An XYZ Parallel Kinematic Flexure Mechanism With Geometrically Decoupled Degrees of Freedom

2011 ◽  
Author(s):  
Shorya Awtar ◽  
John Ustick ◽  
Shiladitya Sen
Keyword(s):  
Degrees Of Freedom ◽  
Element Analysis ◽  
Motion Direction ◽  
Form Analysis ◽  
Flexure Mechanism ◽  
Non Linear ◽  
Decoupled Motion ◽  
Motion Range ◽  
Parallel Kinematic ◽  
Cross Axis

We present the constraint-based design of a novel parallel kinematic flexure mechanism that provides highly decoupled motions along the three translational directions (X, Y, and Z) and high stiffness along the three rotational directions (θx, θy, and θz). The geometric decoupling ensures large motion range along each translational direction and enables integration with large-stroke ground-mounted linear actuators or generators, depending on the application. The proposed design, which is based on a systematic arrangement of multiple rigid stages and parallelogram flexure modules, is analyzed via non-linear finite element analysis. A proof-of-concept prototype of the flexure mechanism is fabricated to validate its large range and decoupled motion capability. The analyses as well as the hardware demonstrate an XYZ motion range of 10 mm × 10 mm × 10 mm. Over this motion range, the non-linear FEA predicts a cross-axis error of less than 3%, parasitic rotations less than 2 mrad, less than 4% lost motion, actuator isolation less than 1.5%, and no perceptible motion direction stiffness variation. Ongoing work includes non-linear closed-form analysis and experimental measurement of these error motion and stiffness characteristics.

An XYZ Parallel-Kinematic Flexure Mechanism With Geometrically Decoupled Degrees of Freedom

2012 ◽  
Vol 5 (1) ◽  
Author(s):  
Shorya Awtar ◽  
John Ustick ◽  
Shiladitya Sen
Keyword(s):  
Degrees Of Freedom ◽  
Finite Elements Analysis ◽  
Motion Direction ◽  
Flexure Mechanism ◽  
Nonlinear Finite Elements ◽  
Decoupled Motion ◽  
Motion Range ◽  
Stiffness Variation ◽  
Parallel Kinematic ◽  
Cross Axis

A novel parallel-kinematic flexure mechanism that provides highly decoupled motions along the three translational directions (X, Y, and Z) and high stiffness along the three rotational directions (θx, θy, and θz) is presented. Geometric decoupling ensures large motion range along each translational direction and enables integration with large-stroke ground-mounted linear actuators or generators, depending on the application. The proposed design, which is based on a systematic arrangement of multiple rigid stages and parallelogram flexure modules, is analyzed via nonlinear finite elements analysis (FEA). A proof-of-concept prototype is fabricated to validate the predicted large range and decoupled motion capabilities. The analysis and the hardware prototype demonstrate an XYZ motion range of 10 mm × 10 mm × 10 mm. Over this motion range, the nonlinear FEA predicts cross-axis errors of less than 7.8%, parasitic rotations less than 10.8 mrad, less than 14.4% lost motion, actuator isolation better than 1.5%, and no perceptible motion direction stiffness variation.

Experimental Characterization of a Large-Range Parallel Kinematic XYZ Flexure Mechanism

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Shorya Awtar ◽  
Jason Quint ◽  
John Ustick
Keyword(s):  
Degrees Of Freedom ◽  
Large Range ◽  
Experimental Setup ◽  
Modular Construction ◽  
Finite Elements Analysis ◽  
Motion Direction ◽  
Flexure Mechanism ◽  
Parallel Kinematic ◽  
Cross Axis ◽  
Exact Constraint

Abstract Previously, we reported the conceptual design of a novel parallel-kinematic flexure mechanism that provides large and decoupled motions in the X, Y, and Z directions, along with good actuator isolation, and small parasitic error motions (Awtar, S., Ustick, J., and Sen, S., 2012, “An XYZ Parallel-Kinematic Flexure Mechanism With Geometrically Decoupled Degrees of Freedom,” ASME J. Mech. Rob., 5(1), p. 015001). This paper presents the detailed design and fabrication of a high-precision experimental setup to characterize and validate the motion attributes of this proposed flexure design via comprehensive measurements. The unique aspects of this experimental setup include a novel modular construction and exact-constraint assembly of the flexure mechanism from 12 identical parallelogram flexure modules. The flexure mechanism along with the sensing and actuation setup in the experiment is designed to enable large range (10 mm) in each direction. Experimental measurements and finite-elements analysis demonstrate <3% variation in motion direction stiffness, 20.4% lost motion, <11.6% cross-axis error, <3.3% actuator isolation, and <9.5 mrad motion stage rotation over the entire 10 mm × 10 mm × 10 mm range of motion.

Constraint-Based Design of Parallel Kinematic XY Flexure Mechanisms

2006 ◽  
Vol 129 (8) ◽  
pp. 816-830 ◽  
Author(s):  
Shorya Awtar ◽  
Alexander H. Slocum
Keyword(s):  
Performance Characteristics ◽  
Element Analysis ◽  
Nonlinear Load ◽  
Flexure Mechanism ◽  
Nonlinear Force ◽  
Parallel Kinematic ◽  
Improved Performance ◽  
Design Tradeoffs ◽  
Cross Axis ◽  
Force Displacement

This paper presents parallel kinematic XY flexure mechanism designs based on systematic constraint patterns that allow large ranges of motion without causing over-constraint or significant error motions. Key performance characteristics of XY mechanisms such as mobility, cross-axis coupling, parasitic errors, actuator isolation, drive stiffness, lost motion, and geometric sensitivity, are discussed. The standard double parallelogram flexure module is used as a constraint building-block and its nonlinear force-displacement characteristics are employed in analytically predicting the performance characteristics of two proposed XY flexure mechanism designs. Fundamental performance tradeoffs, including those resulting from the nonlinear load-stiffening and elastokinematic effects, in flexure mechanisms are highlighted. Comparisons between closed-form linear and nonlinear analyses are presented to emphasize the inadequacy of the former. It is shown that geometric symmetry in the constraint arrangement relaxes some of the design tradeoffs, resulting in improved performance. The nonlinear analytical predictions are validated by means of computational finite element analysis and experimental measurements.

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.

Nonlinear Constraint Model for Symmetric Three-Dimensional Beams

2010 ◽  
Author(s):  
Shiladitya Sen ◽  
Shorya Awtar
Keyword(s):  
Three Dimensional ◽  
Practical Interest ◽  
Nonlinear Constraint ◽  
Element Analysis ◽  
Flexure Mechanism ◽  
Spatial Beam ◽  
Non Linear ◽  
Simplifying Assumptions ◽  
Non Linear Load ◽  
Constraint Model

The constraint-based design of flexure mechanisms requires a qualitative and quantitative understanding of the constraint characteristics of flexure elements that serve as constraints. This paper presents the constraint characterization of a slender, uniform and symmetric cross-section, spatial beam, which is one of the most basic flexure elements used in three-dimensional flexure mechanisms. The constraint characteristics of interest, namely stiffness and error motions, are determined from the non-linear load-displacement relations of the beam. Appropriate simplifying assumptions are made in deriving these relations so that relevant non-linear effects (load-stiffening, kinematic, and elastokinematic) are captured in a compact, closed-form, and parametric manner. The resulting spatial beam constraint model is shown to be accurate, using non-linear finite element analysis, within a load and displacement range of practical interest. The utility of this model lies in the physical and analytical insight that it offers into the constraint behavior of a spatial beam flexure, its use in 3D flexure mechanism geometries, and fundamental performance tradeoffs in flexure mechanism design.

A 2-legged XY parallel flexure motion stage with minimised parasitic rotation

2014 ◽  
Vol 228 (17) ◽  
pp. 3156-3169 ◽  
Author(s):  
Guangbo Hao
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Design Approach ◽  
Analytical Models ◽  
Geometrical Parameters ◽  
Element Analysis ◽  
Motion Range ◽  
Cross Axis

XY compliant parallel manipulators (aka XY parallel flexure motion stages) have been used as diverse applications such as atomic force microscope scanners due to their proved advantages such as eliminated backlash, reduced friction, reduced number of parts and monolithic configuration. This paper presents an innovative stiffness centre based approach to design a decoupled 2-legged XY compliant parallel manipulator in order to better minimise the inherent parasitic rotation and have a more compact configuration. This innovative design approach makes all of the stiffness centres, associated with the passive prismatic (P) modules, overlap at a point that all of the applied input forces can go through. A monolithic compact and decoupled XY compliant parallel manipulator with minimised parasitic rotation is then proposed using the proposed design approach based on a 2-PP kinematically decoupled translational parallel manipulator. Its load–displacement and motion range equations are derived, and geometrical parameters are determined for a specified motion range. Finite element analysis comparisons are also implemented to verify the analytical models with analysis of the performance characteristics including primary stiffness, cross-axis coupling, parasitic rotation, input and output motion difference and actuator nonisolation effect. Compared with the existing XY compliant parallel manipulators obtained using 4-legged mirror-symmetric constraint arrangement, the proposed XY compliant parallel manipulators based on stiffness centre approach mainly benefits from fewer legs resulting in reduced size, simpler modelling as well as smaller lost motion. Compared with existing 2-legged designs with the conventional arrangement, the present design has smaller parasitic rotation, which has been proved from the finite element analysis results.

Finite Element Analysis of the non Linear Behavior of a Multilayer Piezoelectric Actuator

2005 ◽  
Vol 881 ◽  
Author(s):  
M. Elhadrouz ◽  
T. Ben Zineb ◽  
E. Patoor
Keyword(s):  
Degrees Of Freedom ◽  
Constitutive Law ◽  
Element Analysis ◽  
Linear Behavior ◽  
Time Element ◽  
Non Linear ◽  
Multilayer Actuator ◽  
Element Type ◽  
Definition Of ◽  
The Right

AbstractA constitutive law for ferroelectric and ferroelastic piezoceramics is implemented in ABAQUS Standard using the subroutine user element. A linear solid element is defined: it is an eight-node hexahedron having the mechanical displacement components and the electric potential as degrees of freedom for each node. The element is formulated for static analysis and it needs the definition of the contribution of this element to the Jacobian (stiffness) and the definition of an array containing the contributions of this element to the right-hand-side vectors of the overall system of equations The subroutine is called for each element that is of a user-defined element type each time element calculations are required. As an example, the element is used for the simulation of a multilayer actuator made of piezoceramics. In this case, the piezoelectric equations are not valid since the electric loading induces non linear phenomena, which are captured through the constitutive law implemented in the user element.

Characteristics of Beam-Based Flexure Modules

2006 ◽  
Vol 129 (6) ◽  
pp. 625-639 ◽  
Author(s):  
Shorya Awtar ◽  
Alexander H. Slocum ◽  
Edip Sevincer
Keyword(s):  
Finite Element Analysis ◽  
Analytical Framework ◽  
Equilibrium Conditions ◽  
Element Analysis ◽  
Flexure Mechanism ◽  
Important Constraint ◽  
Motion Range ◽  
Stiffness Variation ◽  
Force Displacement ◽  
Force Equilibrium

The beam flexure is an important constraint element in flexure mechanism design. Nonlinearities arising from the force equilibrium conditions in a beam significantly affect its properties as a constraint element. Consequently, beam-based flexure mechanisms suffer from performance tradeoffs in terms of motion range, accuracy and stiffness, while benefiting from elastic averaging. This paper presents simple yet accurate approximations that capture the effects of load-stiffening and elastokinematic nonlinearities in beams. A general analytical framework is developed that enables a designer to parametrically predict the performance characteristics such as mobility, over-constraint, stiffness variation, and error motions, of beam-based flexure mechanisms without resorting to tedious numerical or computational methods. To illustrate their effectiveness, these approximations and analysis approach are used in deriving the force–displacement relationships of several important beam-based flexure constraint modules, and the results are validated using finite element analysis. Effects of variations in shape and geometry are also analytically quantified.

Design of Parallel Kinematic XY Flexure Mechanisms

2005 ◽  
Author(s):  
Shorya Awtar ◽  
Alexander H. Slocum
Keyword(s):  
Performance Measures ◽  
Significant Error ◽  
Nonlinear Analyses ◽  
Element Analysis ◽  
Flexure Mechanism ◽  
Nonlinear Force ◽  
Parallel Kinematic ◽  
Improved Performance ◽  
Design Tradeoffs ◽  
Force Displacement

This paper presents parallel kinematic XY mechanism designs that are based on a systematic constraint pattern. The constraint pattern, realized by means of double parallelogram flexure modules, is such that it allows large ranges of motion without over-constraining the mechanism or generating significant error motions. Nonlinear force-displacement characteristics of the double parallelogram flexure are used in analytically predicting the performance measures of the proposed XY mechanisms. Comparisons between closed-form linear and nonlinear analyses are presented to highlight the inadequacy of the former. Fundamental design tradeoffs in flexure mechanism performance are discussed qualitatively and quantitatively. It is shown that geometric symmetry in the constraint arrangement relaxes some of the design tradeoffs, resulting in improved performance. The nonlinear analytical predictions are validated by means of Finite Element Analysis and experimental measurements.

Design and Analysis of New Large-Range XY Compliant Parallel Micromanipulators

2014 ◽  
Author(s):  
Jingjun Yu ◽  
Zhenguo Li ◽  
Dengfeng Lu ◽  
Guanghua Zong ◽  
Guangbo Hao
Keyword(s):  
Matrix Models ◽  
Mirror Symmetry ◽  
Initial Model ◽  
Element Analysis ◽  
Compliance Matrix ◽  
Parasitic Motion ◽  
Motion Range ◽  
Large Motion ◽  
Symmetry Structure ◽  
Cross Axis

The need for a compliant parallel micromanipulator (CPM) providing large motion range and high precision is increasing. Existing CPMs vary in constraint configurations and therefore it is necessary to verify/compare their characteristics. This paper compares three kinds of typical over-constrained CPMs, and derives their theoretical compliance matrix models pointing out constraint characteristics of the three kinematic configurations. Then the three CPMs are analyzed with FEA (finite element analysis), and results illustrate that the theoretical compliance matrix models are close to their FEA models. Moreover, cross-axis coupling along two motion axes (X&Y), parasitic motion and compliance fluctuation of motion stages are described in details. Through analyzing the FEA results, we present an improved CPM with a mirror-symmetry structure and redundant-constraint characteristic which can effectively constrain in-plane yaw and cross-axis coupling. It is shown that the improved CPM presented in this paper has a series of merits: large motion range up to 10mm×10mm in the dimension of 311mm×311mm×24mm, small compliance fluctuation (only 37.32% of that of the initial model), a smaller cross-axis coupling (only 24.39% of that of the initial model generated by a single-axis 5mm driving), a smaller in-plane parasitic yaw (only 53.57% of that of the initial model generated by double-axis 5mm driving).

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