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- W4361760997 abstract "The design of a closed profile in which the curved elements touch a circle is important for designing the centerline of non-circular wheels. When a polygon rolls along such a profile, its center moves in a circle. If both centers (the center of the curved profile and the center of the polygon) are fixed, then you can roll these figures with simultaneous rotation around their centers. One centroid will be a polygon, and the other will be a constructed closed profile. We consider the rolling of a flat figure in the form of an equilateral polygon along a curved profile. The profile is periodic and is formed by connecting the arc of a symmetric curve in series so that its ends rest on a circle of a given radius. The equation of the curve from which the curved profile is constructed is found provided that the center of the polygon, when it rolls along the profile, must also move in a circle. Rolling occurs in the absence of sliding, so the length of the curve arc is equal to the length of the side of the polygon. To find the equations of the profile curve, a first-order differential equation is written and an analytical solution is obtained. The parametric equations of the curve are obtained in the polar coordinate system. The limits of change in the angular parameter for constructing a profile element that is part of the curve arc are found. The obtained equations are used to construct curved profiles with different numbers of elements. The mathematical relationship between the radius of the circle along which the center of the polygon moves when it rolls and the radius of the described circle of the polygon itself is established." @default.
- W4361760997 created "2023-04-04" @default.
- W4361760997 creator A5090872492 @default.
- W4361760997 date "2021-01-01" @default.
- W4361760997 modified "2023-09-30" @default.
- W4361760997 title "External rolling of a polygon on a closed curved profile" @default.
- W4361760997 doi "https://doi.org/10.31548/machenergy2021.03.113" @default.
- W4361760997 hasPublicationYear "2021" @default.
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