cluster gears changes can be obtained as shown in Table given below. The problem of the machine tool designer is to select tooth numbers for the various gears (2 to 10) so as to produce a reasonable distribution of speeds for the output shaft. The gears 2, 6 and 9 are having 20, 25 and 50 teeth respectively. The input shaft speed is 450 rpm and the output speed can vary from 137 rpm to 580 rpm depending on the sequence of the gears. If the output speed obtained through the gear sequence 2-5-5-8 is 257 rpm and if the minimum and maximum number of teeth in the gear system are 20 and 50 respectively, Determine: (i) Suitable tooth numbers for the remaining gears (3,4,5,7,8 & 10) (ii) Output shaft speed for 2-5-7-10 gear sequence.