Compact design of a novel linear compliant positioning stage with high out-of-plane stiffness and large travel

2017 ◽  
Vol 232 (12) ◽  
pp. 2265-2279
Author(s):  
Hua Liu ◽  
Xin Xie ◽  
Ruoyu Tan ◽  
Dapeng Fan
Keyword(s):  
Degrees Of Freedom ◽  
Compliant Mechanism ◽  
Area Ratio ◽  
Leaf Spring ◽  
Static Stiffness ◽  
Element Analysis ◽  
Compact Size ◽  
Positioning Stage ◽  
Out Of Plane ◽  
Compact Design

Since most of the XY positioning stages with large travel range proposed in previous studies suffer from low out-of-plane stiffness and loose structure, this paper presents a novel two degrees-of-freedom large travel linear compliant positioning stage with high out-of-plane stiffness and compact size. The linear guide compliant mechanism of the stage takes spatial leaf spring parallelograms as the basic units, which are serially connected to obtain large travel, high out-of-plane stiffness, and compact size simultaneously. The theoretical static stiffness and dynamic resonant frequency are obtained by matrix structural analysis. Finite element analysis is carried out to investigate the characteristics of the developed stage. The analytical model is confirmed by experiments. It is noted that the developed stage has a workspace of 4.4 × 7.0 mm2, and the area ratio of workspace to the outer dimension of the stage is 0.16%, which is greater than that of any existing stage reported in the literature. The results of out-of-plane payload tests indicate that the stage can sustain at least 20 kg out-of-plane payload without changing the travel range. And the positioning experiments show that the developed stage is capable of tracking a circle of radius 1.5 mm with 10 µm error and the resolution is less than 2 µm.

scholarly journals Eliminating Underconstraint in Double Parallelogram Flexure Mechanisms

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Robert M. Panas ◽  
Jonathan B. Hopkins
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Experimental Measurement ◽  
Degrees Of Freedom ◽  
Dynamic Performance ◽  
Average Error ◽  
Static Stiffness ◽  
Element Analysis ◽  
Linkage Design ◽  
Analytical Expressions

We present an improved flexure linkage design for removing underconstraint in a double parallelogram (DP) linear flexural mechanism. This new linkage alleviates many of the problems associated with current linkage design solutions such as static and dynamic performance losses and increased footprint. The improvements of the new linkage design will enable wider adoption of underconstraint eliminating (UE) linkages, especially in the design of linear flexural bearings. Comparisons are provided between the new linkage design and existing UE designs over a range of features including footprint, dynamics, and kinematics. A nested linkage design is shown through finite element analysis (FEA) and experimental measurement to work as predicted in selectively eliminating the underconstrained degrees-of-freedom (DOF) in DP linear flexure bearings. The improved bearing shows an 11 × gain in the resonance frequency and 134× gain in static stiffness of the underconstrained DOF, as designed. Analytical expressions are presented for designers to calculate the linear performance of the nested UE linkage (average error < 5%). The concept presented in this paper is extended to an analogous double-nested rotary flexure design.

Flexible Cellular Structures of a Non-Pneumatic Tire

2016 ◽  
Author(s):  
Fanhao Meng ◽  
Dengfeng Lu ◽  
Jingjun Yu
Keyword(s):  
Degrees Of Freedom ◽  
Compliant Mechanism ◽  
Design Method ◽  
Cellular Structures ◽  
Geometrical Parameters ◽  
Analysis Tool ◽  
Element Analysis ◽  
Rectangular Cell ◽  
Cellular Solid ◽  
Vertical Loading

Taking the tire of the lunar rover as the research background, this paper provides two design concepts of non-pneumatic tires (NPTs) with a compliant cellular solid spoke component. In this study, a series of degrees of freedom (DOFs) and stiffness analysis of NPTs with cellular structures are investigated with the same vertical loading conditions using a commercial finite element analysis tool, ANSYS. The research found that the tread relative to the hub only has in-plane translational degree of freedom in the radial direction, without other DOFs. According to this finding, using the improved design method based on the existing cellular structures and the synthetic design method based on the principle of compliant mechanism, two cases of cellular structures are designed: (i) cross arcs cell and (ii) rectangular cell. Analysis of the influence of geometric parameters of the cell on the performance of NPTs is critical to further improve the performance of the NPTs. Finally, by optimizing the geometrical parameters of the cellular structure, the performance of the NPTs with the cross arcs cell and rectangular cell can be enhanced.

Design of a 3-DOF Compliant Parallel Mechanism for Displacement Amplification

2013 ◽  
Author(s):  
Qiang Zeng ◽  
Kornel F. Ehmann
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Heat Balance ◽  
Parallel Mechanism ◽  
Compliant Mechanism ◽  
Element Analysis ◽  
Resonant Frequencies ◽  
Compact Size ◽  
Compliant Parallel Mechanism ◽  
Monolithic Structure

Prevalent general design methods and applications of compliant displacement amplifiers are focused on 1-DOF units composed into serial structures, which are limited by their output motions, stiffness, heat balance, repeatability and resonant frequencies. To improve the output properties of compliant displacement amplifiers, a monolithic structure is presented in the form of a compliant parallel mechanism. In the proposed moving structure, the compliant mechanism of the displacement amplifier is designed with 3-DOF to generate uniformly magnified output properties in all directions. High first resonant frequencies and amplification ratios are achieved in a compact size compared to existing compliant displacement amplifiers. The related kinematics, amplification ratios and resonant frequencies of the amplifier are analytically modeled, and the results are simulated by finite-element analysis. The proposed design is employable for micro/nano positioning stages operating within a prismatic output workspace.

scholarly journals Design and development of a novel monolithic compliant XY stage with centimeter travel range and high payload capacity

2018 ◽  
Vol 9 (1) ◽  
pp. 161-176 ◽  
Author(s):  
Shixun Fan ◽  
Hua Liu ◽  
Dapeng Fan
Keyword(s):  
Nanoimprint Lithography ◽  
Compliant Mechanism ◽  
Tracking Error ◽  
Ultra Violet ◽  
Design Flow ◽  
Compact Structure ◽  
Compact Size ◽  
Payload Capacity ◽  
Out Of Plane ◽  
High Payload

Abstract. This article proposes a novel monolithic compliant spatial parallel XY stage (SPXYS). An important feature of the SPXYS lies in that it can deliver centimeter travel range and sustain large out-of-plane payload while possessing a compact structure, which makes the SPXYS suitable for some special applications such as Ultra-Violet Nanoimprint Lithography and soft-contact lithography. Different from conventional compliant positioning stages, the proposed SPXYS consists of a monolithic spatial parallel linear compliant mechanism (SPLCM) driven by four matching designed voice coil motors (VCMs). The moving platform of the stage is connected to the base by four spatial prismatic-prismatic (PP) joints, which are enveloped from planar PP joint based on the position space reconfiguration (PSR) method to realize desired travel range, payload capacity and compact size. The mechatronic model of the SPXYS is established by integrated using matrix structural analysis (MSA) and the method of images. The design flow chart of the SPXYS is given based on the key parameter sensitivity analysis. Furthermore, a reified SPXYS is designed and manufactured. The analytical design of the stage is confirmed by experiments. The reified stage has a travel range of 20.4 × 20.6 mm2, a compact structure with area ratio 1.87 %, and the resonant frequencies of the two working modes at 22.98 and 21.31 Hz. It can track a circular trajectory with the radius of 4.5 mm. The root mean squares (RMS) tracking error is 2 µm. The positioning resolution is 100 nm. The payload capacity test shows that the reified stage can bear 20 kg out-of-plane payload.

scholarly journals Design of Four-DoF Compliant Parallel Manipulators Considering Maximum Kinematic Decoupling for Fast Steering Mirrors

Actuators ◽  
2021 ◽  
Vol 10 (11) ◽  
pp. 292
Author(s):  
Guangbo Hao ◽  
Haiyang Li ◽  
Yu-Hao Chang ◽  
Chien-Sheng Liu
Keyword(s):  
Degrees Of Freedom ◽  
Compliant Mechanism ◽  
Parallel Manipulators ◽  
Laser Beams ◽  
Element Analysis ◽  
Compliance Matrix ◽  
Precision Control ◽  
Motion System ◽  
Matrix Modelling

Laser beams can fluctuate in four directions, which requires active compensation by a fast steering mirror (FSM) motion system. This paper deals with the design of four-degrees-of-freedom (DoF) compliant parallel manipulators, for responding to the requirements of the FSM. In order to simplify high-precision control in parallel manipulators, maximum kinematic decoupling is always desired. A constraint map method is used to propose the four required DoF with the consideration of maximum kinematic decoupling. A specific compliant mechanism is presented based on the constraint map, and its kinematics is estimated analytically. Finite element analysis demonstrates the desired qualitative motion and provides some initial quantitative analysis. A normalization-based compliance matrix is finally derived to verify and demonstrate the mobility of the system clearly. In a case study, the results of normalization-based compliance matrix modelling show that the diagonal entries corresponding to the four DoF directions are about 10 times larger than those corresponding to the two-constraint directions, validating the desired mobility.

scholarly journals Free and Forced Vibration of Laminated and Sandwich Plates by Zig-Zag Theories Differently Accounting for Transverse Shear and Normal Deformability

Aerospace ◽  
2018 ◽  
Vol 5 (4) ◽  
pp. 108 ◽  
Author(s):  
Ugo Icardi ◽  
Andrea Urraci
Keyword(s):  
Transverse Shear ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Interfacial Stress ◽  
Sandwich Plates ◽  
Displacement Fields ◽  
Element Analysis ◽  
Out Of Plane ◽  
Elasticity Solutions ◽  
Displacement Based

A number of mixed and displacement-based zig-zag theories are derived from the zig-zag adaptive theory (ZZA). As a consequence of their different assumptions on displacement, strain, and stress fields, and layerwise functions, these theories account for the transverse shear and normal deformability in different ways, but their unknowns are independent of the number of layers. Some have features that are reminiscent of ones that have been published in the literature for the sake of comparison. Benchmarks with different length-to-thickness ratios, lay-ups, material properties, and simply supported or clamped edges are studied with the intended aim of contributing toward better understanding the influence of transverse anisotropy on free vibration and the response of blast-loaded, multilayered, and sandwich plates, as well as enhancing the existing database. The results show that only theories whose layerwise contributions identically satisfy interfacial stress constrains and whose displacement fields are redefined for each layer provide results that are in agreement with elasticity solutions and three-dimensional (3D) finite element analysis (FEA) (mixed solid elements with displacements and out-of-plane stresses as nodal degrees of freedom (d.o.f.)) with a low expansion order of polynomials in the in-plane and out-of-plane directions. The choice of their layerwise functions is shown to be immaterial, while theories with fixed kinematics are shown to be strongly case-sensitive and often inadequate (even for slender components).

A Numerical Method for Position Analysis of Compliant Mechanisms With More Degrees of Freedom Than Inputs

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Quentin T. Aten ◽  
Shannon A. Zirbel ◽  
Brian D. Jensen ◽  
Larry L. Howell
Keyword(s):  
Potential Energy ◽  
Equilibrium Position ◽  
Degrees Of Freedom ◽  
Compliant Mechanisms ◽  
Virtual Work ◽  
Compliant Mechanism ◽  
Numerical Approach ◽  
Element Analysis ◽  
Loop Equation ◽  
Body Model

An underactuated or underconstrained compliant mechanism may have a determined equilibrium position because its energy storage elements cause a position of local minimum potential energy. The minimization of potential energy (MinPE) method is a numerical approach to finding the equilibrium position of compliant mechanisms with more degrees of freedom (DOF) than inputs. Given the pseudorigid-body model of a compliant mechanism, the MinPE method finds the equilibrium position by solving a constrained optimization problem: minimize the potential energy stored in the mechanism, subject to the mechanism’s vector loop equation(s) being equal to zero. The MinPE method agrees with the method of virtual work for position and force determination for underactuated 1-DOF and 2-DOF pseudorigid-body models. Experimental force-deflection data are presented for a fully compliant constant-force mechanism. Because the mechanism’s behavior is not adequately modeled using a 1-DOF pseudorigid-body model, a 13-DOF pseudorigid-body model is developed and solved using the MinPE method. The MinPE solution is shown to agree well with nonlinear finite element analysis and experimental force-displacement data.

scholarly journals Modal Measurements and Model Corrections of A Large Stroke Compliant Mechanism

2014 ◽  
Vol 61 (2) ◽  
pp. 347-366 ◽  
Author(s):  
W. Wijma ◽  
S.E. Boer ◽  
R.G.K.M. Aarts ◽  
D.M. Brouwer ◽  
W.B.J. Hakvoort
Keyword(s):  
Degrees Of Freedom ◽  
Design Principle ◽  
Dynamic Behaviour ◽  
Compliant Mechanism ◽  
Leaf Spring ◽  
Internal Stresses ◽  
Multibody Model ◽  
Leaf Springs ◽  
Manufacturing Tolerances ◽  
Exact Constraint

Abstract In modelling flexure based mechanisms, generally flexures are modelled perfectly aligned and nominal values are assumed for the dimensions. To test the validity of these assumptions for a two Degrees Of Freedom (DOF) large stroke compliant mechanism, eigenfrequency and mode shape measurements are compared to results obtained with a flexible multibody model. The mechanism consists of eleven cross flexures and seven interconnecting bodies. From the measurements 30% lower eigenfrequencies are observed than those obtained with the model. With a simplified model, it is demonstrated that these differences can be attributed to wrongly assumed leaf spring thickness and misalignment of the leaf springs in the cross flexures. These manufacturing tolerances thus significantly affect the behaviour of the two DOF mechanism, even though it was designed using the exact constraint design principle. This design principle avoids overconstraints to limit internal stresses due to manufacturing tolerances, yet this paper shows clearly that manufacturing imperfections can still result in significantly different dynamic behaviour.

Design of a Compliant XY Positioning Stage With Large Workspace

2015 ◽  
Author(s):  
Chao-Min Huang ◽  
Hai-Jun Su
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Ball Bearings ◽  
Kinematic Constraint ◽  
Element Analysis ◽  
Positioning Stage ◽  
Motion Range ◽  
Moving Direction ◽  
Operation Parameters

Flexure mechanisms become more and more popular because of their better performance, easy maintenance, wear-free properties and predictability of kinematic variables changes. Comparing to traditional ball bearings or linear slides, however, range of motion limits flexure mechanisms applications in existing market. This paper presents the design of a novel planar XY stage synthesizing the benefits of parallel and serial kinematic constraint. By parallel connecting two mechanisms: the vertical and horizontal subsystems, which both have degrees of freedom (DOFs) in primary moving direction but different degrees of constraints (DOCs) in rotation, this system is able to reduce three parasitic rotation angles (pitch, roll and yaw) less than one micro radium and also have motion range up to 40mm × 40mm. Analytical model and finite element analysis (FEA) are present to validate the performance of this stage and also determine appropriate operation parameters.

A two degrees of freedom comb capacitive-type accelerometer with low cross-axis sensitivity

2019 ◽  
Vol 13 (3) ◽  
pp. 5334-5346
Author(s):  
M. N. Nguyen ◽  
L. Q. Nguyen ◽  
H. M. Chu ◽  
H. N. Vu
Keyword(s):  
Degrees Of Freedom ◽  
Proof Mass ◽  
Vibration Modes ◽  
Electrode Structure ◽  
Element Analysis ◽  
Mechanical Coupling ◽  
Fully Differential ◽  
Mode Effects ◽  
The Finite Element Analysis ◽  
Cross Axis

In this paper, we report on a SOI-based comb capacitive-type accelerometer that senses acceleration in two lateral directions. The structure of the accelerometer was designed using a proof mass connected by four folded-beam springs, which are compliant to inertial displacement causing by attached acceleration in the two lateral directions. At the same time, the folded-beam springs enabled to suppress cross-talk causing by mechanical coupling from parasitic vibration modes. The differential capacitor sense structure was employed to eliminate common mode effects. The design of gap between comb fingers was also analyzed to find an optimally sensing comb electrode structure. The design of the accelerometer was carried out using the finite element analysis. The fabrication of the device was based on SOI-micromachining. The characteristics of the accelerometer have been investigated by a fully differential capacitive bridge interface using a sub-fF switched-capacitor integrator circuit. The sensitivities of the accelerometer in the two lateral directions were determined to be 6 and 5.5 fF/g, respectively. The cross-axis sensitivities of the accelerometer were less than 5%, which shows that the accelerometer can be used for measuring precisely acceleration in the two lateral directions. The accelerometer operates linearly in the range of investigated acceleration from 0 to 4g. The proposed accelerometer is expected for low-g applications.

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