Improving the Positioning Accuracy of a Multi-Link Parallelogram Mechanisms

Abstract

The object of study is a pantograph mechanism of packaging equipment designed for the synchronous movement of multiple carriages along guides. The mechanism structure consists of serially connected parallelogram sections, where motion is transmitted through a system of hinged joints.

The research problem relates to the decrease in carriage positioning accuracy due to clearances in the hinged joints of the multi-link mechanism. In mechanisms with a large number of sections, even minor clearances lead to progressive error accumulation and deviations of the actual carriage position from the calculated one, which is critical for reconfigurable dosing lines.

The study investigates the influence of joint clearances on the kinematic characteristics of the pantograph mechanism. A compr-

?hensive approach was applied to analyze accuracy, including: mathematical modeling for analytical kinematic description using the vector loop method; geometric modeling in a CAD system, which allowed for the determination of limiting carriage deviations upon reaching the physical clearance limits in joints; and a full-scale experiment using a physical prototype. It was established that for a five-section mechanism, the maximum positioning deviation is 9–12 mm, caused by the sequential summation of backlashes in the kinematic pairs.

The results obtained show that the error magnitude increases non-linearly depending on the section opening angle. A comparison of the mathematical modeling results and the geometric CAD modeling data demonstrated high convergence (with deviations within 6.4–8.2%). It was established that a symmetrical arrangement of sections relative to the central point of the mechanism provides partial compensation for accumulated errors and allows for a two-fold reduction in the total carriage position deviation compared to a one-sided linkage scheme.

A distinctive feature of this study is the comprehensive approach combining analytical methods, numerical modeling, and physical experimentation, which enabled the identification of error accumulation patterns and the justification of conditions for their minimization. The proposed methodology allows for the elimination of accuracy constraints during the design phase for mechanisms containing up to 6 actuating units.

The obtained results were used in the analysis of the pantograph mechanism design for packaging equipment and can be applied during the design and modernization of complex multi-link systems where high-precision synchronous movement of multiple working elements is required.