Error Analysis Of Mechanism Research Articles

High-Order B-Spline Finite Difference Approach for Schrodinger Equation in Quantum Mechanics

This paper presents a new numerical method for solving the quantum mechanical complex-valued Schrodinger equation (CSE). The technique combines a second-order Crank-Nicolson scheme based on the finite element method (FEM) for temporal discretisation with nonic B-spline functions for spatial discretisation. This method is unconditionally stable with the help of Von-Neumann stability analysis. To verify our methodology, we examined an experiment utilising a range of error norms to compare experimental outcomes with analytical solutions. Our investigation verifies that the suggested approach works better than current methods, providing better accuracy and efficiency in quantum mechanical error analysis.

Analysis of Mechanical Error in Spherical Geneva Mechanism - A Stochastic Approach by

Analysis of Mechanical Error in Spherical Geneva Mechanism - A Stochastic Approach by

Grammatical and Mechanical Error Analysis as Tool in Writing Improvement Program for Student Journalists

This study aimed to develop a writing improvement program for student journalists in one elementary school in the Philippines. It utilized a case study approach using errors analysis in English written tasks of the target participants. Written tasks were used as main instrument in this study. A total of twelve (12) student journalists who were chosen purposively served as participants. Results show that subject-verb agreement is the most committed error followed by usage of a preposition, tenses, word order, and the last on the ranks involved pronouns. Capitalization ranked first among the three common mechanical errors identified in this study followed by punctuation and spelling Based on these results, a writing improvement program for student journalist was developed. Through this study, root causes of participants’ poor writing were analyzed. While through the study’s output, student-journalists may develop a reasonably good writing skill in English language.

Kinematic and mechanical error analysis of serial spherical linkages using a modular approach

Although spherical mechanisms have been widely implemented in medical and industrial fields, there still lacks a simple and systematic approach for analyzing their kinematics and mechanical errors. Therefore, the purpose of this paper is to provide a modular approach for kinematic and mechanical error analysis of serial spherical mechanisms that can be decomposed into predefined modules. Firstly, the forward and inverse kinematics, described by rotation matrices, of the spherical serial manipulator are derived. Besides, the error propagations of the spherical serial manipulator are formulated based on the derived kinematic equations. The derived algorithms are programed into subroutines to analyze the kinematics and mechanical error of a serial spherical linkage by analyzing each of its substructures as the illustrative examples have shown. Until now, the presented module in this paper is applicable to a variety of serial spherical mechanisms, and the feasibility of this method adopting high-class modules will be explored in the future.

A Modular Method for Mechanical Error Analysis of Planar Linkages Composed of Class II Assur Group Kinematic Chains

Abstract This paper presents a modular method for the mechanical error analysis of complex planar linkages. The topology of the linkage under investigation is decomposed into several class II Assur group kinematic chains (AGKCs) combined in a given sequence. Therefore, the mechanical error of the whole linkage can be analyzed by investigating the error propagations of adopted AGKCs in successive order. Because class II AGKCs are first served as modules, the mechanical error equations of these AGKCs in terms of each error in link lengths and joint variables can be pre-formulated and embedded in form of subroutines in any programmable language. Once the AGKCs constituting the linkage topology are identified, the corresponding subroutines are introduced to compute the error propagations in the linkage. Therefore, the presented modular approach can facilitate the analysis by concentrating on the topology decomposition instead of the algebraic derivation. Numerical examples are provided to illustrate the advantage and flexibility of the modular approach.

Analysis of Mechanical Error’s Effect on the Measurement Accuracy of the Six-Axis Force Sensor

Force sensor based on the six degree of freedom (6-DoF) Stewart platform is universal for wide applications. Mechanism errors are significant for its measuring accuracy. However, because of the multi-variables and the complicated forms, it is difficult to solve the expression directly. The Monte Carlo method is proposed based on the analysis of the system structure and the mathematical model. The effect of mechanism errors on the measurement accuracy was assessed. With this method, a complex accuracy expression of the sensor could be avoided. It also provided a theoretical basis for designing the sensor of the Stewart platform.

Error Analysis of Mechanism with Clearances and Fuzzy Control

The mechanism with clearance is a nonlinear system, then using classical control theory and modern control theory cannot obtain satisfactory control effect. Therefore，In order to control the nonlinear error cause by clearance, the conventional fuzzy control and parameter self-regulation fuzzy control are considered by using the fuzzy control’s humanization and intelligent. The results of test show that: the nonlinear error got smaller and the stability of system got obvious improvement as the introduction of intelligent control system.

Analysis of mechanical error in a fused deposition process using a stochastic approach

A stochastic model has been developed for studying the mechanical error in different rapid prototyping (RP) processes. Tolerances and clearances, which cause mechanical error, have been assumed to be random variables. The coordinates of a point on the work surface traced by the laser beam or the tip of the extruder head is expressed as a function of the random variables involved in the process. Using a unified approach for the RP processes, the mechanical error in the fused deposition process is analysed. In a numerical example, the mechanical error has been found for a grid of points traced by the nozzle tip. The three-sigma bands of the error in tracing example curves are plotted. This is the band in which the nozzle tips of 99.73% of machines, produced on a mass scale, lie for the given tolerances and clearances. Stringent values of tolerances and clearances reduce the error at the nozzle tip, but the cost of manufacturing and assembling the machines may become prohibitive.

Predicting the effects of dimensional and material stiffness variations on a compliant bistable microrelay performance

In this paper we investigate the effects of dimensional and material stiffness variations on a microrelay performance. A linear displacement bistable micromechanism is modelled by pseudo-rigid-body model method and fully characterized. To find the effects of dimensional and material stiffness variation, an analysis of mechanical error is used. The method is a stochastic one and takes into account the random nature of variations. Variations of the contact force and required power of a microrelay example is obtained by the method introduced and the performance of the microrelay is determined. The method introduced is a simple, effective and general that may be used at the design level.

Mechanical error analysis of disk cam mechanisms with a flat-faced follower

By employing the concept of equivalent linkage, this paper presents an analytical method for analyzing the mechanical errors of disk cam mechanisms with a flat-faced follower. The resulting error equations do not really involve the location of the curvature center of the cam profile, and locating the curvature center of the cam profile is not essential. The resulting errors are significantly affected by the pressure angle, and the smaller pressure angle will result in the smaller mechanical error. In the worst case, owing to the joined effects of various design parameters, the accuracy of the follower motion may degrade considerably. For the oscillating follower case, all acceleration error functions have a sudden change at every beginning and at every end of the motion even though the theoretical follower displacement is cycloidal motion.

Stochastic linkage model of a compliant bistable micromechanism for mechanical error analysis

Microelectromechanical systems (MEMS) that have micromechanisms as actuators involve inaccuracy problems due to joint clearances and link length tolerances. Since compliant bistable micromechanisms have a wide range of applications in MEMS devices, analysis of the mechanical error of these mechanisms is very important. For compliant mechanisms, it is important to consider the effects of cross-sectional shape and material stiffness variations. In this paper, a compliant bistable micromechanism called Young is modeled by a clearance vector concept. Then a stochastic method is used to determine the errors of potential energy, required moment and coupler point position of mechanism. The range of variations of critical moment of the micromechanism to move from one stable point to the other and the displacement of the second stable point of the mechanism are determined. The Monte Carlo simulation shows that the stochastic method yields accurate results. The clearance vector model is easier and more general to use for micromechanisms than previous works.

Interval Approach for the Modeling of Tolerances and Clearances in Mechanism Analysis

It is important to conduct error analysis of assemblies in order to ensure that the manufactured parts satisfy the design specifications. Traditionally, mechanical tolerances and clearances are modeled as random variables and the analysis is conducted using probabilistic methods. In this work, a new approach, based on interval analysis, is presented for the modeling and analysis of tolerances and clearances. The basic procedure of interval analysis involving solution of simultaneous nonlinear equations is described. The application of the approach in the fuzzy error analysis of planar and spatial mechanisms is also outlined. The treatment of the tolerances and clearances of the mechanism as interval numbers leads to a better and a more realistic estimation of the analysis results. Numerical examples are presented to illustrate the computational procedures. The results of the interval analysis, although philosophically different, are compared with those given by the probabilistic method for comparable input data; the differences found in the two sets of results are explained in terms of the basic characteristics of the two methods. This work denotes the first application of interval methods for the modeling of tolerances and clearances and the fuzzy error analysis of mechanisms.

Tolerance Optimization for Mechanisms with Lubricated Joints

This paper addresses an analytical approach to tolerance optimization for planar mechanisms with lubricated joints based on mechanical error analysis. The mobility method is applied to consider the lubrication effects at joints and planar mechanisms are stochastically defined by using the clearance vector model for mechanical error analysis. The uncertainties considered in the analysis are tolerances on link lengths and radial clearances and these are selected as design variables. To show the validity of the proposed method for mechanical error analysis, it is applied to two examples, and the results obtained are compared with those of Monte Carlo simulations. Based on the mechanical error analysis, tolerance optimizations are applied to the examples.

Stochastic Linkage Modeling for Mechanical Error Analysis of Planar Mechanisms*

ABSTRACT This paper addresses stochastic linkage modeling for mechanical error analysis of planar mechanisms. Considering the effects of joint angle variations, the effective link length model is generalized. The generalized model produces more accurate predictions of mechanical errors than the effective link length model. However, the generalization requires more complicated mechanical error analysis. This paper proposes a stochastic model to intuitively consider the effects of tolerances and clearances, based on the clearance vector concept. Stochastic models are applied to typical mechanisms and their results are compared with those of Monte Carlo simulations. The comparison shows that the proposed stochastic model is effective for mechanical error analysis. The clearance vector model yields more accurate results and is easier to use than the generalized effective link length model.

Mechanical Error Analysis and Tolerance Design of A Four-Bar Path Generator With Lubricated Joints

This paper addresses an analytical approach to the mechanical error analysis and tolerance design of a four-bar path generator with lubricated joints. The mobility method is applied to consider lubrication effects and the four-bar path generator is stochastically modeled by using the clearance vector model for methanical error analysis. To show the validity of the proposed method, the mechanical errors obtained by applying the method to a four-bar path generator are compared with those by Monte Carlo simulation. Based on this analytical method, an optimal tolerance design problem is formulated and solved for the four-bar path generator.

Application of the Concept of a sSnsitivity Linkage for the Analysis of Mechanical Error in 4-Bar Mechanism

Application of the Concept of a sSnsitivity Linkage for the Analysis of Mechanical Error in 4-Bar Mechanism

Error Analysis of Cam-Follower Systems: A Probabilistic Approach

The actual output kinematic characteristics of a cam-follower system will be different from the theoretical (desired) ones due to errors in manufacture and assembly. A method of evaluating the mechanical error in the kinematic response of cam-follower systems is presented using a stochastic approach. The tolerances on cam profiles and other geometrical parameters are treated as random variables that influence the mechanical error. The equations necessary for the mechanical error analysis of a planar cam-follower system (disc cam with translating roller follower) are derived. The equations for a spatial cam-follower system (globoidal cam with oscillating cylindrical follower) are also given at the end. An optimal synthesis procedure is outlined for the allocation of tolerances so as to minimize the manufacturing costs while satisfying a constraint on the maximum mechanical error in the kinematic response of cam-follower systems. The application of analysis and synthesis procedure is demonstrated with reference to a disc cam with translating roller follower.

Synthesizing linkages with minimal structural and mechanical error based upon tolerance allocation

Methods to synthesize linkages with minimum structural error have been reported extensively while the work reported on the mechanical error analysis and synthesis of linkages is scanty. All these methods are indirect approach to the problem. The present work suggests a direct method for minimizing the structural error together with the mechanical error due to manufacturing tolerances on the link dimensions, which are assumed random in nature and follow normal distribution. Also allocation of tolerances to limit the mechanical error below a specified value is explained and illustrated.

Mechanical Error Analysis of Spatial Linkages

In this paper the effect on the output error of function-generating spatial linkages due to tolerances on the links and clearances at the hinges is analyzed. Tolerances on link lengths are assumed to be normally distributed. For the clearance error in spherical, prismatic, and revolute joints, uniform probability density function is assumed. However, the models developed and the analysis procedure proposed can be used for any other probability density function including the mean and variance values derived from experimental information. A synthesis procedure to allocate tolerances and clearances on different members of linkages to restrict the output error within specified units is developed. Results of analysis and synthesis are given for two example problems involving RRSS and RSSR mechanisms.

A Systematic Analysis of Planar Multilink Mechanisms

Considering the Mechanisms to be constructed with several kinds of basic open chains, the relative displacements of links in each basic open chain and the connecting conditions of the open chains have been generally described by the transformation functions. The transformation functions enable the systematic displacement analysis of planarmultilink mechanisms without the derivation of displacement equations. In the analysis, all of the possible motions can be separately evaluated in correspondence with the conjugate positions of mechanisms. The method has been applied also to the error analysis of mechanisms.