Motion of an Articulated Straw Along a Vibrating Rod

H. Takano

Russian journal of nonlinear dynamics, Tome 20 (2024) no. 4, pp. 529-551.

Résumé

When an articulated drinking straw is slid over a rod vibrated by a motor, the straw moves up and down continuously. To clarify the mechanism for this motion, a straw was created that was narrower at the center than at the ends and the mechanism for the up-and-down motion as well as its reversal at the rod’s tip was examined. The angle $\psi$ between the rod and the straw is constant because they are in contact at three points, i. e., at both ends and the center. Therefore, when the straw rotates around the rod, it will move unidirectionally according to the sign of $\psi$. This velocity is determined as a function of the straw half-length and the number of rotations of the nut to which the rod is attached. As the straw rises, the rod’s tip enters the straw, and the ascent stops when $\psi$ reaches zero because the rate of ascent is proportional to $\psi$. The sign of $\psi$ then reverses to start the downward motion, and the straw returns. When it reaches a reflector disk, the sign of $\psi$ reverses again and the straw rises. Experiments were conducted to measure the velocities of three straws with different lengths, and the results showed that the theoretical velocities were greater than the experimental ones. The reason for this is assumed to be that although in theory the straw does not slip at the point of contact between its center and the rod, in reality it does slip. However, the theoretical and experimental velocities decreased in similar ways with increasing straw half-length, and the agreement between them was determined by the relative error. For half-lengths below 1.0 cm, the average agreement was approx. 80 all lengths it was approx. 73 for the effects of slippage between the straw and the rod, the presence of nodes and antinodes of the rod vibration, and deformation in the central portion of straw. Considering these effects, the experimental values support the validity of the mechanistic considerations of the straw motion and the theoretically determined velocity.

Détail

Keywords: articulated straw, vibrating rod, up-and-down motion

Bibliographie

[1] Keijiro Sato: He Is a Composer and Kinetic Artist (1927–2009), His works are in the collection of the Museum of Fine Arts (Gifu, Japan)

[2] Gifu Susuki Clump'99 (Susuki: Pampas Grass), , 1999 www.ntticc.or.jp

[3] Vertical Motion of a Styrofoam Ball Passing through an Oscillating (Orbiting) Rod, , 2023 youtu.be/P52kCnPnn5w

[4] Takano, H.,, Motion of Straws with Different Radii at Both Ends through a Vibrating Rod, in preparation, 2024

[5] Vertical Motion (the Tip of the Rod Is Up), , 2023 youtu.be/kZ4-EjJ-G9I

[6] Horizontal Motion, , 2023 youtube.com/shorts

[7] Vertical Motion (the Tip of the Rod Is Down), , 2023 youtube.com/shorts

[8] Motion of a Straw with a Small Radius at the Center, , 2023 youtu.be/FN1HaecUY7I

[9] Motion of Straws with Different Radii at Both Ends: 1, , 2023 youtu.be/V3JZPwuFig8

[10] Motion of Straws with Different Radii at Both Ends: 2, , 2023 youtu.be/Uh5BtW14dXg

[11] Motion of One Paper Cup, , 2023 youtu.be/RjnxDmwZedY

[12] Motion of Two Paper Cups, , 2023 youtu.be/StdNC-oOB7E

[13] Takano, H., “Analyzing the Motion of a Washer on a Rod”, Regul. Chaotic Dyn., 28:2 (2023), 227–250 | DOI | MR | Zbl

[14] JCRA: Japan Chatter Ring Association, jaringa.web.fc2.com