Flexure hinges have been used in many engineering areas where high precision and sensitivity are required. Many kinds of flexure profiles were proposed during the past decade. Therefore, a general closed-form solution for flexure hinges of different profiles that incorporates the profile selection and parameter design will be of great benefit to the hinge design. The present work brings circular, right-circular, and elliptical profiles together by proposing a generalized flexure hinge model, which we call elliptical arc flexure hinges (whose maximum eccentric angle phi(m) ranges from 0 to pi/2) to distinguish from the existing elliptical flexure hinge (phi(m)=pi/2). Based on the theories of mechanics of materials, all the elements in the compliance matrix for elliptical arc flexure hinges are deduced by introducing the eccentric angle of ellipse as the integral variable. These compliance equations simply boil down to four integrals, thus simplifying the compliance calculation. These equations also apply to elliptical (phi(m)=pi/2), circular (a=b), and right-circular (phi(m)=pi/2 and a=b) hinges. These compliance equations were checked by comparing them with the results of finite element analysis, the existing equations, and experiment results. The comparison results show that these generalized equations are concise and adequate for most design purposes.

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In this article, an online monitoring technology applied to transmission line towers is proposed to overcome the problems that the foundation deformation is difficult to find in the mining area, river, hillside, and other special areas. The measurement of the stress or the strain caused by the tower foundation deformation are rarely issued, though the tower status can be possibly assessed by the stress or the strain. A new online monitoring technology of tower foundation deformation of transmission lines is developed which consists of three parts. In the first part, the stress or the strain of the key elements is effectively analyzed under the different deformations such as foundation settlement, inclination, and side-slip with the tower finite element model built and the wind load and ice load applied on the tower. In the second part, the experimental platform of tower stress tests is set up, and the internal relations between the stress variation and the tower foundation deformation are determined. In the third part, the online monitoring technology of tower foundation deformation of transmission lines is developed based on fiber Bragg grating stress sensor and successfully applied in Jibei power grid in China. The results show that all the monitored stresses fluctuating with the wind speed are small in case that the condition of tower foundation is normal; on the contrary, the corresponding stresses will change greatly.