Design of flexure revolute joint based on compliance and stiffness ellipsoids

In view of the problems of low accuracy, small rotational angle, and large impact caused by flexure joints during the deployment process, an integrated flexure revolute (FR) joint for folding mechanisms was designed. The design was based on the method of compliance and stiffness ellipsoids, using a compliant dyad building block as its flexible unit. Using the single-point synthesis method, the parameterized model of the flexible unit was established to achieve a reasonable allocation of flexibility in different directions. Based on the single-parameter error analysis, two error models were established to evaluate the designed flexure joint. The rotational stiffness, the translational stiffness, and the maximum rotational angle of the joints were analyzed by nonlinear finite element analyses. The rotational angle of one joint can reach 25.5° in one direction. The rotational angle of the series FR joint can achieve 50° in one direction. Experiments on single and series flexure joints were carried out to verify the correctness of the design and analysis of the flexure joint.

Kinetostatic Modeling of Dual-Drive H-type Gantry with Exchangeable Flexure Joints

The flexure joints are proposed to replace the rigid assembly between the cross-arm and the moving carriages of dual-drive H-type gantry (DHG), for higher reliability and fine rotational alignments. In prior literature, the flexure joint of the DHG is modeled as an ideal linear torsional spring, resulting in inaccurate estimation of the cross-arm's angle. In this work, a generalized analytical kinetostatic model of flexure-linked DHG is built by considering the geometric nonlinearities. The expressions of beam coefficients in the model are obtained from either beam constraint model (BCM) or Timoshenko BCM (TBCM), according to the given criterion of length-to-thickness ratio. The model is capable to accurately estimate any two variables among the rotation angle of the cross-arm, the misalignment of two carriages, and the net driving force, as long as the other is known. Simulations and experiments on the testbed validate the accuracy and show practical appeals of the proposed model.

Optimization of Translational Flexure Joints Using Corrugated Units Under Stress Constraints

When optimizing 2-DOF corrugated flexure stages, most approaches for calculating the maximum stress on the corrugated flexure (CF) beam depend on finite element analysis (FEA). The current paper introduces the design optimization for stages using CF units under stress constraints. The stress state is solved; then, based on that, the maximum displacement under stress constraints is deduced. The natural frequency formula of the micropositioning stage is further derived from the results of the stiffness matrix. The stage configurations corresponding to the maximum displacement are optimized by restricting the off-axis/axial stiffness ratio and natural frequency of the stage. The optimal results of different types are validated by FEA and experiments.

A Non-Prismatic Beam Element for the Optimization of Flexure Mechanisms

Flexure joints are rapidly gaining ground in precision engineering because of their predictable behavior. However the range of motion of flexure joints is limited due to loss of support stiffness in deformed configurations. Most of the common flexure joints consist of prismatic leaf springs. This paper presents a simple non-prismatic beam formulation that can be used for the efficient modelling of non-prismatic leaf springs. The resulting stiffness and stress computed by the non-prismatic beam element are compared to the results of a finite element analysis. The paper shows that the support stiffness of two typical flexure joints can be increased up to a factor of 1.9 by using non-prismatic instead of prismatic leaf springs.

Design and Analysis of a Novel Compliant Mechanism with RPR Degrees of Freedom

Magnetic drive pump has gotten great achievement A novel compliant mechanism with RPR degrees of freedom (DOF) is proposed where R and P represent rotation and translation DOFs, respectively. The proposed compliant mechanism is obtained from dimension synthesizing a 2-RPU-UPR rigid parallel mechanism with the method of optimization of motion/force transfer characteristic, where R, P and U represent rotation, translation and universal pairs, respectively. Firstly, inverse kinematics and Jacobian matrix are analyzed for the dimensional synthesis. Then, output transmission indexes of branches in the parallel mechanism are given. Dimensional synthesis is completed based on the normalized design parameter. And optimization of flexure joints based on constrained energy is carried out. Afterwards, the novel compliant mechanism is obtained by direct replacing method. Mechanical model of the compliant mechanism including static stiffness and input stiffness is built based on the pseudo-rigid body model method and virtual work principle for its future application. Finally, FEA simulation by Ansys Workbench is carried out to verify DOF, effectiveness of the dimension synthesis, and compliant model. Optimization of motion/force transfer characteristic is first applied for the design of compliant mechanisms to suppress drift of rotation axis in the paper.