# Structural Optimization Method of a FinRay Finger for the Best Wrapping of Object
## 1 Introduction  
Adaptive gripping is one of the main areas of soft robotics applications [1]. Soft gripping, in which the gripper adapts to differently shaped objects, is in great demand in unknown or dynamically changing environments [2]. Their properties enable the gripping and manipulation of objects of various shapes, while their softness and flexibility allow them to manipulate even fragile objects. As a result, they find their application not only in industrial robotics, such as the automotive industry [3], but especially in service robotics, where they can be used, for example, in the food industry to collect fragile crops whose shapes and sizes vary [1, 4], or in the home environment for handling objects of various shapes (such as keys, pens, mugs, etc.) [5, 6].  
There are several possible principles for solving such grippers. For example, pneumatic 3D printed soft grippers that change shape according to internal pressure [7], vacuum soft grippers [8], soft and shape adaptive electroadhesive grippers [9, 10], shape adaptive and reversible magnetorheological elastomer-based grippers [11], and electrically controlled soft 3D printed hand shearing auxetics grippers [12].  
This work is focused on gripers with passively adaptive structures using the Fin Ray effect [4]. This effect is based on the biomechanical principles of fish fins [13]. After pressing the object on the FinRay finger, the finger flexibly wraps around it [1]. This effect is used not only for gripping objects [14; 15] but can also be used, for example, for locomotion of a robot in water [16]. Due to their shape and necessary mechanical properties, 3D printing from flexible materials is mainly used for their production [4]. Since 2016, company Festo has been offering three differently sized types of these fingers [17]. Several studies have already been conducted on Fin Ray structures. Some of them dealt with the dependence of the gripping force on the deformation of the finger when changing the internal geometry and filling [4; 13; 18], or deal with mathematical models [1] or simulation [1; 19]. Some works evaluate the suitability of given fingers only for deformation at the point of contact according to the load [4; 13]. Other work [15] evaluate the suitability only for the maximum deformation at the endpoint of the finger. However, the measurement at a single point is insufficient to describe the wrapping of the finger around the object. So far, however, no specific way has been determined to evaluate the proposed finger regarding its ability to wrap around the object.  
This work comes up with a new and simple way to mathematically evaluate the finger's wrapping around the object by measuring two dimensions. This work aim is not to find the overall most optimal finger structure that can exist but to describe a new method by which it will be possible to easily compare variants of different structures and find the optimal one between them. Several internal structures were created for testing, in which their specific parameters were changing. Basic testing takes place in a simulation program for creating nonlinear analyzes. Based on the simulations results and the evaluation method, the most suitable finger structures were printed by the Fused Filament Fabrication method, and their mechanical properties verified on a real test device. The results of this work are intended to make it easier for designers to assess their designed fingers from the point of view of wrapping their finger around the object. They also can use graphs from the results of this work and determine the finger's dimensions without the inner filling according to the required force and deflection.