# Stress Dispersion Design in Continuum Compliant Structure toward Multi-DOF Endoluminal Forceps
## 1 Introduction  
Advances in endoscopic equipment have enabled early diagnosis and minimally invasive resection of esophageal, gastric, and colorectal cancers. In particular, endoscopic submucosal dissection (ESD) is an advanced method that allows setting an arbitrary excision range. Moreover, ESD enables the accurate excising of larger lesions than other procedures [1, 2]. However, ESD is a time-consuming and challenging procedure. The risk of bleeding or perforation with a slight operation error is present. Specifically, in cases where the submuc is not completely visible, the submucosal dissection is challenging. A good field of view with counter traction can facilitate and save the ESD procedure [3, 4]. In this regard, articulated forceps are effective in obtaining adequate traction. Previous studies have developed multi-DOF endoluminal forceps with articulated joint structures [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]. For instance, Anubiscope [5], STRAS [6], EndoMaster [7], and K-FLEX [8] have improved workability. Their effectiveness has been demonstrated by performing ESD procedures using a porcine stomach and colon and comparing specimensize and dissection speed. Similarly, \(i^{2}\)_Snake_[9], EndoSamurai [10], ViaCath [11], and Flex robotic system [12] are endoscopic surgical systems for natural orifice transluminal endoscopic surgery (NOTES) or other endoscopic surgery. These devices [5; 6; 7; 8; 9; 10; 11; 12] are equipped with articulating segments. However, their diameters are not sufficiently small to be inserted into the 2.8 mm channel of commercially available prevailing standard flexible endoscopes. Other articulated devices [13; 14; 15; 16; 17; 18; 19] are within 2.6 mm in diameter. Thus, these devices might be used with standard flexible endoscopes even though each mechanism has its own limitations. [PERSON] et al. 's [13] and [PERSON] et al. 's [14] devices have only one-DOF of bending. [PERSON] et al. 's [15] device has a problem that the bending radius becomes large because it is bent by rotating a multi-layered concentric tube. [PERSON] et al. 's [16; 17; 18] and [PERSON] et al. 's [19] mechanisms contain several micro-parts, which increases their cost. Considering size and cost, a mechanism with the simplest possible structure is desirable. Therefore, we designed a multi-DOF monolithic-structured forceps within 2.6 mm in diameter. The designed forceps have a compact configuration composed of a grasping segment, bending segment, and tendon-sheath driving segment. The grasping and bending segments have a monolithic structure relying on a compliant mechanism [20], which is a flexible mechanism achieving force and motion transmission through elastic body deformation. The compliant mechanism has the advantages of being integrally molded with a smaller size, lighter weight, and simpler structure than conventional mechanisms. However, when a compliant joint bends, the stress generally concentrates at the end of the base, placing heavy loads on the first few joints, leading to fatigue failure. This limits the range of motion of the mechanism and is a typical inconvenience of continuum robots using similar compliant joints [21; 22; 23]. In this regard, some studies have used FEA to improve the design of the joint structures [24; 25; 26; 27]. For instance, [PERSON] et al. [24] and [PERSON] et al. [25] evaluated the design optimization by changing the thickness of the hinge using FEA. [PERSON] et al. [26] studied the structural behavior of the snake-like mechanism depending on the dimensions of individual joints and sought to achieve a particular curvature. Furthermore, the thickness of the hinge varies along the structure. [PERSON] et al. [27] presented the design optimizations by changing the thickness of the hinge for each segment using FEA to adjust a uniform stress distribution. The design optimization approach was validated using a 1-DOF compliant joint with three segments of elastic hinges.