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For manually operated machine tools, the accuracy of the machine tool structure limits the accuracy of the parts produced. Such is not necessarily the case with computer numerically controlled (CNC) machine tools. This concept may not be immediately obvious to the engineering undergraduate. The method of error compensation is presented here in a manner that is accessible to the undergraduate engineering student. A homogeneous transformation matrix (HTM) model quantifies the geometric errors of a machine tool, which can be compensated for in software. The mathematical treatment is reduced to only essential elements to emphasize physical understanding. A key feature of this presentation is the application of the model to a three-axis milling machine. This illustration enables the undergraduate student to grasp the concept with ease. Another feature is that the entire model is developed from first principles, which does not require the student to invoke any empirical relationships. Three solved numerical problems illustrate the application of the model to practical situations. Information provided here may be used by the teacher as a template to introduce this subject at the undergraduate level.

Background. The object of the study is the design and configuration control of a manipulator mounted on an unmanned aircraft and designed to carry out individual rescue operations. The purpose of the work is to solve the problem of manipulator configuration management taking into account its design. Materials and methods. The task is reduced to solving direct and inverse kinematics problems. The apparatus of homogeneous transformation matrices and the description of generalized characteristics of the manipulator configuration represented by Denavit-Hartenberg parameters are used. Results. The direct kinematics problem for the manipulator under consideration is solved, including by the method of a recursive algorithm. An algorithm for manipulator configuration control by solving the inverse kinematics problem is proposed. Conclusions. The methods used to solve the problem of manipulator configuration management allow using a manipulator of the proposed design mounted on an unmanned aircraft to carry out rescue operations. The proposed algorithm for manipulator configuration control, which consists in determining the generalized characteristics of the final effector, then determining the generalized characteristics for its parent segments, setting the orientation and position in space of the intermediate effector (in particular, the arm rotation segment of the manipulator) and its parent segments with further setting the orientation and position of its child segments (including the working end of the manipulator), allows you to build the manipulator segments in an optimal configuration, taking into account the conditions of a rescue operation (such as the presence of obstacles in the work area, the orientation and position of the object over which the operation is performed).

Recently, the modelling of variation propagation in multistage machining processes has drawn significant attention. In most of the recently developed variation propagation models, the dimensional variation is determined through kinematic analysis of the relationships among error sources and dimensional quality of the product, represented by homogeneous transformations of the actual location of a product's features from their nominal locations. In design and manufacturing, however, the dimensional quality is often evaluated using Geometric Dimensioning and Tolerancing (GD&T) standards. The method developed in this paper translates the GD&T characteristic of the features into a homogeneous transformation representation that can be integrated in existing variation propagation models for machining processes. A mathematical representation using homogeneous transformation matrices is developed for position, orientation and form characteristics as defined in ANSI Y14.5; further, a numerical case study is conducted to validate the developed methods. [ABSTRACT FROM AUTHOR]

The improvement of the accuracy grade of main components in the production process through balancing between function and cost helps to improve the overall accuracy of machine tools. Therefore, this paper presents an improved value analysis method and uses the method of global sensitivity analysis and geometric error correlation analysis to analyze and optimize the error parameters of a 4-axis machining tool based on the proposed method. The geometric error modeling of the 4-axis machine tool was established by using the homogeneous transformation matrices (HTMs). By using global sensitivity analysis, the degree of influence of each error parameter on the accuracy of machine tool was obtained, and functional coefficient and cost coefficient of value analysis were gained by correlation analysis. An optimization model for geometric error budget of machine tool was established according to the improved value analysis theory, and the machining accuracy of machine tool was optimized according to the improved value analysis method. [ABSTRACT FROM AUTHOR]