 Today we are going to learn the velocity and acceleration in mechanism. Learning outcome at the end of this lecture, student will be able to draw and determine the velocity and acceleration diagram for a given mechanism by relative velocity method. The statement of the problem, the crank and slider mechanism rotates clockwise at a speed of 300 rpm, the crank is 150 mm and the connecting rod is 600 mm long. The crank is designed to define the linear velocity and acceleration of midpoint of a connecting rod and angular velocity and angular acceleration of connecting rod at a crank angle 45 degree from the inner dead center position. So first of all, the space diagram is to be plot according to the suitable scale. So crank is making an angle of 45 degree with IDC, so draw a line OB which will represent the crank then from point B draw a line AB which will represent the connecting rod of 600 mm long. Now this point O is fixed and the point B is rotating with respect to O in clockwise direction. So first of all find out the velocity of point B with respect to O, so velocity of any point with respect to another point that is given by omega into link length OB. So angular velocity that will be given by 2 pi n upon 60 into link length OB that is crank it is given 150 mm, so in meters it is 0.150 and therefore by putting the value of rpm 2 pi into 300 divided by 60 multiplied by 0.15 you will get the velocity of B with respect to O in magnitude that is 4.713 meters per second. And now for drawing the velocity triangle take certain suitable scale depending upon the magnitude of VBO, so 1 centimeter is equal to I will take the scale 1 centimeter is equal to 0.7 meters per second. Now first of all mark the fixed point in space, so as the point O is fixed in space diagram so mark point O in space as a fixed point of pole. So velocity of B with respect to O whose magnitude is 4.713 meters per second, so velocity of B with respect to O that will be perpendicular to link OB. Now that perpendicular whether in this direction or in the downward direction perpendicular to OB whether it is in the downward or upward that will depend upon the direction of rotation of link OB, so this link OB is rotating in clockwise direction. So velocity of B with respect to O it will be perpendicular to link OB which is represented by VB and hence from fixed point O draw a vector OB which is perpendicular to OB or parallel to this VB. So from point O just draw a vector OB with the scale and this vector OB will represent the velocity of point B with respect to O or simply it is called as VB. Now the next link AB, so velocity of A with respect to B at this moment we do not know the magnitude but we can determine the direction of relative velocity of A with respect to B. So as we have discussed earlier the relative velocity of any point with respect to other point when both point lies on the same link that will be perpendicular to that particular line joining the point A and B. So velocity of A with respect to B whose magnitude is unknown but the direction will be perpendicular to AB and hence from vector B that is from point B draw a vector perpendicular to AB. So from point B just draw a vector perpendicular to link AB at this moment we do not know the magnitude hence just draw a vector from B perpendicular to link AB. Now this sliding block as your crank rotates the sliding block will slide along the line of reciprocation. So this slider will slide along this line of reciprocation OA with respect to fixed point O and hence from point O draw a vector parallel to path of reciprocation of slider. So from point O just draw a vector parallel to path of reciprocation of the slider. So this vector will meet the previous vector at point A. So vector BA this will represent the velocity of A with respect to B vector OA represents the velocity of A linear velocity of slider A. Now here point D is the midpoint of link AB. So as already we have discussed the ratio in which point D divides the link AB in the same ratio the vector D will divide the vector AB. So we can determine the position of vector D either from vector A or from B. So let us calculate the position of vector D from A. So vector AD which is unknown divided by vector AB is equal to link length AD divided by link length AB. So AD is to be determined measure the length AB. So this length AB vector AB is 4.9 centimeter link length AD as D is midpoint of AB it will be 300 divided by link length AB 600. And by doing the calculation you will get the vector length AD that will be equal to 2.45 centimeter. And hence from point A mark the point D on vector AB. So mark the vector D on this vector AB and then join OD. So this vector OD will represent the velocity of point D. And now what is asked the linear velocity of midpoint of connecting work. So velocity of D so by measurement the velocity of point D that can be represented by vector OD. So measure the vector length OD that will be equal to 5.8 centimeter. So velocity of D vector OD multiplied by scale and so that will be 5.8 into 0.7. This will give the velocity of point D which is equal to 4.1 meter per second. Similarly we have to calculate the angular velocity of connecting rod. So angular velocity of connecting rod that can be determined angular velocity of AB that will be equal to relative velocity of A with respect to B divided by link length AB. So first of all we have to calculate the velocity of A with respect to B. So from the velocity diagram measure the vector length AB. Vector length AB will be equal to 4.9 centimeter. And therefore velocity of B with respect to A that will be 4.9 multiplied by scale that is 0.07. And therefore velocity of A with respect to B or B with respect to A that will be equal to 3.4 meters per second. And therefore put the value of relative velocity of A with respect to B 3.4 meter divided by link length AB 0.6 meter. This will give the angular velocity of link AB that is 5.67 radians per. The next part that acceleration diagram for this particular problem we will see in the next session. The material is referred from the book of theory of machines by R. S. Khurmi and S. S. Vatan. Thank you.