Visual Measurement and Calibration of Geometric Errors of Rotating Axes for Five-axis Platform

In this paper, a method for identifying and decoupling geometric errors of rotation axes using vision measurement is proposed. Based on screw theory and exponential product formula, identification equations of position-dependent geometric errors (PDGEs) and position-independent geometric errors (PIGEs) of the rotation axes are established. The mapping relationships between the error twist and geometric errors are established. The error model provides the coupling mechanism of PDGEs and PIGEs. Furthermore, a progressive decoupling method is proposed to separate PDGEs and PIGEs without additional assumptions. The pose parameters, required for solving the identification equations, are obtained by visual measurement. Then, the error terms of PIGEs and PDGEs are determined. Lastly, the error calibration of the rotation axes is investigated, thus providing an average rotary table orientation error reduction of 28.1% compared to the situation before calibration.

Conceptual design and error analysis of a cable-driven parallel robot

This paper develops the conceptual design and error analysis of a cable-driven parallel robot (CDPR). The earlier error analysis of CDPRs generally regarded the cable around the pulley as a center point and neglected the radius of the pulleys. In this paper, the conceptual design of a CDPR with pulleys on its base platform is performed, and an error mapping model considering the influence of radius of the pulleys for the CDPR is established through kinematics analysis and a full matrix complete differential method. Monte Carlo simulation is adopted to deal with the sensitivity analysis, which can directly describe the contribution of each error component to the total orientation error of the CDPR by virtue of the error modeling. The results show that the sensitivity coefficients of pulleys’ geometric errors and geometric errors of the cables are relatively larger, which confirms that the cable length errors and pulleys’ geometric errors should be given higher priority in design and processing.

Quantification of geometric errors made simple: application to main-group molecular structures

Nearly all electronic structure simulations begin with obtaining approximate geometries, making a systematic quantification of errors in approximate molecular structures of key importance. Recently, the geometric energy offset (GEO) framework based on a single and natural measure for quantifying and analysing these errors has been proposed [J. Phys. Chem. Lett. 2020, 11, 99579964]. An accurate and way less costly approximation to GEO is utilized here to readily quantify errors in main-group structures and analyze them in a chemically intuitive way. The use of semiexperimental geometries as a reference further simplifies the analysis. The analysis reveals new insights into the geometric performance of methods, new rankings, as well as patterns across different classes of methods and basis sets that arise from the analysis.

Effect of Geometric Error on Friction Behavior of Cylinder Seals

The tribological characteristics of the cylinder directly affect the operation accuracy of the pneumatic servo system. However, the geometric error has a significant effect on its tribological behavior and the related research is insufficient. Thus, the dynamic friction process of rubber seals has been investigated considering the influence of geometric errors. Firstly, based on the self-made friction test platform, the friction force of the rubber seals was studied and the influence law of geometric error on the contact area of the rubber seal ring was revealed. Secondly, the numerical model of the friction and contact of the rubber seals for the cylinder segment was developed by using the finite element simulation method and the influence laws of machining errors, such as roundness and straightness on the friction characteristics, were revealed. Finally, synergy effects of roundness and straightness in the friction behavior of rubber seals considering geometric errors was investigated, which lays a foundation for the accurate prediction of cylinder dynamic mechanical properties.