 Hello everyone, I am Sachin Rathod working as assistant professor in mechanical engineering department from Walton Stop Technology Swallapur College. Today we have to see the numericals on velocity and acceleration mechanism by using the relative velocity method. The learning outcome of this session is student will able to calculate the velocity and acceleration of given mechanism. At given as a one numerical, the PQRS is a 4 bar link mechanism in which PS is fixed and the length of the link that given as a dimension PQ is equal to 62.5 mm, QR 175 mm, RS 112.5 mm, PS 200 mm. The cranks PQ, PQ is the crank rotates as 10 radian per second means they are given as a angular velocity of PQ is equal to 10 radian per second in clockwise direction. Draw the velocity and acceleration diagram, angle QPS is equal to 60 degree and Q and R lies on the same side of the PS, find the angular velocity and angular acceleration of Q1 and RS. So as per the given data, we can easily draw the space diagram by using so and this PQ rotates in the clockwise direction that given as with 10 radian per second. The value of this omega is 10 radian per second. So we have to find out the angular velocity and angular acceleration of link, QR and RS. For that purpose we have to draw the velocity diagram as well as the acceleration diagram. So first of all we can draw the velocity diagram. Now drawing the velocity diagram, just remember these things. The velocity of any link which is having the rotary motion, the velocity of that link should be perpendicular to that motion, perpendicular to the link. Suppose PQ, first of all we will draw one point on the space at which the velocity is 0. So P and S are the fixed points so at that point the velocity is 0. So suppose one point we have taken in the space at that point PS, this is a PS at which the velocity is 0. Next PQ makes the angular velocity of omega in clockwise direction, the value is 10 radian per second. Now we are drawing the velocity diagram. So we have to find out the velocity of this link, they are given as angular velocity. So we are knowing this is the space diagram, space diagram. Now they are given as angular velocity. Otherwise simply make one table in which link radius, velocity, if you consider the link PQ, QR and RS and RS, the radius of the link PQ is 62.5 mm is equal to 0.0625, the link QR 0.175 this radius in meter and the link RS is 0.1125 meter and the velocity, the link velocity PQ, link velocity we can find out that is the angular velocity of PQ, we are knowing V is equal to r omega that is the, we have to find out the velocity of PQ therefore radius of PQ into angular velocity of PQ. The radius of the PQ is 0.0625 into the angular velocity of PQ that is given as a 10 radian per, 10 radian per second into 10. So we are getting 0.625 meter per second. So we are getting the angular velocity of PQ is 0.625 meter per second. So we are knowing the magnitude as well as the direction of velocity of link PQ. So this is the P point, PQ rotates in the clockwise direction. So from the P point you draw the perpendicular line, so this is the perpendicular line. So from the P point we have drawn perpendicular line to the PQ link which is having the magnitude of 0.625 so we are getting the Q point. Next from the Q point QR is another link which is having the angular motion. So from the Q point again we have draw the perpendicular line for getting the velocity of Q with respect to r. So from the Q points draw the perpendicular line. Next one, rs is another link, the velocity of the rs link is perpendicular to that link. So from the r or s, r point we are not knowing. So from the s points draw the perpendicular line to the link rs. So from the s points we have drawn the perpendicular line. At this point we are getting the point r. So in this diagram we are getting the velocity of Q with respect to P. This will give the velocity of r with respect to s. This will give the velocity of Q with respect to r. So by using this velocity diagram we can just calculate the value of velocity of rs, velocity of QR so we are getting the velocity of rs as 0.38 and 0.34. Now by using this table now we are finding the acceleration diagram. For drawing the acceleration diagram in the acceleration diagram there are the two components that is the radial component as well as the tangential component. So we have to find out the radial component of each link. So we are we can just write down the radial component. So radial component is nothing but the v square by r. Now here we are knowing the velocity and radius so we have to calculate the radial component. So we are getting by calculating 6.25, 0.825 and 1.027 these are the radial component. By calculation we are finding this radial component. Now we go further for the acceleration diagram. For drawing the acceleration diagram just there are the two links that is the radial component and another is the tangential component. So each link having the two components radial and the tangential. So first of all one point at which the acceleration is 0 so P and s are the fixed point so consider any one point at which the acceleration is 0 we can give as a name P dash s dash at which the acceleration is 0. Next link PQ. PQ is rotated with the uniform angular velocity so it is having the only one component that is the radial component. So radial component of the PQ is 6.25 and the radial component is parallel to this link. So the Q point is moving parallelly in the downward direction which will give the radial component. So from the P point we are getting the Q point in the downward direction. So we will draw the parallel line to this in the downward direction. So we are getting the Q point and having the magnitude is equal to 6.25. So after the Q point QR is another link so it is having the two component perpendicular as well as the tangential and normal or radial. So the Q point already we have calculated the QR. The radial component of the QR is 0.825. So the radial component is nothing but the parallel line. So we have to draw the parallel line to this and the magnitude. This is the Q point. So the radial component of the QR it is moving in the downward direction. So we are getting the X point below the Q point. So we will give you as a X point and this magnitude is equal to 0.825. This is the X point. This is the radial component. Radial and the tangential component are perpendicular to each other. So from the X points we will draw the perpendicular line. This is a perpendicular line. But the tangential component of the value we are not knowing. So keep it as it is. Okay. This will give the tangential component but the magnitude we are not knowing. So consider the next link that is the QS. It is having the two component radial as well as the tangential. We are knowing the S point and then the radial component of the QS is 1.027. This is the S point. So the radial component is moving in the downward direction. So we are getting the component below the S point and for the radial component we have to draw the parallel line. So parallel to this link we have to draw the radial component. This is the radial component of RS and the magnitude is 0.127. And perpendicular to this tangential component will lie. This is the perpendicular. This is the tangential component. So the intersecting point will give you the R point. Radial component of RS, tangential component. If I join this it will give the acceleration of QR link and if I join this it will give the acceleration of PS link. So this radial component if I shown like this or like this in the downward direction. This is the acceleration of Q with respect to R so it will give the like the direction radial component of QR this is in the downward direction tangential component of QR. Similarly if I drawn diagram like this acceleration of R with respect to S it will give the radial component of R with respect to S tangential component of R with respect to S and it is the acceleration of Q with respect to P. Like this way we can find out the acceleration of each link. So they had asked find the angular velocity angular velocity this velocity we are knowing angular velocity and angular acceleration of QR and RS. The angular velocity of QR velocity we are knowing V is equal to R omega radius this is a QR radius of QR angular velocity of QR we have to find out the angular velocity velocity we are knowing the radius we are knowing like this we can find out the angular velocity and angular acceleration of each link. So I have taken this reference thank you.