Flexibility calculation and performance analysis of a new single-sided straight-circle-ellipse hybri1

Abstract:

Flexible hinges play a crucial role in the field of micro-electromechanical systems (MEMS). This paper introduces a new type of flexible hinge called the single-sided straight-circle-ellipse hybrid flexible hinge. The flexibility of this hinge is calculated using Karl's second theorem, and the results are validated through finite element analysis. The structural parameters of the hinge are analyzed to determine their influence on its flexibility. A comparison is also made between the single-sided and double-sided straight-circle-ellipse hybrid flexible hinges, and it is concluded that the single-sided hinge offers better rotation capacity and load sensitivity. Overall, the single-sided hybrid flexible hinge provides a promising solution for compact and highly displacement applications in engineering.

In the rapidly evolving fields of micro-electromechanical technology, aerospace, and biological engineering, traditional rigid mechanisms are no longer sufficient to meet the design and usage requirements. Flexible mechanisms, with their small size, absence of mechanical friction and gaps, and high motion sensitivity, have gained significant traction in various disciplines, including machinery, robotics, computers, automatic control, and precision measurement. The key component of flexible mechanisms is the flexible hinge, which utilizes elastic deformation and self-recovery properties to eliminate lost motion and mechanical friction, thereby achieving higher displacement resolution. Single-axis flexible hinges can be classified based on their cross-sectional shapes, such as arc, lead angle, ellipse, parabola, and hyperbola types. Among these, the straight-round and lead angle hinges are widely used due to their simple structures. However, in some cases where space is constrained, the need for compact structures has led to the emergence of single-sided flexible hinges, which have found extensive applications in precision measurement and positioning. Building upon the advantages of hybrid and unilateral flexible hinges, this paper proposes a unilateral hybrid flexible hinge, which offers a novel approach to the engineering application of flexible hinges with compact structures and large displacements.

Flexibility Calculation of the Unilateral Straight-Circle-Ellipse Hybrid Flexible Hinge:

The unilateral straight-circle-ellipse hybrid flexible hinge comprises half of a unilateral straight-circle hinge and half of a unilateral elliptical hinge. Its geometric parameters include hinge width (b), minimum thickness (t), straight-circle radius (R), hinge length (l), major axis of the ellipse (m), and semi-minor axis of the ellipse (n). The analysis of the flexible hinge is based on the assumption of a small-deformed cantilever beam, with the right end fixed and bending deformation caused by force and moment. The influence of axial load is considered, while shear and torsion effects are neglected. According to the second theorem of Cassette, the relationship between the hinge's deformation at point 1 and the applied load can be determined. The flexibility calculation formula is derived based on this relationship and the coordinates of the hinge's cross-section. Through integral calculations, the flexibility of the unilateral straight-circle-ellipse hybrid flexible hinge can be obtained.

Example Calculation and Finite Element Verification:

An example calculation is performed using the derived flexibility calculation formula for different values of the semi-minor axis (n) of the ellipse. The results are compared with the finite element analysis (FEA) results to verify the accuracy of the formula. The error between the two sets of results is found to be less than 8%, confirming the validity of the flexibility calculation formula.

Performance Analysis of the Unilateral Straight-Circle-Ellipse Hybrid Flexible Hinge:

The flexibility of the hinge is influenced by its material and structural parameters. The flexibility calculation formula reveals that the elastic modulus (E) is inversely proportional to the hinge's width (b). Other parameters, such as the straight-circle radius (R), semi-major axis of the ellipse (m), semi-minor axis of the ellipse (n), and minimum thickness (t), also affect the flexibility. An analysis of the flexibility calculation formula shows that its parameters are most sensitive to changes in the minimum thickness (t) of the hinge.

Performance Comparison with Bilateral Straight-Circle-Ellipse Hybrid Flexible Hinge:

The unilateral straight-circle-ellipse hybrid flexible hinge is compared with the double-sided straight-circle-ellipse hybrid flexible hinge proposed in the literature. The flexibility ratio is used as a performance index, defined as the ratio of the unilateral flexibility to the bilateral flexibility. The results show that the unilateral hybrid flexible hinge offers better rotation capacity and load sensitivity compared to the bilateral hybrid hinge.

The proposal of a new type of flexible hinge, the unilateral hybrid flexible hinge, brings new possibilities for engineering applications that require compact structures and large displacements. The flexibility calculation formula is derived based on Karl's second theorem and validated through finite element analysis. The structural parameters of the hinge are found to impact its flexibility, with the minimum thickness exerting the most significant influence. The unilateral hybrid flexible hinge performs better than the bilateral hybrid hinge in terms of rotation capacity and load sensitivity. Overall, the unilateral hybrid flexible hinge offers promising prospects for various engineering applications.