Design of a 3DOF XYZ Bi-Directional Motion Platform Based on Z-Shaped Flexure Hinges

This paper presents a design of a 3DOF XYZ bi-directional motion platform based on Z-shaped flexure hinges. In the presented platform, bridge-type mechanisms and Z-shaped flexure hinges are adopted to amplify its output displacement. Bi-direction motion along the X-axis and Y-axis follows the famous differential moving principle DMP, and the bi-directional motion along the Z-axis is realized by using the reverse arrangement of the Z-shaped flexure hinges along the X-axis and Y-axis. Statics analysis of the proposed platform is carried out by the energy method, compliance matrix method, and force balance principle. Meanwhile, the Lagrange method is used to analyze the dynamics of the platform. A series of simulations are conducted to demonstrate the effectiveness of the proposed design. The simulation results show that the average displacements of the platform in the XYZ-axis are ±125.58 μm, ±126.37 μm and ±568.45 μm, respectively.

Optimal Design for Compliant Mechanism Flexure Hinges: Bridge-Type

Compliant mechanisms’ design aims to create a larger workspace and simple structural shapes because these mechanical systems usually have small dimensions, reduced friction, and less bending. From that request, we designed optimal bridge-type compliant mechanism flexure hinges with a high magnification ratio, low stress by using a flexure joint, and especially no friction and no bending. This joint was designed with optimal dimensions for the studied mechanism by using the method of grey relational analysis (GRA), which is based on the Taguchi method (TM), and finite element analysis (FEA). Grey relational grade (GRG) has been estimated by an artificial neural network (ANN). The optimal values were in good agreement with the predicted value of the Taguchi method and regression analysis. The finite element analysis, signal-to-noise analysis, surface plot, and analysis of variance demonstrated that the design dimensions significantly affected the equivalent stress and displacement. The optimal values of displacement were also verified by the experiment. The outcomes were in good agreement with a deviation lower than 6%. Specifically, the displacement amplification ratio was obtained as 65.36 times compared with initial design.

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.

Compliance Model and Structure Optimization Method Based on Genetic Algorithm for Flexure Hinge Based on X-Lattice Structure

In order to obtain a new structure of beam flexure hinge with good performance, the flexure hinge based on the X-lattice structure is researched in this paper. The truss model in the finite element method is used to model the 6-DOF compliance of the flexure hinge based on the X-lattice structure. The influence of structural parameters on the compliance and compliance ratio of flexure hinges is analyzed based on this model, and the performance is compared with the traditional beam flexure hinge of the same size. In order to design a flexure hinge based on the X-lattice structure with good comprehensive performance, this paper proposes an intelligent structure optimization method based on a genetic algorithm. The feasibility of the optimization algorithm is verified by an example.