MATHEMATICAL MODEL OF MECHANICAL SYSTEM WITH ROLLER-RECIRCULATING MECHANISM ON BASIS OF RAUSES EQUATIONS
Abstract
Roller-recirculating mechanisms have found wide application in engineering. Design peculiarities of these mechanisms permit not only to transform one type of motion to another but also to control an actuator in the process of operational motions. Analysis and synthesis of transitional processes of such system are possible only on the basis of correct dynamic and mathematical model. The paper of the paper is to develop a mathematical model of roller-recirculating mechanisms transforming a rotary motion to a reciprocating one. The dynamic model of the considered mechanism is presented by the system of two generalized links of reduction, forming non-holonomic kinematics pair that admits two independent motions with two requirements of non-integrated connections. While formulating motion equations equations of non-holonomic mechanics in the form of Rauses equation have been used. The Rauses equation is a combination of Lagranzhs methods of generalized coordinates and indeterminate multipliers. As a result of it a mathematical model of the investigated object is obtained in the form of two differential equations with variable factors.
References
1. Uhing J. Rolling nut for transforming a rotary movement of a shaft into a thrust movement of the rolling unit. United States Patent № 4,614,124. U.S. Cl. 74/89, 74/25, Int. Cl. F16H 21/16. Date of Patent: Sept. 30, 1986.
2. Насонова, Л. С. Уравнения движения машинного агрегата с валико-кольцевым механизмом, преобразующим вращательное движение в поступательное / Л. С. Насонова // Машиностроение… (Изв. высш. учеб. заведений). – 1975. – № 4. – С. 52–55.
Review
For citations:
Lapanovich I.O. MATHEMATICAL MODEL OF MECHANICAL SYSTEM WITH ROLLER-RECIRCULATING MECHANISM ON BASIS OF RAUSES EQUATIONS. Science & Technique. 2008;(2):23-25. (In Russ.)
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