Existing research on flexible hinges corresponds to complex expressions for flexibility and rotational accuracy calculations. To address this issue, a new type of catenary flexure hinge was designed, and a method for establishing the hinge’s compliance and rotational accuracy model by approximating arc segments with straight-line segments was proposed.

Firstly, by defining the flexure hinge as a series combination of tapered and expanded sections, the curve in the tapered segment was divided into several arc segments, and the curve segments were approximated with straight segments. Based on the Castigliano’s second theorem, a method by calculating the flexibility of the tapered section and then establishing the hinge flexibility and rotational accuracy model through matrix operations was established. Secondly, using specific examples, the derived formula, literature formulas, and the finite element method were employed for calculations. When the curve segment was finely divided, the calculation results align well, thereby verifying the formula’s correctness. Thirdly, the influence of structural parameters on the flexibility, rotation accuracy, and flexibility-accuracy ratio of catenary flexure hinges was analyzed. Finally, the bending flexibility and flexibility-accuracy ratio of the catenary, conic, and their hybrid hinges were analyzed with the same structural parameters.

The results show that a single parameter has a negative correlation with flexibility and rotation accuracy of the catenary hinge, and reducing the minimum thickness is the best way to improve flexibility. Under the same structural parameters, the flexibility and flexibility-accuracy ratio of the catenary hinge is between parabolic and circular shapes. Choosing a hybrid hinge with a section of high flexibility for the tapered section and a section of low flexibility for the expanded section allows for a balance between flexibility and motion accuracy.The greater the difference in flexibility, the better the flexibility-accuracy ratio.