Accuracy Improvement of Multi-Axis Systems Based on Laser Correction of Volumetric Geometric Errors

Teleshevsky, V. I.; Sokolov, V. A.; Pimushkin, Ya.I.

doi:10.1088/1742-6596/998/1/012034

Cited by 2 publications

(1 citation statement)

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“…Multi-axis systems with software-controlled movement of units and mechanisms are a an important part of modern mechanical engineering, in terms of both the technological equipment (machine tools, industrial robots) and measuring technologies (coordinate measuring machines). Highly efficient use of such systems at the moment is no longer possible without a systemic increase in the volumetric accuracy (VA) of the actuator equipment, that reflects the ability to accurately reproduce complex three-dimensional surfaces with a measuring tip or cutting edge of a tool [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

Solution of the Rodriguez Equation in Modeling Volumetric Geometric Accuracy of Multi-Coordinate Systems

Stebulyanin

Pimushkin

2021

EPJ Web Conf.

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The article describes the solution to the Rodrigues equation for determining the volumetric accuracy of multi-axis CNC-controlled systems. An algorithm for calculating the position of the axis of a rotary kinematic pair in problems of volumetric accuracy of mechanical motion of a portal-type system with an additional pair of rotation. The algorithm is based on the analytical solution of the Rodrigues equation in the inverse problem of finding the vector of the final rotation of the known modulus from the known initial and final values of the characteristic vector of the rotated rigid body. In contrast to the well-known direct problem, where based on a finite rotation vector known in direction and magnitude, and the initial value of the characteristic vector of a body, its final value is found, the inverse problem of the Rodrigues equation is not that common due to the nonlinearity and need to solve a nonlinear coupled system of second order equations. The results of this work make it possible to expand the dimension of the space of generalized coordinates of the system analyzed for the volumetric accuracy from three to four. This is expected contribute to the development of ultra-precise systems of controlled mechanical movement. The analytical results of this study were verified by comparing with numerical solutions of the inverse problem in Maple.

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Section: Introductionmentioning

confidence: 99%