 Myself, Mr. A. N. Subadeh, Assistant Professor, Department of Mechanical Engineering from Walshchan Institute of Technology, Solapur. Today, we are going to study relative velocity in a mechanism. Learning outcome, at the end of this lecture, student will be able to identify and determine the velocity of a point on a link. Consider a rigid link A, B where A and B are the two extremities of this rigid link and this rigid link A, B is rotating with angular velocity omega radians per second in clockwise direction. So, this point B, one of the extremities of this rigid link A, B rotates with respect to fixed point A or with respect to point A. So, relative velocity of B with respect to A that can be determined by drawing a velocity. So, this is a fixed point A. So, there will be no relative velocity of point B with respect to A along the line A, B or along the link A, B because the length of link A, B is same or constant for any instant. Relative velocity of B with respect to A that may not be possible in this particular direction which is represented by V of B, A because in this case the point B will move away from A which is practically not possible. And therefore, the relative velocity of point B with respect to A will be perpendicular to the line joining the point B. And that is shown by V B A. So, in order to determine the velocity of B with respect to A mark point A in space. And now as we know the velocity of B with respect to A is always a perpendicular to the line joining the point A and B. And hence from point A draw a vector A, B perpendicular to link A, B or parallel to V, B, A. So, this vector A, B will represent the velocity of B with respect to A. Now, this particular link A, B is rotating with angular speed omega radians per second in clockwise direction. Therefore, velocity of B with respect to A that is represented by vector A, B as shown in the figure that is equal to angular speed of link A, B multiplied by link length A, B. This is my equation number 1. So, relative velocity of B with respect to A is represented by vector A, B and that is given by omega into link length A, B. Now, if you consider any point C on this link A, B then how to locate the vector C in the velocity diagram? So, as the point C is lying on link A, B, the velocity of point C with respect to A that can be determined by angular speed of link A, B. Multiply by link length A, C. This is my equation number 2. So, here as point C lies on link A, B, the angular velocity of C will be same as that of link A, B. And now, the vector C is to be located on vector A, B. Therefore, as we know, the angular velocity of C is the ratio in which the point C divides the link A, B. In the same ratio, the vector C will divide the vector A, B. And hence, from point A mark point C on this particular velocity diagram. So, this vector A, C it will represent the velocity of C with respect to A. And therefore, velocity of C with respect to A, it is represented by vector A, C which is equal to omega into link length A, C. This is my equation number 3. So, here velocity of C with respect to A, it is represented by vector A, C. And now, in order to locate this point C from equation 3 and from equation 1, we can obtain V C A divided by V B A is equal to vector A, C divided by vector A, B which is equal to omega into link length A, B divided by omega into link length A, C. So, angular speed omega will get cancelled and from this equation, we will get vector A, C divided by vector A, B which is equal to A, B divided by A, C. So, this is my equation number 4. So, my dear student, please think what we can conclude from equation number 4. So, in order to locate this point C or vector C on vector A, B, this equation number 4 can be used. So, we have to find out the vector length of A, C. So, the ratio A, C is equal to in which the point C divides the link A, B. In the same ratio, vector C will divide the vector A, B. So, vector length A, C will be equal to A, B upon A, C multiplied by vector length A, B. So, from this, we can determine the vector length A, C and we can plot or we can mark the vector C on this particular diagram. So, from this, what we can conclude relative velocity of a point with respect to other point when both point lies on the same link. The velocity is always a perpendicular to the line joining the point B and A in the space diagram. Now, let us consider one more example where the link A, B is rotating with angular speed 50 radians per second and link length A, B is 50 mm. So, from this, we can calculate the relative velocity of B with respect to A, that is omega A, B multiplied by link length A, B. So, omega is given 50 radians per second and link length A, B is 35 mm. So, it is in meter 0.035. So, velocity of B with respect to A is 1.75 meters per second. So, take certain suitable scale, 1 centimeter is equal to 1 meter per second. So, we mark point A in the space and now we have to draw a vector A, B which is perpendicular to link A, B. So, from fixed point draw a vector A, B perpendicular to link A, B. So, that will be 1.75 according to the scale. So, this is the vector A, B which will represent V, B A in magnitude and direction. Now, if point C is the midpoint of link A, B then how to locate this point C on this vector diagram A, B. So, for that, take the ratio A, C upon vector A, B is equal to link length A, C divided by link length A, B and therefore, A, C will be equal to A, C upon A, B. A, B is 1.75 centimeter and A, C as point C is the midpoint of A, B, then this will be equal to 0.0175 meter divided by link length A, B 0.035 and from this you can calculate the length of vector A, C which is equal to 0.875 centimeter. That means the point C on this particular vector diagram will lie at 0.875 centimeter that is it will be the midpoint of vector A, B and therefore, this vector A, C will represent the velocity of C with respect to A. The material is referred from the book of theory of machines by R S Khurmi and S S Vatan. Thank you.