# Optimization Method of the Clamping Force for Large Cabin Parts
## 1 Introduction
In the underactuated mechanism, the number of actuated elements is less than its DOFs and contains underactuated elements such as linear springs and torsional springs. The underactuated mechanism can be applied to the structural design of robotic hands. Underactuated robotic hands can adapt to the different shapes of objects and finally achieve the envelope clamping of the objects. If the underactuated mechanism in the robotic hands is reasonably designed, the robotic hands will have the feature of shape-adaptive envelope clamping, which can realize powerful envelope clamping of various objects of different shapes and sizes. Many scholars have studied the related features of underactuated mechanisms. [PERSON] et al. [1] proposed that the main grasp configuration of an underactuated finger mechanism could perform self-adaptive enveloping according to the object's shape, and they designed a linkage underactuated robotic finger mechanism in [2]. The mechanism can perform a compliant grasp for different objects' shapes and easily achieve a powerful envelope grasp. It is also very suitable for low-cost easy-operation grasper or robotic hand applications. [PERSON] et al. [3] proposed an underactuated hand with a spring as the design parameter. The spring's softness and rigidity directly affect the underactuated hand's adaptability to grasp objects with irregular shapes. [PERSON] et al. [4] introduced linear springs and torsion springs into the finger mechanism, giving the robotic hands the shape-adaptive ability to the grasped object. [PERSON] et al. proposed different configuration schemes of the joint and spring in the finger mechanism that provided a theoretical reference for the design of the underactuated mechanism and flexible mechanism. [PERSON] et al. [5] pointed out that the number of DOFs was more than that of the actuated elements in the underactuated clamping fixture. Its main clamping configuration is multi-finger envelope clamping and the clamping process of the underactuated clamping fixture is easy to control and operate. [PERSON] et al. [6,7] designed an underactuated finger based on static grasp balance criteria and optimized its connecting rod sizes and spring parameters. [PERSON] et al. [8, 9, 10] developed a low-cost underactuated robotic hand with a simple structure and moderate dexterity, which could adapt to complex grasped objects. The ring pneumatic fixture clamping a workpiece is similar to the robotic hands grasping an object. In the clamping process, especially in the clamping process of a large cabin part, the improper adjustment of the clamping force will cause serious consequences. If the clamping force is too large, it will not only lead to the deformation and damage of the  
Figure 2: The actual application scenario of the ring pneumatic fixture. workpiece surface but also cause damage to and energy waste of the clamping mechanism, which finally affects the processing accuracy. If the clamping force is too small, it will lead to the deviation of the clamping mechanism and scraping of the workpiece, which will cause a serious accident. Therefore, in order to realize the stable clamping to the workpiece of each clamping mechanism, it is necessary to study the clamping force of the clamping mechanism. The essential requirement is to achieve the clamping force exerted by the clamping mechanism onto the workpiece balanced to the external force of the workpiece, and the friction force of each clamping mechanism needs to meet the constraints of the friction cone under a given clamping configuration. The minimum clamping force that satisfies these above conditions is the optimization problem of the clamping force. It can be seen from these conditions that the clamping force optimization problem of the clamping mechanism is similar to the grasping force optimization problem of the robotic hand. They both need to deal with the nonlinear constraints brought by the friction force and select an appropriate optimization method. It can provide a certain reference for the optimization of the clamping force.