Q1:- The Number of teeth in the gears are Ts=18, Tp=24, Tc=12, TA=72 as shown in Fig. P and C from a compound gear carried by the arm a and the annular gear A are held stationary. Determine the speed of the output at a. Also, find holding torque required on A if 5kW is delivered to S at 800rpm with an efficiency of 94%
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First, we need to find the gear ratios between the gears. Gear ratio between S and P (Rs_p) = Ts / Tp = 18 / 24 = 3 / 4 Gear ratio between C and A (Rc_a) = Tc / TA = 12 / 72 = 1 / 6 Show more…
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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 second gear in a single-stage gear train has 6 teeth and an angular velocity of 90 revolutions per minute. The first gear has 54 teeth. Find the angular velocity of the first gear.
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