A gear reduction system consists of three gears A, B, and C. Knowing that gear A rotates clockwise with a constant angular velocity ωA=600 rpm, determine (a) the angular velocities of gears B and C, (b) the accelerations of the points on gears B and C which are in contact.
Answers
The angular velocity of gear B and C is 100 rpm and the accelerations of the points on gears B and C which are in contact is 1974 in / s² and 658 in / s².
What is angular velocity?Angular velocity is defined as the speed at which two bodies move apart angularly or at which an item spins or rotates about an axis. The rotational axis is parallel to the direction of the angular velocity.
Let E is the contact point between gear B and C
vD = f EB ωB = 2 x 10λ = 20λ in / s²
ωC = vE = f EC = 20λ / 6
= 3.333 λ rad / s 60 / 2λ = 100 rpm
Acceleration at point E
On gear B
aB = v²E / r EB
= (20λ)² / 2 = 1973 in / s²
On gear C
aC = v²E / r EC
= (20λ)² / 6 = 658 in / s²
Thus, the angular velocity of gear B and C is 100 rpm and the accelerations of the points on gears B and C which are in contact is 1974 in / s² and 658 in / s².
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