 Hello Friends, Myself, SMWAT, Assistant Professor, Department of Mechanical Engineering from Walsh and Institute of Technology, Solapur. Today I am explaining regarding how to calculate the length of belt in the cross belt drive. The basic learning outcome from this video is at the end of this session student will be able to calculate the length of cross belt drive. Pause the video, see the triangle and calculate the value of sin x and cos x. Now the answers are here sin x is equal to this opposite side upon hypotenuse and cos x is equal to adjacent side upon hypotenuse. Here I am showing the diagram and with continuation with explaining the how to calculate the derivation of the cross belt drive. Here the two pulleys are there, one is O1 pulley that is a driver, second is O2 pulley that is a D11 and is a continuous belt from A to B, B to F, F to C, C to D, D to E and E to A again. So now today we have to calculate the length of this belt. So basically R1 is a radius for the driver pulley and R2 is a radius for the driven pulley. Now belt come in contact that is A to E, E to D and belt come in contact we can contact with the smaller pulley C to F, F to B. So and the belt not in contact with the pulley that is AB and CD. Now R1 is a radius of larger pulley and R2 is a radius of this smaller pulley and C is a distance between the two pulleys, C is a distance between these two pulleys. Now length L is equal to total length you have to calculate L is equal to arc AED, it is arc AED, length L is equal to arc AED plus AED plus length DC, length DC plus arc CFB, arc CFB and length belt BA, length BA. Now this CD and AB are equal, AB is equal to CD that is you have to taking the two times and here arc AED means it is a arc ED that is two times of arc, arc AE is equal to arc ED. So you have to taking it as arc two times, so length L is equal to two times into bracket ED, arc ED plus AB is equal to CD. So AB and CD taking as one of the length AB plus arc CFB means two times of arc BF, two times of arc BF. Now what is the value of arc ED and arc BF, arc ED means it is a pi by 2 plus alpha because belt income in contract with this angle is angle DO1D, so D dash O angle D dash O1D is equal to alpha is equal to angle B dash O2B or B O2B dash is alpha is equal to alpha. So it is a total is pi D, so pi by 2 plus alpha. So length L is equal to two times into bracket, two times into bracket pi by 2 plus alpha, pi by 2 plus alpha, it is a pi by 2 plus alpha into R1, radius of R1, R1 plus length AB plus again here BF means pi by 2 plus alpha into R2, pi by 2 plus alpha into R2, bracket complete. So multiplying this one is equal to two times result cancelled pi R1 plus 2 alpha R1 plus length AB plus this two get cancelled here that is pi R2 plus 2 alpha R2. So it is a total length bracket complete, now we have to calculate the length AB, how to calculate the length AB, this length AB is equal to length CD, it is given here. Now this angle alpha, you draw one more line CD parallel one line from O2 to the CD it and you have to extend this line name it as a G, so it is a 90 degree, this is also 90 degree. So these two lines are parallel to each other, so this angle is alpha, so cos alpha is equal to because you have to calculate the length CD. So cos alpha is equal to O2G divided by C, C means that is the two pulleys that is O2G divided by C and this O2G is a parallel to CD, so here AB is equal to CD is equal to O2G. So here you have to write is equal to instead of O2G you have to write AB that is C. So therefore AB is equal to C cos alpha, so AB is equal to C into cos alpha, AB is equal to C cos alpha, name it as 1. So put this value here, so length L is equal to pi R1 plus 2 alpha R1 plus C cos alpha, these are all there are two times C cos alpha sorry not two times pi R1 2 alpha R1 plus C cos alpha plus pi R2 plus 2 alpha R2 bracket complete. Now length L is equal to this pi R1 and this pi R2 common pi into bracket R1 plus R2 plus this 2 alpha R1 into this 2 alpha R2, so 2 alpha into bracket R1 plus R2 plus C cos alpha. So C cos alpha, so here this is the formula to calculate the total length of the build name it is formula 2 1, length L is equal to pi into bracket R1 plus R2 plus 2 alpha into bracket R1 plus R2 plus C cos alpha, but here some values we have to calculate it that is value of cos alpha and value of alpha, because you know that sin alpha is equal to alpha when the values are very less means which values the radius are very small and the distance between the two shafts are big one, so you have to calculate the exact length of that build in the next section with calculating of value of alpha cos alpha and sin alpha.