Workspace of a Flexure Hexapod Nanopositioner

2012 ◽  
Author(s):  
Hongliang Shi ◽  
Hai-Jun Su
Keyword(s):  
Analytical Model ◽  
Compliant Mechanisms ◽  
Kinematic Model ◽  
Element Model ◽  
Small Range ◽  
Torsion Angles ◽  
Maximum Deformation ◽  
Design Engineers ◽  
Flexure Joints ◽  
Six Degree Of Freedom

This paper studies the workspace of a flexure-based, hexa-pod nanopositioner previously built by the National Institute of Standards and Technology (NIST) which can produce high-resolution motions in six degree of freedom by actuating linear actuators on planar tri-stage. Because there is a lack of work in workspace of such kind of compliant mechanisms, the controller is typically limited to a very small range of motion in order to avoid material failure. In this work, we seek to derive a kinematic model for predicting the workspace of such kind of flexure based platforms by assuming that their workspace is mainly constrained by the deformation of flexure joints. We first study the maximum deformation including bending and torsion angles of each flexure joint. We then derive the inverse kinematics and calculation of bending and torsion angles of this compliant platform. To obtain the workspace of the mechanism, we developed a computational algorithm that varies the displacement of the top platform to extreme positions till the deformation of any flexure exceeding a maximum value. To demonstrate this approach, we provided example studies including constant orientation workspace and constant position workspace. We compare results with a finite element model of the entire platform. The error is 4.74% for original analytical model and 8.26% for simplified analytical model. This model is beneficial in guiding design engineers in maximizing workspace of flexure based parallel compliant mechanisms. To the end-users of the positioner, it gives them a guidance on how to efficiently exploit the workspace of the nanopositioner.

An Analytical Model for Calculating the Workspace of a Flexure Hexapod Nanopositioner

2013 ◽  
Vol 5 (4) ◽  
Author(s):  
Hongliang Shi ◽  
Hai-Jun Su
Keyword(s):  
Analytical Model ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Parallel Mechanisms ◽  
Torsion Angles ◽  
Maximum Deformation ◽  
Practical Applications ◽  
Six Degrees Of Freedom ◽  
Workspace Analysis ◽  
Flexure Joints

This paper presents an analytical model for calculating the workspace of a flexure-based hexapod nanopositioner previously built by the National Institute of Standards and Technology (NIST). This nanopositioner is capable of producing high-resolution motions in six degrees of freedom by actuating linear actuators on a planar tri-stage. However, the workspace of this positioner is still unknown, which limits its uses in practical applications. In this work, we seek to derive a kinematic model for predicting the workspace of such kinds of flexure based platforms by assuming that their workspace is mainly constrained by the deformation of flexure joints. We first study the maximum deformation including bending and torsion angles of an individual flexure joint. We then derive the inverse kinematics and calculation of bending and torsion angles of each wire flexure in the overall mechanism with given position of the top platform center of the hexapod nanopositioner. At last, we compare results with finite element models of the entire platform. This model is beneficial for workspace analysis and optimization for design of compliant parallel mechanisms.

Circular-Hinge Line Element for Finite Element Analysis of Compliant Mechanisms

2005 ◽  
Vol 127 (4) ◽  
pp. 766-773 ◽  
Author(s):  
Nicolae Lobontiu ◽  
Ephrahim Garcia
Keyword(s):  
Finite Element ◽  
Line Element ◽  
Compliant Mechanisms ◽  
Rectangular Cross Section ◽  
Constant Width ◽  
Element Model ◽  
Element Analysis ◽  
Finite Element Software ◽  
Total Potential ◽  
Six Degree Of Freedom

A three-node six degree-of-freedom per-node line element that is sensitive to axial, bending, and torsional loading is introduced to model single-axis right circular hinges of constant width that are utilized in compliant mechanisms. The Timoshenko model is applied for bending because this particular configuration is virtually short, and provisions are taken that the element is shear-locking free. The Saint Venant theory, which includes warping, is utilized to model torsion of the variable rectangular cross-section circular hinge. The principle of minimum total potential energy is employed to formulate the elemental stiffness and mass matrices, as well as the elemental nodal vector. Static force deflection and modal simulation that are performed based on this finite element model produce results that are in agreement with simulation by commercially available finite element software. The three-node line element is also compared to an analytical model in terms of stiffness and the results are again concurring.

Zero Gravity Validation of Smart Aperture Antennas

1999 ◽  
Author(s):  
Hwan-Sik Yoon ◽  
Gregory Washington
Keyword(s):  
Spherical Shell ◽  
Analytical Model ◽  
Stress Function ◽  
Spherical Shape ◽  
Element Model ◽  
Shallow Spherical Shell ◽  
Zero Gravity ◽  
Governing Equations ◽  
Homogeneous Solutions ◽  
Calculated Stress

Abstract In this study, a smart aperture antenna of spherical shape is modeled and experimentally verified. The antenna is modeled as a shallow spherical shell with a small hole at the apex for mounting. Starting from five governing equations of the shallow spherical shell, two governing equations are derived in terms of a stress function and the axial deflection using Reissner’s approach. As actuators, four PZT strip actuators are attached along the meridians separated by 90 degrees respectively. The forces developed by the actuators are considered as distributed pressure loads on the shell surface instead of being applied as boundary conditions like previous studies. This new way of applying the actuation force necessitates solving for the particular solutions in addition to the homogeneous solutions for the governing equations. The amount of deflections is evaluated from the calculated stress function and the axial deflection. In addition to the analytical model, a finite element model is developed to verify the analytical model on the various surface positions of the reflector. Finally, an actual working model of the reflector is built and tested in a zero gravity environment, and the results of the theoretical model are verified by comparing them to the experimental data.

Effect of End Rubber Gasket on the Performance of Parabolic Leaf Spring

2020 ◽  
Author(s):  
Junhong Zhang ◽  
Feiqi Long ◽  
Hongjie Jia ◽  
Jiewei Lin
Keyword(s):  
Ride Comfort ◽  
Orthogonal Experiment ◽  
Element Model ◽  
Considerable Effect ◽  
Leaf Spring ◽  
Static Stiffness ◽  
Rubber Gasket ◽  
Maximum Deformation ◽  
Leaf Springs ◽  
Parabolic Leaf Spring

Abstract Leaf springs play an important role in the handling stability and ride comfort of vehicle. End rubber gaskets are widely used to reduce the friction between leaves, but they also have considerable effect on the stiffness of the suspension assembly. The ride comfort may deteriorate with the stiffness of leaf spring changes. In this paper the influence of the end rubber gasket on the static stiffness performance of a parabolic leaf spring is studied. A finite element model of the leaf spring is developed and verified against the static stiffness test. Effects of the end rubber gasket parameters on the static stiffness of the leaf spring are analyzed based on an orthogonal experiment. The sensitivities of the five parameters are identified including the width, the length, the end thickness, the tail thickness and the distance to the end of the middle leaf. It is found that the contributions can be ranked in descending order as the tail thickness, the end thickness, the distance from end rubber gasket to the end of Leaf 2, and the width and length. The first two factors are considered of significant effects on the leaf spring stiffness. According to single-factor analysis, it is found that under the same load, as the tail thickness and the end thickness increase, the maximum deformation of the rubber gasket decreases, the stiffness of the rubber gasket increases, and the stiffness of the leaf spring increases, which provides a reference for the forward design of the end rubber gasket and the stiffness matching of leaf springs.

A New Self-Adjusting CVT Configuration Using Compliant Mechanisms

2002 ◽  
Author(s):  
Myles T. Christensen ◽  
Spencer P. Magleby ◽  
Larry L. Howell ◽  
Robert H. Todd ◽  
Clint Mortensen
Keyword(s):  
Analytical Model ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Continuously Variable Transmission ◽  
Special Design ◽  
Design Considerations ◽  
Variable Transmission

This paper introduces a new configuration of a Continuously Variable Transmission (CVT) that is self-adjusting and designed as a compliant mechanism. This new configuration is called the Pivot-Arm CVT. The criteria for classification as a Pivot-Arm CVT is discussed. An analytical model describing the performance of the Pivot-Arm CVT is developed. Special design considerations which may be useful in implementing Pivot-Arm CVTs are introduced and explained. The Pivot-Arm CVT model is validated through controlled testing of two Pivot-Arm CVT prototypes.

scholarly journals Co-Simulation of an Inverter Fed Permanent Magnet Synchronous Machine

2014 ◽  
Vol 6 (1) ◽  
pp. 19-25
Author(s):  
Gergely Máté Kiss ◽  
István Vajda
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Analytical Model ◽  
Element Model ◽  
Electrical Machine ◽  
Permanent Magnet Synchronous Machine ◽  
Variable Speed ◽  
Analytical Variable ◽  
Drive Model ◽  
The Finite Element Model

Abstract Co-simulation is a method which makes it possible to study the electric machine and its drive at once, as one system. By taking into account the actual inverter voltage waveforms in a finite element model instead of using only the fundamental, we are able to study the electrical machine's behavior in more realistic scenario. The recent increase in the use of variable speed drives justifies the research on such simulation techniques. In this paper we present the co-simulation of an inverter fed permanent magnet synchronous machine. The modelling method employs an analytical variable speed drive model and a finite element electrical machine model. By linking the analytical variable speed drive model together with a finite element model the complex simulation model enables the investigation of the electrical machine during actual operation. The methods are coupled via the results. This means that output of the finite element model serves as an input to the analytical model, and the output of the analytical model provides the input of the finite element model for a different simulation, thus enabling the finite element simulation of an inverter fed machine. The resulting speed and torque characteristics from the analytical model and the finite element model show a good agreement. The experiences with the co-simulation technique encourage further research and effort to improve the method.

scholarly journals Terrain-Perception-Free Quadrupedal Spinning Locomotion on Versatile Terrains: Modeling, Analysis, and Experimental Validation

2021 ◽  
Vol 8 ◽  
Author(s):  
Hongwu Zhu ◽  
Dong Wang ◽  
Nathan Boyd ◽  
Ziyi Zhou ◽  
Lecheng Ruan ◽  
...  
Keyword(s):  
Motion Tracking ◽  
Center Of Mass ◽  
Kinematic Model ◽  
Linear Quadratic Regulator ◽  
Small Scale ◽  
Small Range ◽  
Linear Quadratic ◽  
Stability Margins ◽  
Uneven Terrain ◽  
Quadruped Robots

Dynamic quadrupedal locomotion over rough terrains reveals remarkable progress over the last few decades. Small-scale quadruped robots are adequately flexible and adaptable to traverse uneven terrains along the sagittal direction, such as slopes and stairs. To accomplish autonomous locomotion navigation in complex environments, spinning is a fundamental yet indispensable functionality for legged robots. However, spinning behaviors of quadruped robots on uneven terrain often exhibit position drifts. Motivated by this problem, this study presents an algorithmic method to enable accurate spinning motions over uneven terrain and constrain the spinning radius of the center of mass (CoM) to be bounded within a small range to minimize the drift risks. A modified spherical foot kinematics representation is proposed to improve the foot kinematic model and rolling dynamics of the quadruped during locomotion. A CoM planner is proposed to generate a stable spinning motion based on projected stability margins. Accurate motion tracking is accomplished with linear quadratic regulator (LQR) to bind the position drift during the spinning movement. Experiments are conducted on a small-scale quadruped robot and the effectiveness of the proposed method is verified on versatile terrains including flat ground, stairs, and slopes.

Statics Analysis of Integral Impeller Based on Finite Element

2013 ◽  
Vol 753-755 ◽  
pp. 1124-1127
Author(s):  
Li Da Zhu ◽  
Shuai Xu ◽  
Wen Wen Liu ◽  
Ji Jiang Wu ◽  
Jian Shi ◽  
...  
Keyword(s):  
Finite Element ◽  
Element Model ◽  
Stress And Strain ◽  
Total Deformation ◽  
Suction Surface ◽  
Maximum Deformation ◽  
Blade Tip ◽  
Tip Position ◽  
Element Theory ◽  
The Finite Element Model

Aim at the problem of machining integral impeller, a method of using finite element theory to carry out the statics analysis of impeller in this paper is studied. The finite element model is established, and then the nephogram of the impeller stress, strain and total deformation are obtained. The result is attained: in the case of impeller rotation and statics load, the maximum of stress and strain occur at the root of suction surface, the maximum of total deformation occurs on the blade tip position of suction surface, while the maximum deformation position has not changed, which increases with the increasing of rotation and statics load. The data results provide a theoretical reference for the machining of integral impeller.

Modelling of 4H-SiC VJFETs with Self-Aligned Contacts

2016 ◽  
Vol 858 ◽  
pp. 913-916 ◽  
Author(s):  
Konstantinos Zekentes ◽  
Konstantin Vassilevski ◽  
Antonis Stavrinidis ◽  
George Konstantinidis ◽  
Maria Kayambaki ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Analytical Model ◽  
Element Model ◽  
Experimental Results ◽  
Compact Model ◽  
Channel Lengths ◽  
The Finite Element Model

Purely vertical 4H-SiC JFETs have been modeled by using three different approaches: the analytical model, the finite element model and the compact model. The results of the modeling have been compared with experimental results on a series of fabricated self-aligned devices with two different channel lengths (0.3 and 1.1μm) and various channel widths (1.5, 2, 2.5, 3, 4 and 5 μm). For all the considered models I-V and C-V characteristics could be satisfactorily simulated.

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