 Hello friends, myself as I am a student professor from Mechanical Engineering Department of Walsh and Institute of Technology, Solaapur. Today I am explaining regarding the calculating the length of the open belt drive. In the previous, I am explaining regarding the calculating the length of the cross belt drive. The learning outcomes for this session is student will able to calculate the length of the open belt drive. Now in the previous one, I am explaining regarding the derivation of the cross belt drive. I hope you are going through this video last video and understand it. Now it is a question for that one, if motion transmission from clockwise to anti-clockwise direction, which belt drive is used? I hope you have to think over that. I am explaining in the last video regarding this one. Yes, for answer for this one is for transmission of motion from clockwise to anti-clockwise direction you can use the cross belt drive. Now today I am explaining regarding the transmission of motion from the clockwise to the clockwise direction that is for the open belt drive. So here I am showing the diagram, this is a driver having radius R1 and it is a R2. So here O1 is the center of the driver shaft or driver pulley and O2 is the center of the driven shafts and the distance between these two is a C. Now the belt is coming in contact with starting from at a point A to B that is belt is not in contact with the pulley. And again come in contact with from BFD dash BF and then it comes to C to D and from CEA. So that is the total length of the belt you have to calculate how much the belt length of the belt you have to require. Now R1 is the radius for this larger pulley this R1 and R2 is the radius for the smaller pulley. C is the distance between the two shafts. Now for the length of total length you have to go for length L is equal to this RCEA which RCEA CEA plus this length AB plus RBFD BFD. So CEA AB BFD and the last one is DC arc sorry length DC. Now you have to assume that this length AB and CD are equal one. So AB is equal to CD AB is equal to CD. Now length total length is equal to this arc CEA is double of that that is arc EA that is arc AE and arc EC is the same one. So you have to take here two times arc EA plus this AB AB and CD are equal one I am taking as AB two times of AB plus arc again BFD. So FB is a and FD are equal one so I am taking two times of arc BF. Now this arc EA means it is a pi by 2 plus alpha what is alpha? So from O2 draw one line parallel to AB so it is a point G it intersected. So O2 G O2 G is perpendicular to O1 A and again and this angle that is G O2 1 G O2 G O2 O1 is equal to alpha is equal to angle the same angle that is angle AO1 A dash AO1 A dash is equal to angle again BO2 B dash so this is angle alpha. So now this length AB because here you have to calculate the length AB this length AB is equal to AB and O2 G are equal one. So cos alpha is equal to O2 G by O1 O2 therefore cos alpha is equal to cos alpha is equal to O2 G by O1 O2 O2 G by O1 O2 O2 G means AB is equal to AB by O1 O2 O1 O2 means this distance C1 C therefore AB is equal to C cos alpha this is the value of AB now put the value of and again one more thing is here sin alpha because you have to calculate the value of alpha then you have to go for the length what is the sin alpha sin alpha is equal to sin alpha is equal to O1 G divided by O1 O2 O1 G divided by O1 O2 what is the O1 G O1 G this total length is R2 O1 G means AO1 minus G O1 AO1 this AO1 total radius minus G O1 divided by O1 O2 O1 O2 means C1 so what is AO1 AO1 means R1 minus G O1 means it is equal to R2 same length is to be there so R1 minus this length is R2 R1 minus R2 by C that is the sin alpha therefore sin alpha is equal to R1 minus R2 by C so it is the value of AB this is the value of sin alpha now as you have to check that this what you call this value O1 AO1 minus G O1 is a very small AO1 and G O1 this subtraction is very small and when the distance between the center of the two shafts or the two pulley is larger one and C is larger this value C then sin alpha is nearer to alpha as it is a very small okay sin alpha is equal to now you know the value of AB you know the value of sin alpha you know the value of sin alpha as very close to this one you have to calculate the value of cos alpha that is cos square alpha plus sin square alpha is equal to 1 therefore cos square alpha is equal to sorry cos alpha is equal to 1 minus sin square alpha or cos alpha is equal to 1 minus sin square alpha raise 1 by 2 or cos alpha is equal to 1 minus 1 by 2 sin square alpha plus 1 by 2 sin square alpha plus by binomial expansion it is a binomial expansion this value cos alpha is equal to 1 minus 1 by 2 sin square alpha but alpha sin alpha is equal to alpha therefore cos alpha is equal to 1 minus 1 by 2 alpha square this is the value so it is the value first this sin alpha 2 3 and this value so 4 1 so you have to calculate all this value AB that is length sin alpha value of sin alpha r 1 minus r 2 by c and co-value of cos alpha now you have to take on the first equation this one what is the length so length l is equal to 2 times r a e put the value 2 times what is the r e a r e a means pi by 2 plus alpha pi by 2 plus alpha into r 1 this is the value of r e a what is the value of AB AB is the value of c cos alpha c into cos alpha and then value of r b f value of r b f means is pi by 2 minus alpha here you have to take pi by 2 plus alpha for larger pulley and for smaller pulley this length is pi by 2 minus alpha pi by 2 minus alpha into r 2 now length l is equal to 2 times into bracket pi by 2 into r 1 plus alpha into bracket pi by 2 into r 1 plus alpha r 1 plus c cos alpha plus pi by 2 into r 2 minus alpha into r 2 now multiply 2 in the bracket multiply in the bracket so length l is equal to pi r 1 plus 2 alpha r 1 plus 2 c cos alpha plus pi r 2 minus 2 alpha r 2 now taking the group together pi into bracket r 1 plus r 2 these two values plus 2 alpha into bracket r 1 minus r 2 plus 2 c cos alpha what is the value of cos alpha value of 1 minus 1 by 2 1 minus 1 by 2 alpha square so length l is equal to pi into bracket r 1 plus r 2 plus 2 alpha r 1 minus r 2 plus 2 c into 1 minus 1 by 2 r 1 minus r 2 plus 2 c into 1 minus 1 alpha what is the value of alpha r 1 minus r 2 sin alpha is equal to r 1 minus r 2 alpha is equal to because sin alpha is equal to alpha r 1 minus r 2 by c you have to write r 1 minus r 2 by c bracket square so length l is equal to pi into bracket r 1 plus r 2 plus again here alpha is r 1 minus r 2 by c into r 1 minus r 2 plus r 2 minus r 2 c into bracket sorry 2 c minus 2 c minus 2 to get cancelled c is get cancelled r 1 minus r 2 bracket square by c so length l is equal to pi into bracket r 1 plus r 2 plus 2 into bracket r 1 minus r 2 bracket square upon c plus 2 c minus r 1 minus r 2 bracket square upon c this get cancelled here so length l is equal to pi into bracket r 1 plus r 2 plus to r 1 minus r 2 square by c r 1 minus r 2 by 1 get cancelled here so it is r 1 minus r 2 bracket square upon c plus 2 c so total exact length of the open belt l is equal to pi into bracket r 1 plus r 2 plus 2 c plus r 1 minus r 2 bracket square by c so it is a formula for calculating the exact length of the open belt r for a b b f d from d c and c e a what is the formula length l is equal to pi into bracket r 1 plus r 2 plus 2 c plus r 1 minus r 2 bracket square by c where c is equal to distance between the two shafts or two pulley r 1 is radius this r 1 is radius for the larger pulley r 2 is radius for the smaller pulley so from this formula you can calculate the exact length of the open belt line so for this references I am using for this video b k single book