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NEW 375 Lecture13

NEW 375 Lecture13 - INTERACTION OF GEARS If a torque is...

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INTERACTION OF GEARS If a torque is applied at E, both shafts will be twisted. Since end D of shaft AD is fixed, the angle of twist of AD is measured by the angle of rotation φ A of end A.

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INTERACTION OF GEARS Note that equal and opposite forces F and F’ are applied on the two gears at point C. Observe that the arcs CC’ and CC” of the meshed gears must be equal, then: r A φ A = r B φ Β F F’ T r r r r T r ' F r F T B A A B A A D = = = = T D
On the other hand, since both ends of shaft BE rotate, the angle of twist of BE, φ E/B , is equal to the difference between the angles of rotation φ B and φ , i.e., the angle of twist is φ E/B = φ - φ B

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Let r A be the radius of the currently selected back wheel gear and r B the radius of the pedal gear, and let us hypothesize that r a >r b . If we apply a torque T through the pedals, the corresponding T D that is developed at wheel pin is: On the other hand, the rotation of wheel is: A FAMILIAR EXAMPLE F T T r r T B A D = T D b b a b a r r φ φ φ < = F’ Less effort Less speed
Example Problem The two solid steel shafts shown are coupled together using the meshed gears. Determine the angle of twist of end A of shaft AB when the torque T = 45 N-m is applied.

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NEW 375 Lecture13 - INTERACTION OF GEARS If a torque is...

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