# Investigation on the Tip Positioning Accuracy of Cable-Driven Serpentine Manipulators
## 4 Conclusions  
The CDSM was driven by cables, and the tip positioning accuracy of the manipulator decreased due to the flexibility of the cable. This paper focused on the influence factors that affected the tip positioning accuracy, including the cable length error and cable hole location error.  
Firstly, the mappings among the joint angles, the end pose, and the cable lengths were analyzed and a kinematic model was derived in this paper. Next, the error analysis method was illustrated. According to the proposed error analysis method, we respectively studied the influence of the cable length error, cable hole location error, and combined error of them on the tip positioning accuracy by taking a planar CDSM with 3 joints and 6 cables as the experimental model. The results showed that the cable length and cable hole location errors indeed affected the tip positioning accuracy, and especially  
Figure 12: Manipulators in a singular state. (**a**) Initial configuration under a singular state; (**b**) adding \(-\)1 mm cable length error under a singular state.  
at some special points in the workspace, this could cause an approximate 30 mm deviation in position. The effect of the cable hole location error was smaller than that of the cable length error; generally the position deviation caused by the cable length error was 2 to 50 times as large as the cable hole location error. In order to verify the theoretical value obtained through simulation, an experimental prototype was established. Through comparing the simulation and the experimental measurement results, we verified the correctness of the influence trend of the cable length error on the tip position.  
Therefore, the tip positioning accuracy of the end-effector could be improved by increasing cable control accuracy and making the cable hole size close to the cable diameter. For one thing, if the cable hole size was much larger than the cable diameter, it would increase the cable location error in the experiment. Because the center of the hole was considered as the position of cable that passes through the disk in simulation, too large a cable hole would make the cable deviate from the center during the actual experiment. For another, if the cable hole size was very close to the cable diameter, it could be difficult for the cable to pass through the hole. If the cable was stuck too tight, the friction increased and it was difficult for the cable to slide. Results indicate that the tip positioning accuracy was affected greatly by the error in some special points in the workspace of the manipulator. If we can avoid these special points in trajectory planning, the tip positioning accuracy will be significantly improved.  
Conceptualization, H.Y.; methodology, W.Z.; software, C.L.; validation, W.Z.; formal analysis, W.Z.; investigation, H.Y.; resources, H.Y.; data curation, C.L.; writing--original draft preparation, W.Z. and C.L.; writing--review and editing, H.Y.; visualization, C.L.; supervision, H.Y.; project administration, H.Y.; funding acquisition, H.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (Grant No. 61803125), the National Natural Science Foundation of Guangdong Province China (Grant No. 2018A030313247), and the Basic Research Program of Shenzhen (Grant No. JCYJ20190806144416980 and JCYJ20180507183644237).  
The authors declare no conflict of interest.