Now in this video we will look at these three mechanisms or these three you know arrangement of linkages and try and find out the degrees of freedom for this. Okay, so the Kurzweil criterion or the Kurzweil equation was degrees of freedom is equal to 3 into n. minus 1 minus 2 into p1 minus p2 that is the kurzbach equation where p1 is the you can say number of lower pairs with one degree of freedom and this is the number of higher pairs with 2 degrees of freedom okay so in this figure let's count the number of links first so you have the same fixed link so you have 1 2 this is the single link so this becomes link 3 link 4 and link 5 so total number of links is 5 so capital N becomes 5 Let's find out the total number of lower pairs or 1 degree of freedom.
It will be P1, isn't it? You will have 1, 2, 3, 4, 5. Okay, most of you would also choose this as a single degree of freedom but that is incorrect. This would be a 2 degree of freedom because at this point this joint will also have certain amount of slippage in addition to the turning effect.
So this will be P2. So P1 becomes 1, 2, 3, 4, 5. and P2 becomes 1. So even if you choose this as a P1 joint, your degree of freedom will become 0. But if you give this a value 1, then the degree of freedom will become 1. So there will be a lot of difference because this will have a little bit amount of slipping also. right so f would be in this case 3 x 5-1-2 x 5-1 that is 12-10-1 1 so this is a mechanism with the degree of freedom as 1 okay so the catch over here was to recognize this as a p2 okay let's come to this one Let's count the number of links first of all.
So this is link 1, link 2. This is a ternary link. So this is link 3. This is link 3. This is link 4, link 5. This would be link 6 and this would be link 7. Don't count this as link 8 because these both are same links. So this is also link number 1. So 1. 1, 2, 3, 4, 5, 6, 7, 7 links.
So I would write down capital N as 7. Okay, now let's talk about P1 and P2. So it is very clear that there is no P2 in this case. all are single degree of freedom joints so you will have 1, 2, 3, 4, 5, 6, 7 and 8 so your value of P1.
becomes 8 and then this p2 is 0. So, for this mechanism the degree of freedom will become 3 into 7 minus 1 minus 2 into 8. This becomes 18 minus 16 which is 2. So you have a degree of freedom as to for this mechanism. Let's come to the last one. In this the number of links, now it clearly shows that there is a higher pair involved that is between these two rulers.
because they have a line contact or a point contact so there is a value of P2 involved lets write that down straight away number of links you have 1, 2 and 3 so there are 3 links in total this is a single link so I would say number of links is 3 number of lower pairs 1 and I would say 2. So, P1 is 2. Alright, so let's calculate the degrees of freedom for this. So degrees of freedom would be 3 into 3 minus 1 minus 2 into 2 minus 1. So you will get 6 minus 4 minus 1, 1. So the degree of freedom for this is 1. Okay, so this is how you have to go on practicing. finding out the degrees of freedom for various mechanisms.
So I hope you got this. Now this ends the chapter on the introduction to mechanisms. Now in the next chapter onwards we will start with the kinematic analysis of mechanisms and we will start with the velocity analysis of mechanisms.