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The purpose of this paper is to propose a method for selecting the position and attitude trajectory of error measurement to improve the kinematic calibration efficiency of a one translational and two rotational (1T2R) parallel power head and to improve the error compensation effect by improving the properties of the error identification matrix.

First, a general mapping model between the endpoint synthesis error is established and each geometric error source. Second, a model for optimizing the position and attitude trajectory of error measurement based on sensitivity analysis results is proposed, providing a basis for optimizing the error measurement trajectory of the mechanism in the working space. Finally, distance error measurement information and principal component analysis (PCA) ideas are used to construct an error identification matrix. The robustness and compensation effect of the identification algorithm were verified by simulation and through experiments.

Through sensitivity analysis, it is found that the distribution of the sensitivity coefficient of each error source in the plane of the workspace can approximately represent its distribution in the workspace, and when the end of the mechanism moves in a circle with a large nutation angle, the comprehensive influence coefficient of each sensitivity is the largest. Residual analysis shows that the robustness of the identification algorithm with the idea of PCA is improved. Through experiments, it is found that the compensation effect is improved.

A model for optimizing the position and attitude trajectory of error measurement is proposed, which can effectively improve the error measurement efficiency of the 1T2R parallel mechanism. In addition, the PCA idea is introduced. A least-squares PCA error identification algorithm that improves the robustness of the identification algorithm by improving the property of the identification matrix is proposed, and the compensation effect is improved. This method has been verified by experiments on 1T2R parallel mechanism and can be extended to other similar parallel mechanisms.

The purpose of this paper is to develop a means of the kinematic calibration of a parallel manipulator with full-circle rotation.

An error-mapping model based on the space vector chain is formulated and parameter identification is proposed based on double ball-bar (DBB) measurements. The measurement trajectory is determined by the motion characteristics of this mechanism and whether the error sources can be identified. Error compensation is proposed by modifying the inputs, and a two-step kinematic calibration method is implemented.

The simulation and experiment results show that this kinematic calibration method is effective. The DBB length errors and the position errors in the end-effector of the parallel manipulator with full-circle rotation are greatly reduced after error compensation.

By establishing the mapping relationship between measured error data and geometric error sources, the error parameters of this mechanism are identified; thus, the pose errors are unnecessary to be measured directly. The effectiveness of the kinematic calibration method is verified by computer simulation and experiment. This proposed calibration method can help the novel parallel manipulator with full-circle rotation and other similar parallel mechanisms to improve their accuracy.

The problem of measurement errors in the national accounts has been recognized for a long time. The error chiefly arises from various source data and the timing of the flow of data received from providers. This chapter first discusses the type of measurement errors confronted by statistical agencies. Second, it presents a model of their behavior that illustrates the trade-offs that must be made in dealing with such errors. Third, the chapter discusses how the quality of the estimates can be gauged given measurement error and the inability to conduct standard statistical tests. Although the focus is on the production of U.S. Gross Domestic Product, the principles are applicable to all national statistical agencies.

The coupling impact of hybrid uncertain errors on the machine precision is complex, as a result of which the designing method with multiple independent error sources under uncertainties remains a challenge. For the purpose of precision improvement, this paper focuses on the robot design and aims to present an assembly precision design method based on uncertain hybrid tolerance allocation (UHTA), to improve the positioning precision of the mechanized robot, as well as realize high precision positioning within the workspace.

The fundamentals of the parallel mechanism are introduced first to implement concept design of a 3-R(4S) &3-SS parallel robot. The kinematic modeling of the robot is carried out, and the performance indexes of the robot are calculated via Jacobian matrix, on the basis of which, the 3D spatial overall workspace can be quantified and visualized, under the constraints of limited rod, to avoid the singular position. The error of the robot is described, and a probabilistic error model is hereby developed to classify the hybrid error sensitivity of each independent uncertain error source by Monte Carlo stochastic method. Most innovatively, a methodology called UHTA is proposed to optimize the robot precision, and the tolerance allocation approach is conducted to reduce the overall error amplitude and improve the robotized positioning precision, on the premise of not increasing assembly cost.

The proposed approach is validated by digital simulation of medical puncture robot. The experiment highlights the mathematical findings that the horizontal plane positioning error of the parallel robotic mechanism can be effectively reduced after using UHTA, and the average precision can be improved by up to 39.54%.

The originality lies in UHTA-based precision design method for parallel robots. The proposed method has widely expanding application scenarios in industrial robots, biomedical robots and other assembly automation fields.

The purpose of this paper is to model how geometric errors of a machined surface (or manufacturing errors) are related to locators’ error, workpiece form error and machine tool volumetric error. A kinematic model is presented that puts into relationship the locator error, the workpiece form deviations and the machine tool volumetric error.

The paper presents a general and systematic approach for geometric error modelling in drilling because of the geometric errors of locators positioning, of workpiece datum surface and of machine tool. The model can be implemented in four steps: (1) calculation of the deviation in the workpiece reference frame because of deviations of locator positions; (2) evaluation of the deviation in the workpiece reference frame owing to form deviations in the datum surfaces of the workpiece; (3) formulation of the volumetric error of the machine tool; and (4) combination of those three models.

The advantage of this approach lies in that it enables the source errors affecting the drilling accuracy to be explicitly separated, thereby providing designers and/or field engineers with an informative guideline for accuracy improvement through suitable measures, i.e. component tolerancing in design, machining and so on. Two typical drilling operations are taken as examples to illustrate the generality and effectiveness of this approach.

Some source errors, such as the dynamic behaviour of the machine tool, are not taken into consideration, which will be modelled in practical applications.

The proposed kinematic model may be set by means of experimental tests, concerning the industrial specific application, to identify the values of the model parameters, such as standard deviation of the machine tool axes positioning and rotational errors. Then, it may be easily used to foresee the location deviation of a single or a pattern of holes.

The approaches present in the literature aim to model only one or at most two sources of machining error, such as fixturing, machine tool or workpiece datum. This paper goes beyond the state of the art because it considers the locator errors together with the form deviation on the datum surface into contact with the locators and, then, the volumetric error of the machine tool.

The purpose of this paper is to describe a novel error‐ranking methodology and two compensation strategies for hybrid parallel kinematic machines (HPKMs).

The paper outlines an error analysis methodology developed for HPKMs and applies the technique to a typical industrial HPKM. Based on the results of this, two compensation strategies are developed and implemented, for both mass‐induced and thermal errors.

The paper demonstrates and quantifies the performance improvements possible with appropriate error compensation strategies.

The paper introduces a novel and generic methodology for error source analysis and describes two fully implemented compensation strategies which result in a significantly improved level of system performance.

The purpose of this study is to assess the level and variability of Ghanaian property and liability insurer’s reserve estimates to examine its sources and ascertain if reserve errors are random or not (i.e. manipulated or not).

It uses information on insurer claim reserve provisions, claims outstanding, claims incurred and claims paid for the period of 2000-2010. Categorizing the sources of variation as endogenous and exogenous, the authors use the panel correlated standard error regression model to determine sources and magnitude of industry reserve error.

The study finds that size, age, lag of loss reserve error, inflation rate and real gross domestic product are significant in determining the degree of reserve error variation. Type of ownership (domestic or foreign) is, however, not a significant source of variation. Further, the authors found that industry reserve errors are random (not manipulated) across firms, suggesting that sampled insurers act independently on reserve error decision making and are not influenced by industry trends and competition.

The main research study limitation is the difficulty involved in obtaining annual statements from insurance companies in Ghana. Reluctance of companies to make statements available impeded on the smooth flow of the study during data collection.

Policy-wise, this suggest that regulatory bodies can uniquely set reserve error levels for existing firms with little influence on competition. Further, the Ghanaian insurance regulator does not to focus on the type of ownership (foreign or local) when setting regulatory standards. However, size of the company and age (length of operation) should be considered.

This paper is the first empirical study to examine the loss reserve error and loss reserve variability of Ghanaian property and liability insurance companies.

The purpose of this paper is to contribute to the literature on the determinant factors of government budget balance forecast errors for Eurozone countries based on four different database sources from 1998 to 2011.

Besides the analysis on quality and efficiency of government budget balance projections, panel data analysis is made from different methods taking into account economic, political, institutional and governance factors, and lagged forecast errors for estimations of budget balance forecast errors.

The results show that even with the concern and pressure due to the fiscal crisis in the Eurozone, the bias in fiscal forecasts remains.

One contribution of this paper, in comparison to other studies, is the use of longer time periods for the analysis of forecast errors as well as the employment of different data sources for detecting systematic patterns of errors, and the use of various estimation methods for the fiscal forecast error determinants, which gives insights into the reliability and robustness of results obtained in earlier studies. In particular, the introduction of variables such as fiscal council and fiscal rules allows one to check whether institutional behavior may change the effect from debt on fiscal forecast errors.

One component of revenue forecast error has been attributed to the phenomena of consistent underestimation bias due asymmetrical loss. Because underestimation of revenue forecast results in less loss to forecasters than overestimations, there appears to be a bias for forecasters to underestimate revenue forecasts. This paper confirms this hypothesis. Additionally, with the greater usage of national forecasting organizations that provide economic forecasts on which revenue forecasts are based, a secondary source of forecaster bias may be present in many state level forecasts. This hypothesis is supported by the increase in number of states using such organizations and a decrease in the standard deviation of the annual mean percentage state forecast error.

This chapter draws from an understanding of measurement error to address practical issues that arise in measurement and research design in the day-to-day conduct of research. The topics include constructs and measurement error, the measure development process, and the indicators of measurement error. The discussion covers types of measurement error, types of measures, and common scenarios in conducting research, linking measurement to research design.