Research Article Prediction of Fatigue Life for a New 2-DOF Compliant Mechanism by Clustering-Based ANFIS Approach NgocThoaiTran, 1 Thanh-PhongDao , 2,3 ThaoNguyen-Trang , 4,5 andChe-NgocHa 5 1 Faculty of Mechanical Engineering, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam 2 Division of Computational Mechatronics, Institute for Computational Science, Ton Duc ang University, Ho Chi Minh City, Vietnam 3 Faculty of Electrical & Electronics Engineering, Ton Duc ang University, Ho Chi Minh City, Vietnam 4 Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc ang University, Ho Chi Minh City, Vietnam 5 Faculty of Mathematics and Statistics, Ton Duc ang University, Ho Chi Minh City, Vietnam Correspondence should be addressed to Che-Ngoc Ha; chengocha@tdtu.edu.vn Received 1 November 2020; Revised 27 January 2021; Accepted 23 February 2021; Published 2 March 2021 Academic Editor: Mingwei Lin Copyright © 2021 Ngoc oai Tran et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Two-degree-of-freedom (2-DOF) compliant mechanism has some outstanding characteristics in accurate positioning systems. Studying the fatigue life for the 2-DOF compliant mechanism is a meaningful task to ensure a long working. However, a study for fatigue life prediction of this mechanism has not been conducted so far. In this article, a method for fatigue life prediction of 2- DOF compliant mechanism is developed for the first time. is method is the combining of the differential evolution algorithm and the adaptive neuro-fuzzy inference system (ANFIS) with subtractive clustering. e numerical results on two case studies consisting of material steel A-36 and the material AL 6061-T6 show that the accuracy of the proposed method is very high. Compared to the actual fatigue life, the root mean square error of the proposed method lies in the range [1.7, 3.97] cycles for Case 1 and [2.03, 10.38] cycles for Case 2. e statistical test also indicates that the proposed method outperforms the traditional method using triangular membership function, bell-shape, and Gaussian membership function, with the significance level from 0.05 to 0.1. ese results demonstrate the feasibility of the proposed approach in fatigue life prediction of 2-DOF compliant mechanism. 1.Introduction Two-degree-of-freedom (2-DOF) compliant mechanism is a monolithic structure that has been widely utilized in ultra- high precise engineering. Basically, the 2-DOF compliant mechanism inherits outstanding characteristics such as minimal positioning error, free friction, reduced assemble, and easy machining [1]. Several applications of this mech- anism can be found in the nanopositioning system [2], micropositioning system [3–9], space pointing mechanism [10], and so on. Although the 2-DOF compliant mechanism proposes excellent advantages in precision engineering and manipulators, this mechanism still exists major drawbacks, including nonlinear kinematic behaviors and fatigue influences. Considering the first disadvantage, nonlinear kinematic behaviors can be modeled and analyzed by pseudorigid-body model [11], compliance matrix method [12], and pseudostatic model [13]. Regarding the second disadvantage, fatigue influences on the 2-DOF compliant mechanism can result in a failure under dynamic working conditions. In similarity to rigid-link mechanisms, fatigue life of the 2-DOF complaint mechanism is a term indicating how long an object will last before it fails due to concentrated stresses. Evaluation of the fatigue life is a critically important task in design process of compliant mechanisms so as to guarantee the working safety and reliability. Practically, compliant mechanisms are often subjected to cyclic and reversed loads. Hindawi Mathematical Problems in Engineering Volume 2021, Article ID 6672811, 14 pages https://doi.org/10.1155/2021/6672811