; 18]. In addition, the motors, cables, joints, and end effectors of SAM involve complex mapping relationships, all of which have a coupling effect on the cable traction forces. As a result, the dynamic modelling of SAM and the solution of cable traction force in the movement process become increasingly complicated. Currently, there are two main methods for modelling the dynamics of a continuum SAM: the piecewise constant curvature method and the variable curvature method [19; 20; 21]. The former involves solving the dynamic equation of the entire arm by assuming that the deformation angle between each adjacent continuum is approximately equal (constant curvature) [22]. The latter involves performing dynamic modelling compensation of SAM using various compensation algorithms under the influence of gravity and load to improve the calculation accuracy [23]. Whereas the dynamic equation of a hyper-redundant SAM is similar to that of a rigid link robot, the configuration of the hyper-redundant series-parallel connection and the coupling effect of the drive cable increase the complexity of dynamic modelling [24; 25].