Concept explainers
Figure 21−9 shows a compound gear train. Gears B and C are keyed to the same shaft; therefore, they turn at the same speed. Gear A and gear C are driving gears. Gear B and gear D are driven gears. Set up a proportion for each problem and determine the unknown values, x, y, and z in the table. Round the answers to 1 decimal place where necessary.
(a)
To find the speed of the different gears given in the problem.
Answer to Problem 16A
Speed of gear B is
Speed of gear C is
Speed of gear D is
Explanation of Solution
Given information:
A gear and pinion arrangement is given as below.
Calculation:
We have been given below information,
As we know that in a gear arrangement,
13
So,
Hence, speed of gear B is
Since, gear B and C are on same shaft. So, speed of both gear is equal.
Therefore, speed of gear C is
Again,
Hence, speed of gear D is
Thus, speed of gear B is
Speed of gear C is
Speed of gear D is
(b)
To find the number of teeth in the gear and the speed of the gear.
Answer to Problem 16A
Number of teeth in gear B is
Number of teeth in gear D is
Speed of gear C is
Explanation of Solution
Given information:
A gear and pinion arrangement is given as below.
Calculation:
We have been given below information,
As we know that in a gear arrangement,
So,
Hence, number of teeth in gear B is
Since, gear B and C are on same shaft. So, speed of both gear is equal.
Therefore, speed of gear C is
Again,
Hence, number of teeth in gear D is
Thus, number of teeth in gear B is
Number of teeth in gear D is
Speed of gear C is
(c)
To find the number of teeth as well as speed of the gear.
Answer to Problem 16A
Number of teeth in gear A is
Speed of gear B is
Speed of gear C is
Explanation of Solution
Given information:
A gear and pinion arrangement is given as below.
Calculation:
We have been given below information,
As we know that in a gear arrangement,
So,
Since, gear B and C are on same shaft. So, speed of both gear is equal. i.e.
Again,
Hence, speed of gear B and gear C is
Putting,
Thus, number of teeth in gear A is
Speed of gear B is
Speed of gear C is
(d)
To find the speed of the different gears and the number of teeth.
Answer to Problem 16A
Number of teeth in gear C is
Speed of gear A is
Speed of gear B is
Explanation of Solution
Given information:
A gear and pinion arrangement is given as below.
Calculation:
We have been given below information,
As we know that in a gear arrangement,
So,
Since, gear B and C are on same shaft. So, speed of both gear is equal. i.e.
Putting
Hence, speed of gear A is
Again,
Hence, number of teeth in gear C is
Thus, number of teeth in gear C is
Speed of gear A is
Speed of gear B is
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Chapter 21 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
- Of two gears that mesh, the one that has the greater number of teeth is called the gear, and the one that has the fewer teeth is called the pinion (Figure 218). For each of the problems, set up a proportion, and determine the unknown value, x. Round the answers to 1 decimal place where necessary.arrow_forwardIn Figure 208, gear A is turning at 120 revolutions per minute and gear B is turning at 3.6 revolutions per second. Determine the ratio of the speed of gear A to the speed of gear B.arrow_forwardA double-threaded square-thread screw is shown in Figure 5-7. The pitch of a screw is the distance from the top of one thread to the same point on the top of the next thread. The lead is the distance the screw advances for each complete turn or revolution of the screw. In a double-threaded screw, the lead is twice the pitch. Given the number of turns and the amount of screw advance, determine the lead and pitch.arrow_forward
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