 Hello everyone, I am Mr. Sachin Rathod working as assistant professor in mechanical engineering department from Walsh Institute of Technology, Swalapur. Today we are dealing with a reverted gear train. So in this session, the learning outcome is at the end of this session student will be able to calculate the speed ratio of, so the simple diagram is there for the reverted gear train. So in this diagram, so reverted gear train is nothing but if the input axis and output axis of the shaft on which the gears are mounted are coaxial, then it is called as a reverted gear train. So in this gear, gear number one is a driver, consider gear number one is a driver and gear number four is a driven. Speed ratio is nothing but it is the ratio of speed of driver divided by speed of driven. So this is a, we can call driver gear divided by speed of driven gear. So it is called as a speed ratio. So the speed of the driver gear divided by speed of the driven gear. It is nothing but the speed of the driver is nothing but the one and driven is nothing but the four. It is equal to the N1 by N12. So it is also kind of the compound reverted gear train. So we can find out the speed ratio in terms of the number of the teeth is nothing but number of the teeth we can calculate. It is equal to product of number of teeth on driven gear divided by product of number of teeth on driver gear. So if you observe this mechanism, this is the driver gear. This is the driver gear for this driven gear and this is the driven gear. So this is the driver gear for this driven gear. So one and three are the driver gear for two and four driven gear. So we can call product of number of teeth on the driven gear. So two and four are the driven gear. So we can call T2 into T4 divided by product of number of teeth on the driver gear. So one and three, T1 into T3. So it is nothing but N1 by N4. So we can formula for finding the speed ratio. And second thing is that if you observe this mechanism, the distance between the two shafts, these two shafts, suppose we can call the distance between the two shafts is x. So we are getting, so this is the radius. Suppose the gear number one is having the PCDs this much, so the radius we are getting this much. So this we can call for the gear number one, this is R1, gear number two, it is R2. That is the pitch circle radius. Gear number three, it is R3, gear number four, it is R4. So x is the distance between the two shafts is equal to R1 plus R2 is equal to R3 plus R4. Just we require these two formulas. By using these two formulas, we can easily find out the speed ratio or any geometry from this reverted gear type. So you can think about what are the applications of reverted gear type. So this is the question for you. So generally if you observe the lathe machine at the back gear box of the lathe machine, we are using the reverted gear train. So the application, main application in case of the back gear of lathe machine. So consider this numerical, so we have to solve this numerical. So in this question, the speed ratio of the reverted gear train as shown in the figure is 12. So speed ratio is nothing but we are knowing speed of the driver divided by speed of the driven. So here the NA and ND is the driver by driven. So we are getting NA by ND is equal to 12. The module of the pitch of the gear A and B is 3.125. Therefore MA is equal to MB is equal to 3.125. And CND that is MC is equal to MD is equal to 2.5. So calculate the suitable number of the teeth on the gears. So you have to calculate the number of the teeth that is TA, TB, TC, TD that you have to calculate. So in this question, so the speed ratio they are given us. So we can simplify this. So the speed ratio is nothing but NA by ND. And in case of the reverted gear train we are knowing that the speed ratio that is the speed of the driver by speed of the driven is calculated by the product of number of the teeth on the driven gear divided by product of number of teeth on the driver gear. So we are getting TB into TD divided by TA into TC. So by using this formula we can calculate the speed ratio. So here they are given as the speed ratio is equal to 12. So we can simplify this we are getting TB by TA is equal to square root of 12 and TD by TC is equal to square root of 12. Because in these two gears the transmitted power should be the same. That is why we are getting TB by TA is equal to, if we make the product of this we are getting the speed ratio is equal to 12. So we can easily calculate TB is equal to square root of 12 TA and TD is equal to square root of 12 TC. So we are getting the relation between A and B. So this is the first equation and the second equation. The next expression we are knowing the distance between the two shafts that is the x that is given as 200 mm. Therefore x is equal to RA plus RB is equal to RC plus RD. Therefore we are getting x is equal to 200. 200 is equal to RA. We are knowing the relation between R and M. Here the R is equal to MT by 2. So therefore we are getting MA TA by 2 plus MB TB by 2 is equal to MC TC by 2 plus MB TD by 2. So we are getting MA TA plus MB TB is equal to 400 and MC TC plus MB TD is equal to 400. Just you have taken a common 1 by 2 it will get 400, 200 into 2 we are getting the 400. So we are getting the two equation. So the MA MB are the same 3.125 therefore we are getting TA plus TB is equal to 400 divided by 3.125. And TC plus TD is equal to 400 divided by here the MC and MB are the same 2.5. It is coming to 2.5. Therefore TA plus TB is equal to 400 by this TC plus TD is equal to 400 by this. So we have to solve this equation number 3 equation number 4. So by comparing the equation number 1, 2, 3 and 4 we have to calculate the value of TA TB TC TD. So for making the calculation we are getting here TA plus TB is equal to for the calculation purpose 400 divided by 3.125. We are getting 128, 128 and TC plus TD is equal to 400 by 2.5 we are getting 160. So this is equation number 5 equation number 6. So here we are getting TB is equal to square root of 12, square root of 12 3.464, 3.464 TA and TD is equal to 3.464 TC. Therefore by putting the value TB is equal to 3.464 we are getting TA plus 3.464 TA is equal to 128. Therefore TA is equal to 128 divided by 4.3. So we are getting 28.67. Similarly TC and TD if you put TD is equal to 3.4. Therefore we are getting TC plus 3.464 TD is equal to 160. Therefore TC is equal to 160 divided by 4.464 is equal to 35.84. Therefore if you consider is equal to 28 TA is equal to and TC is equal to 36. Therefore if you put this value in this equation number 5 we are getting TB is equal to 128 minus 28 is equal to 100 and TD is equal to 160 minus 36. So these are our answers. So we are getting TA is equal to 28, TB is equal to 100, TC is equal to 36 and TD is equal to… So like this we have to solve the equations. So here are the calculation for this TD and TB calculation. So these are my references. Thank you.