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Title of the article ANALYTICAL APPROACH TO DETERMINING THE ANGULAR COORDINATES OF LINKS OF PLANETARY MECHANISMS
Authors

PROTASENYA Oleg N., Ph. D. in Eng., Assoc. Prof., Associate Professor of the Department “Mechanical Engineering and Machine Parts”, Belarusian National Technical University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

KALINA Alla A., Ph. D. in Eng., Assoc. Prof., Head of the Department “Mechanical Engineering and Machine Parts”, Belarusian National Technical University, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.
In the section GENERAL ISSUES OF MECHANICS
Year 2026
Issue 1(74)
Pages 23–30
Type of article RAR
Index UDK 621.8
DOI https://doi.org/10.46864/1995-0470-2026-1-74-23-30
Abstract The article considers the generally accepted kinematic theory of calculation of planetary mechanisms, based on the principle of equivalence of the real and reversed mechanisms (Willis method). The paper proposes evaluation criteria (relative angular velocity of the satellite; number of satellite teeth engaged with the central wheel per unit of time) that prove, using specific examples of calculating a planetary mechanism and its reversed versions (planetary with zero inversion and differential with arbitrary inversion), the equivalence of the real kinematic scheme and its virtual states. A universal equation is also provided for determining the rotation angles of the satellite during one revolution of the sun gear. An algorithm is given for distributing circumferential forces and their reactions in the engagement of the satellite and central wheels based on the Archimedean lever. The paper considers the issues of complex rotational motion of a planetary mechanism’s satellite, determines the relative and absolute gear ratios between the mechanism’s links, and calculates the satellite’s force balance.
Keywords planetary series, differential mechanism, Willis method for planetary gears, relative angular velocity, law of lever forces
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