The figure shows a gear train. Gears have the following properties: N2 = 15 teeth N6 = 75 teeth N3 = 90 teeth N4 = 15 teeth Pd = 16 N5 = 75 teeth Pd = 12 N7 = 15 teeth Pd = 8 N8 = 60 teeth Determine the speed and direction of rotation of gear 8 when gear 2 drives to 3600 rpm clockwise. Determine the distance between centers of gears 2 and 8, as well as determine the ratio of angular velocity and mechanical advantage of the gear train.
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Figure 8 shows a single-stage gear train. Gear trains are used in many products, such as clocks and automotive transmissions, to reduce or increase the angular velocity of a component. The size of each gear is measured by the number of teeth rather than the radius. Suppose the first gear has $n_{1}$ teeth and the second gear has $n_{2}$ teeth. Because the spacing of the teeth is the same for both gears, the ratio of their radii will be equivalent to the corresponding ratio of the number of teeth. When two gears are meshed together, they share the same linear velocity. If $\omega_{1}$ and $\omega_{2}$ are the angular velocities of the first and second gears, respectively, then $$\begin{aligned}v_{2} &=v_{1} \\r_{2} \omega_{2} &=r_{1} \omega_{1} \\\omega_{2} &=\frac{r_{1}}{r_{2}} \omega_{1} \\\omega_{2} &=\frac{n_{1}}{n_{2}} \omega_{1} \end{aligned}.$$ The first gear in a single-stage gear train has 42 teeth and an angular velocity of 2 revolutions per second. The second gear has 7 teeth. Find the angular velocity of the second gear.
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The tooth numbers for the gear train illustrated are N2 = 20-T, N3 = 16-T, N4 = 30-T, N6 = 36-T, and N7 = 46-T. Gear 7 is fixed. If shaft-a has an angular speed of ωa = 18 rad/s (c.w.), a) Determine the magnitude and direction of rotational velocities of shaft-b, gear-3 and gear-4 in revolutions per minute [rpm]. [24 pts.] b) If the input power is Hin = 12 kW, determine the torque transmitted by shaft-a (Ta) and shaft-b (Tb) in [N-m]. [16 pts.]
Sri K.
In an epicyclic gear train, an arm carries two gears with 36 and 45 teeth respectively. If the arm rotates at 150 rpm in the anticlockwise direction about the center of the fixed gear, and there is a separate shaft connected to the gear, determine the speed of the gear. See figure below. Given: Ta = 36; Te = 45; Tc = 30; NARM = 150 rpm (CCW); Na = 0
Madhur L.
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