Design methodology and performance analysis of application-oriented flexure hinges

Design and analysis of the power-trigonometric function-shaped flexure hinges

In this paper, a generalized flexure hinge model, that is, power-trigonometric function-shaped flexure hinges (PTFHs), is proposed. The power function and trigonometric function in the curve function are changed, which obtains different notch types of flexure hinges to meet the needs of flexure hinges in different scenarios. For the flexure hinge model, the notch curve equation of the hinge is presented first, and the influence of the degree of power function, degree of trigonometric function, and other parameters on the structure of the curve is analyzed. Then, the compliance and rotation precision equations of the flexure hinge are derived based on Castigliano's second theorem. Both equations are verified using the finite element method and achieve errors of less than 8.5%. Then, based on the flexure hinge equation, the influence of the size parameters on the compliance and rotation precision of the hinge is analyzed, and a new comparison method is proposed. Parameter β is defined to analyze the influence of five parameters on β. Through the comparison of PTFHs and three commonly used flexure hinges, the results prove that the proposed PTFHs have better comprehensive performance. Then, the flexure hinge is statically analyzed. Finally, a test system for flexure hinges is established to verify the performance of the model.

A Substructure Condensed Approach for Kinetostatic Modeling of Compliant Mechanisms with Complex Topology

Compliant mechanisms with complex topology have previously been employed in various precision devices due to the superiorities of high precision and compact size. In this paper, a substructure condensed approach for kinetostatic analysis of complex compliant mechanisms is proposed to provide concise solutions. In detail, the explicit relationships between the theoretical stiffness matrix, element stiffness matrix, and element transfer matrix for the common flexible beam element are first derived based on the energy conservation law. The transfer matrices for three types of serial-parallel substructures are then developed by combining the equilibrium equations of nodal forces with the transfer matrix approach, so that each branch chain can be condensed into an equivalent beam element. Based on the derived three types of transfer matrices, a kinetostatic model describing only the force-displacement relationship of the input/output nodes is established. Finally, two typical precision positioning platforms with complex topology are employed to demonstrate the conciseness and efficiency of this modeling approach. The superiority of this modeling approach is that the input/output stiffness, coupling stiffness, and input/output displacement relations of compliant mechanisms with multiple actuation forces and complex substructures can be simultaneously obtained in concise and explicit matrix forms, which is distinct from the traditional compliance matrix approach.

Analytical Compliance Equations of Generalized Elliptical-Arc-Beam Spherical Flexure Hinges for 3D Elliptical Vibration-Assisted Cutting Mechanisms

Elliptical vibration-assisted cutting technology has been widely applied in complicated functional micro-structured surface texturing. Elliptical-arc-beam spherical flexure hinges have promising applications in the design of 3D elliptical vibration-assisted cutting mechanisms due to their high motion accuracy and large motion ranges. Analytical compliance matrix formulation of flexure hinges is the basis for achieving high-precision positioning performance of these mechanisms, but few studies focus on this topic. In this paper, analytical compliance equations of spatial elliptic-arc-beam spherical flexure hinges are derived, offering a convenient tool for analysis at early stages of mechanism design. The mechanical model of a generalized flexure hinge is firstly established based on Castigliano's Second Theorem. By introducing the eccentric angle as the integral variable, the compliance matrix of the elliptical-arc-beam spherical flexure hinge is formulated. Finite element analysis is carried out to verify the accuracy of the derived analytical compliance matrix. The compliance factors calculated by the analytical equations agree well with those solved in the finite element analysis for the maximum error; average relative error and relative standard deviation are 8.25%, 1.83% and 1.78%, respectively. This work lays the foundations for the design and modeling of 3D elliptical vibration-assisted cutting mechanisms based on elliptical-arc-beam spherical flexure hinges.

A novel design of a high-performance flexure hinge with reverse parallel connection multiple-cross-springs

Deformation of leaf springs leads to axis drift and warping of traditional cross-spring flexure hinges, which result in rotation errors. To restrain the axis drift and warping, a design idea of reverse parallel connection was proposed by combining the invention principles of "merging," "symmetry," "the other way round," and "another dimension." Based on the idea, the Reverse Parallel Multiple-Cross-Spring (RPMCS) flexure hinge without warping was designed. Taking the RPMCS-3 flexure hinge as an example, experimental and simulation results of the flexure hinge consistently demonstrate that the rotational stiffness remains nearly constant under driving torque, and the relative error is substantially stabilized within 10%. In addition, the rotation accuracy of quasi-zero axis drift under torque is demonstrated by simulation results. Furthermore, the anti-interference performance of rotational stiffness and rotation accuracy is studied, which provides a reference for analyzing the performance and stability of the flexure hinge under disturbances. The rotational performance of the flexure hinge is obviously higher than other flexure hinges that existed.

Note: Design and capability verification of fillet triangle flexible support

By increasing the section thickness of a triangular flexible hinge, this study focuses on optimal selection of parameters of fillet triangle flexible hinges and flexible support. Based on Castigliano's second theorem, the flexibility expression of the fillet triangle flexible hinge was derived. Then, the case design is performed, and the comparison of three types of flexible hinges with this type of flexible hinge was carried out. The finite element models of fillet triangle flexible hinges and flexible support were built, and then the simulation results of performance parameters were calculated. Finally, the experiment platform was established to validate analysis results. The maximum error is less than 8%, which verifies the accuracy of the simulation process and equations derived; also the fundamental frequency fits the requirements of the system. The fillet triangle flexible hinge is proved to have the advantages of high precision and low flexibility.