Parasitic Error Research Articles

An efficient formulation for linear and geometric non-linear membrane elements

Utilizing the straingradient notation process and the free formulation, an efficient way of constructing membrane elements will be proposed. This strategy can be utilized for linear and geometric non-linear problems. In the suggested formulation, the optimization constraints of insensitivity to distortion, rotational invariance and not having parasitic shear error are employed. In addition, the equilibrium equations will be established based on some constraints among the strain states. The authors' technique can easily separate the rigid body motions, and those belong to deformational motions. In this article, a novel triangular element, named SST10, is formulated. This element will be used in several plane problems having irregular mesh and complicated geometry with linear and geometrically nonlinear behavior. The numerical outcomes clearly demonstrate the efficiency of the new formulation.

Design principle of high-precision flexure mechanisms based on parasitic-motion compensation

In design of flexure mechanism, diminishing the parasitic-motion is a key point to improve the accuracy. However, most of existing topics concentrate on improving the accuracy of linear-motion flexure mechanisms via compensating the parasitic error, but few research the multi-dimensional flexure mechanisms. A general design principle and method for high-precision flexure mechanisms based on the parasitic-motion compensation is presented, and the proposed method can compensate the parasitic rotation in company with translation, or the parasitic translation in company with rotation, or both. The crucial step for the method is that the parasitic motion of a flexure mechanism is formulated and evaluated in terms of its compliance. The overall compliance matrix of a general flexure mechanism is formulated by using screw theory firstly, then the criteria for the parasitic motions is introduced by analyzing the characteristics of the resultant compliance matrix as well as with aid of the concept of instantaneous rotation center. Subsequently, a compliance-based compensation approach for reducing parasitic-motion is addressed as the most important part. The design principles and procedure are further discussed to help with improving the accuracy of flexure mechanisms, and case studies are provided to illustrate this method. Finally, an analytical verification is provided to demonstrate that the symmetry design philosophy widely used in flexure design can effectively improve accuracy in terms of the proposed method. The proposed compensation method can be well used to diminish the parasitic-motion of multi-dimensional flexure mechanisms.

A robust triangular membrane element

To analyze the plane problem with irregular mesh and complicated geometry, it is helpful to utilize the triangular element. In this study, several optimization criteria will be elaborated. By utilizing these provisions and satisfying the equilibrium conditions, a novel triangular element, named SST, is developed. To demonstrate the high accuracy and efficiency of the new element, a variety of structures will be solved. The findings will prove that the presented element has a low sensitivity to the geometric distortion. Moreover, the parasitic shear error will not arise when this element is employed. In addition to these, the proposed element is rotational invariant. Comparison studies will reveal that the SST element is more robust than the other well-known triangular ones.

Electrical capacitance of bean (Vicia faba) root systems was related to tissue density—a test for the Dalton Model

The capacitance method offers a rapid and non-destructive method for root measurement. We tested a four terminal (4 T) capacitance (C, Farads) measurement circuit, which removes parasitic errors. We also tested the plausibility of Dalton Model’s assumptions that roots act as cylindrical capacitors and that their entire length contributes to measured C. Faba bean (Vicia faba) was grown in sand and harvested at different ages to determine fresh root mass. Length and radii were determined using scanning software. Tissue density ρ was determined from observing buoyancy in water and from scanned dimensions. Relative permittivity e r was calculated using an empirical model fitted to the data. Parasitic errors were small. C was a poor predictor of root dimensions. An empirical model L ∝ (C/ρ k )m, was a reasonable predictor (R2 = 0.56; P < 0.05) of root length L and was not related to root allometry. This relation also allowed calculation of a plausible average value of e r . The well-watered conditions ensured that contact resistances were low. It appeared that the entire root system was contributing to measured C and average calculated e r was plausible for cortex tissue, if roots were assumed to be cylindrical capacitors (i.e. the Dalton Model)

Formulating an effective generalized four-sided element

Abstract A new four-sided element is proposed for plane stress and strain problems. This generalized shape element is formulated based on the strain states. Error assessment, improvement and increase of the efficiency can conveniently be implemented in the suggested approach. The proposed element satisfies equilibrium necessities and produces good results in individual element test. In addition, the optimized stiffness matrix is also obtained by utilizing some important conditions. Insensitivity to the coordinates and aspect ratio, and lack of the parasitic shear errors are some of the specifications of this new generalized four-sided element. The performance of several numerical tests along with comparison between the capabilities of the proposed element and other researchers' well-known elements indicate significant efficiency and accuracy of the new one. The element described in the paper is an incompatible finite element which cannot pass the patch test.

Pure Nano-Rotation Scanner

We developed and tested a novel rotation scanner for nano resolution and accurate rotary motion about the rotation center. The scanner consists of circular hinges and leaf springs so that the parasitic error at the center of the scanner in the X and Y directions is minimized, and rotation performance is optimized. Each sector of the scanner's system was devised to have nano resolution by minimizing the parasitic errors of the rotation center that arise due to displacements other than rotation. The analytic optimal design results of the proposed scanner were verified using finite element analyses. The piezoelectric actuators were used to attain nano-resolution performances, and a capacitive sensor was used to measure displacement. A feedback controller was used to minimize the rotation errors in the rotation scanner system under practical conditions. Finally, the performance evaluation test results showed that the resonance frequency was 542 Hz, the resolution was 0.09 μrad, and the rotation displacement was 497.2 μrad. Our test results revealed that the rotation scanner exhibited accurate rotation about the center of the scanner and had good nano precision.

ESTUDIO DEL ÁNGULO DE GIRO DE ELEMENTOS FLEXIBLES APLICADO A MECANISMOS PARALELOS

ABSTRACT This paper analyses the flexible hinge parasitic error in function of the rotation angle in the 0-45o range. First, an analysis of the different geometries -taking into account considerations such as the stiffness and the rotation angle- is carried out, and a new kinematic model of two degrees of freedom parallel mechanism is developed. This mechanism consists of a exible system that allows us to obtain the azimuth and elevation angles. The model developed is based on the Denavit-Hartenberg method. The kinematic chain containing flexible elements is therefore modelled by adding ransformation matrices that consider the angle and translation error of those elements with respect to the initial reference systems. Subsequently, he flexible hinge geometric parameters are determined, by means of a simulation software based on the finite element method in order to obtain a system that allows us to perform the desired rotations. Finally, the element has been experimentally characterized, for two selected materials: aluminium EN AW-7075 and steel F-1430 and the rotation axis error in function of the rotated angle is obtained. This characterization let us observe which material is more suitable in function of the work range, and know for a particular application, the rotation magnitude that can be achieved with the flexible element in function of the desired accuracy.

A millimeter-range flexure-based nano-positioning stage using a self-guided displacement amplification mechanism

We propose a mechanism for a single-axis flexure-based nano-positioning stage. A self-guided displacement amplification mechanism enables a large range of motion—up to a millimeter—with a compact stage size. Our device has a skewed double-compound parallelogram structure that acts as a motion guide and provides displacement amplification, thereby eliminating a serial connection. Its structural symmetry improves positioning accuracy by reducing parasitic motion error and thermal deformation. A millimeter-range piezo-actuated nano-positioning stage is implemented using the self-guided displacement amplification mechanism. The stage was designed using design optimization frameworks to obtain the highest fundamental resonance frequency under constraints for predetermined travel range, stress, and size. The effectiveness of the proposed mechanism is experimentally verified. Also, we demonstrate that the fabricated stage has superior volume efficency compared to other stages of similar size.

New combination SOC-WCIP method for the analyze of a low pass filter

The combination of the Wave Concept Iterative Process (WCIP) method combined with the Short-Open Calibration SOC technique to micro strip discontinuity is presented. This SOC technique is directly accommodated in the WCIP method. It is used to remove the unwanted parasitic errors brought by the approximation of the impressed voltage sources and the feed lines. The WCIP is formulated in such a way that the port voltages and currents are explicitly represented through relevant network matrices. The scattering parameters of the filter structure can be obtained through the development and the simulation. This result for micro strip discontinuities is compared with the conventional WCIP method. These instructions provide you guidelines for preparing papers for International Journal. Use this document as a template and as an instruction set. Key words: Short open calibration (SOC), wave concept iterative process (WCIP), micro strip discontinuity, third-order filter.

Synthesis of precision serial flexure systems using freedom and constraint topologies (FACT)

Abstract In this paper we introduce the principles necessary to synthesize the complete body of serial flexure system concepts, which satisfy desired design requirements using Freedom and Constraint Topologies (FACT). FACT utilizes a comprehensive library of geometric shapes that represent regions were constraints may be placed for synthesizing flexure systems that possess designer-specified degrees of freedom (DOFs). Prior to the theory of this paper, FACT was limited to the synthesis of parallel flexure systems only. The ability to synthesize serial flexure systems is important because serial flexure systems (i) may possess DOFs not accessible to parallel flexure systems, (ii) exhibit larger ranges of motion, and (iii) enable cancellation of parasitic errors. Geometric shapes that represent motions only accessible to serial flexure systems have been derived and added to the existing body of FACT shapes initially intended for parallel flexure synthesis only. Systematic rules and guidelines have been created that help designers use these shapes to generate every parallel and serial flexure concept that satisfies the desired functional requirements. We demonstrate how to use these shapes to utilize or avoid underconstraint in serial flexure synthesis. A serial flexure system is designed that interfaces the lead screw of a lathe to the carriage that it drives as a case study to demonstrate the theory of this paper.

Corrigendum to “A screw theory basis for quantitative and graphical design tools that define layout of actuators to minimize parasitic errors in parallel flexure systems” [Precis. Eng. 34 (4) (2010) 767–776

Corrigendum to “A screw theory basis for quantitative and graphical design tools that define layout of actuators to minimize parasitic errors in parallel flexure systems” [Precis. Eng. 34 (4) (2010) 767–776

Dynamic Characteristic Analysis and Machining Error Study Based on Solid Vibration Beam Rate Sensor

Machining error of vibration beam rate sensor and its influencing to the performance of solid vibration inertial sensor were studied. The dynamics model was analyzed, and the mechanism error caused by the technology limit was studied and the theory of deducing the error was presented. Numerical calculations combined with 100mm alloyed vibration beam have been made. Results showed that quadrature error is the primary factor of affecting gyro’s performance; the error caused by mass center deviation of vibration beam change with angular acceleration, which can be ignored under the condition that small angular acceleration. The affects of parasitic Coriolis error on performance is minimal, which can be neglected. Finally, the quadrature error’s simulation results were consistent with expected results. The result also proved that restraining and compensating quadrature errors is one of the key technology to increase the performance.

Matching Relationship between Frequency Characteristic and Parasitic Error of Compliant Linear Buffer Mechanism

A novel compliant linear buffer mechanism (CLBM) is designed for impact isolation. In view of the incompatible relationship between frequency characteristic and parasitic error of compliant linear mechanism, the mixed compliant linear mechanism(MCLM) is proposed by combining the Lumped Compliant Mechanism(LCM) and the Distributed Compliant Mechanism(DCM).The topology matrices for four kinds of parallelogram linear compliant mechanisms are built through the method of type synthesis. The characteristic polynominal (CP) for the compliant mechanism matrices[CM] are calculated for the isomorphism detection of compliant mechanism. The finite element analysis (FEA) model of these four kinds of linear compliant mechanism is built to complete numerical analysis on the structure frequency and parasitic error with different sizes, and the relationship between the frequency characteristic and parasitic error of the compliant linear mechanism is found out. MatlabTM software is used to obtain the functional formulas by the method of polynomial curve fitting (PCF) for The FEA results show that the structure configuration of MCLM can achieve a higher structure frequency and a greater kinetic precision over the pure LCM and DCM at the same time, and also indicates that the analysis method of frequency characteristic and parasitic error for compliant mechanism is efficient and should be effective on the structure optimization of the novel CLBM.

A screw theory basis for quantitative and graphical design tools that define layout of actuators to minimize parasitic errors in parallel flexure systems

Abstract In this paper we introduce a visual approach for placing actuators within multi-axis parallel flexure systems such that position and orientation errors are minimized. A stiffness matrix, which links twists and wrenches, is used to generate geometric shapes that guide designers in selecting optimal actuator locations and orientations. The geometric shapes, called actuation spaces, enable designers to (i) visualize the regions wherein actuators should be placed so as to minimize errors, (ii) guide designers in selecting these actuators to maximize the decoupling of actuator inputs, and (iii) determine actuator forces and displacements for actuating specific degrees of freedom. These new principles, the means to practice them, and a comparison of theory verses measured behavior, are demonstrated within a case study.

Stability constraints of active magnetic bearing control systems

Direct Lyapunov stability method is employed to analyse the closed-loop stability of an electromagnetically suspended rotor system in which non-linearity and singular perturbation nature are embedded. Five explicit sets of stability constraints are proposed so that the state feedback loop is not over-designed. Under impact of modeling inaccuracy, due to neglected higher-order terms, stability conditions for equilibrium point, slow-mode manifold and boundary layer are studied. In addition, the singular perturbation order-reduction technique is used to simplify the feedback loop and reduce the order of a state feedback controller. The stability margin can be numerically evaluated as long as the upper bound of the singular perturbation parameter is available. The proposed state feedback controller is verified by intensive computer simulations such that superior performance in terms of stiffness, rise time and overshoot is illustrated, in comparison to output feedback law and deadbeat control. The reported state feedback loop not only stabilizes the inherently unstable open-loop system, but also preserves the robustness with respect to the parasitic parameter variation and modeling error due to neglected higher-order terms of magnetic control force.

Analysis of microstrip discontinuities by FDTD method combined with SOC technique

In this paper, the application of the finite-difference time-domain (FDTD) algorithm combined with the short-open calibration SOC technique to three-dimensional microstrip discontinuity is presented. This SOC technique is directly accommodated in the FDTD algorithm. It is used to remove the unwanted parasitic errors brought by the approximation of the impressed voltage sources and the feed lines. The FDTD is formulated in such a way that the port voltages and currents are explicitly represented through relevant network matrices. This new method is also used to analyze finite periodic structures. The scattering parameters of the whole periodic structure can be approximately obtained through analyzing only one cell of it. The results for microstrip discontinuities and finite periodic structures are compared with the conventional FDTD method.

Impact of Intrinsic Parasitic Extraction Errors on Timing and Noise Estimation

In this letter, we discuss the impact of intrinsic error in parasitic capacitance extraction programs which are commonly used in today's SoC design flows. Most of the extraction programs use pattern-matching methods which introduces an improvable error factor due to the pattern interpolation, and an intrinsically inescapable error factor from the difference of boundary conditions in the electro-magnetic field solver. Here, we study impact of the intrinsic error on timing and crosstalk noise estimation. We experimentally show that the resulting delay and noise estimation errors show a scatter which is normally distributed. Values of the standard deviations will help designers consider the intrinsic error compared with other variation factors.

Constraint-Based Design of Parallel Kinematic XY Flexure Mechanisms

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.

Design and Evaluation of Two Dimensional Metrological Atomic Force Microscope using a Planar Nanoscanner

An atomic force microscope (AFM) using a laser interferometer is regarded as one of the best solutions for the standardization of two dimensional length measurement systems. We propose a new two dimensional (2D) metrological AFM system, which uses an orthogonally decoupled XY scanner and a commercial AFM head. We designed a decoupled planar scanner having minimal parasitic errors, particularly crosstalk errors. The parasitic tilt error was measured and evaluated using an autocollimator. Furthermore, we evaluated the uncertainty of the combined system according to the Guide to the Expression of Uncertainty in Measurement.

Measuring and compensating for 5-DOF parasitic motion errors in translation stages using Twyman–Green interferometry

A new metrological method is presented that performs simultaneous real-time measurements and compensates for 5-DOF parasitic motion errors in translation stages for precision profiling of optical surfaces. Two plane mirrors are used to obtain motion-dependent interferometric fringes generated by the optical principles of Twyman–Green interferometry. The fringes generated are monitored using high-speed 2D photodiode arrays and analyzed to determine the five separate motion error components in real time. Simultaneously, null control is performed to suppress the measured motion errors independently using piezoelectric actuators through real-time feedback control while the machine axis is moving. The experimental results demonstrate that 5-DOF parasitic motion errors are effectively measured and compensated to within 10 nm for translational motions and 0.15 arcsec for angular motions.