Bending, Tensile and Compressive Stiffness Analysis and Application of Four Composite Flexible Hinge1

Summary: Based on the relevant knowledge of material mechanics and calculus, the calculation formulas of bending stiffness, tension and compression stiffness of four composite flexible hinges are derived. Taking the rounded straight beam flexible hinge as an example, the derived stiffness calculation formula is verified using the finite element method. The stiffness properties of the four composite flexible hinges are compared and analyzed. The results show that the elliptical straight beam composite hinge has the smallest bending and tensile stiffness. In the flexible T-shaped joint structure, the flexible T-shaped joint composed of elliptical straight beam composite hinge has the strongest deformation compensation ability.

Flexible hinges are widely used in applications that require small angular displacement and high-precision rotation, eliminating air travel and mechanical friction. Based on the structure type, flexible hinges can be categorized into different types. Stiffness is an important performance indicator for flexible hinges, reflecting their ability to resist external loads and their flexibility. This study aims to derive the stiffness calculation formulas for four composite flexible hinges and compare their stiffness properties.

1. Establishment of stiffness calculation formula:

1.1 Calculation formulas for bending stiffness of rounded straight beam and elliptical straight beam composite hinges are derived based on material mechanics and calculus.

1.2 Stiffness calculation formulas for parabolic and hyperbolic straight beam composite hinges are derived using Karl's second theorem.

2. Verification of stiffness calculation formula:

The derived stiffness calculation formula for the rounded straight beam flexible hinge is verified using the finite element method. The calculated bending and tensile/compression stiffness values are compared with the analytical solutions to determine the accuracy of the formula.

3. Analysis of the stiffness of the four composite flexible hinges:

The stiffness properties of the four composite flexible hinges are compared and analyzed. Based on the derived stiffness calculation formulas, the bending and tensile stiffness values for each hinge are calculated and compared.

4. Application examples:

The four composite flexible hinges are applied to a flexible T-shaped joint structure. The stiffness properties of each flexible T-shaped joint are analyzed using the finite element method. The results show that the flexible T-shaped joint composed of elliptical straight beam composite hinge has the strongest deformation compensation ability.

The derived stiffness calculation formulas for the four composite flexible hinges are verified to be accurate. The stiffness properties of the four hinges are compared and analyzed, and the flexible T-shaped joint composed of elliptical straight beam composite hinge is found to have the best motion capacity and load sensitivity. This study provides valuable insights for the design and application of composite flexible hinges in various fields.