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A circle C of radius 2r has its center at the origin. A circle of radius r rolls without slipping in the counterclockwise direction around C. A point P is located on a fixed radius of the rolling circle at a distance b from its center, 0

A circle C of radius 2r has its center at the origin. A circle of radius r rolls without slipping in the counterclockwise direction around C. A point P is located on a fixed radius of the rolling circle at a distance b from its center, 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A circle C of radius 2r has its center at the origin. A circle of radius r rolls without slipping in the counterclockwise direction around C. A point P is located on a fixed radius of the rolling circle at a distance b from its center, 0<b<r. Let L be the line from the center of C to the center of the rolling circite and be the angle that L makes with the positive x-axis. Using t as a parameter we will see in a video (coming soon) that parametric equations of the path traced out by P are x(t) = 3r cost + b cos 3t and y(t) = 3r sint + b sin 3t. In most rotary engines the sides of the equilateral triangle (the rotor) are replaced by arcs of circles centered at the opposite vertices, thus the diameter of the rotor is constant. Show that the rotor will fit in the epitrochoid if b ≤ 3/2 (2 - √3)r
Transcribed Image Text:A circle C of radius 2r has its center at the origin. A circle of radius r rolls without slipping in the counterclockwise direction around C. A point P is located on a fixed radius of the rolling circle at a distance b from its center, 0<b<r. Let L be the line from the center of C to the center of the rolling circite and be the angle that L makes with the positive x-axis. Using t as a parameter we will see in a video (coming soon) that parametric equations of the path traced out by P are x(t) = 3r cost + b cos 3t and y(t) = 3r sint + b sin 3t. In most rotary engines the sides of the equilateral triangle (the rotor) are replaced by arcs of circles centered at the opposite vertices, thus the diameter of the rotor is constant. Show that the rotor will fit in the epitrochoid if b ≤ 3/2 (2 - √3)r
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