 Hello everyone, I am Mr. Sachin Rathod working as an assistant professor in mechanical engineering department from Waltz University of Technology, Sallapur. Today we are going to deal with velocity in mechanism. So today's session outcome is at the end of this session student will able to understand the relative velocity method. So first of all you can think about so where is the necessity to find out the velocity or in which case the we have to find out the velocity. So you can think about this why we are finding the velocity. I will explain you suppose if you consider the slider crank mechanism in that case we are giving input to the shaft so from the shaft we are knowing the angular velocity of the crank. So we have to find out the velocity of slider at that time we can use this relative velocity method for finding the velocity of slider as well as we can find out the angular velocity of connecting rod. So we will see some basic concept used in relative velocity method. So now we are going to see the basic terms used in relative velocity method. So first one is the linear displacement it is denoted by later as so suppose one body is moving with respect to another fixed point then it is called as a linear displacement. Suppose this one is a fixed body A so another body is moving with respect to the A it is moving up to the B distance so it is called as a linear displacement and it is denoted by the later as next one linear velocity it is denoted by the later V it is nothing but the rate of change of linear displacement with respect to time it is given by ds by dt. Next one linear acceleration it is nothing but it is the rate of change of linear velocity with respect to time it is denoted by the later A is equal to dV by dt. Next angular displacement suppose OB is one line and it travel a angle of delta theta with short interval of the time then delta theta delta theta is the angle taken to take the new position that is OB to OC. So this delta theta is called as a angular displacement angular velocity it is a rate of change of angular displacement with respect to time it is denoted by the later omega is equal to d theta by dt. Next angular acceleration it is a rate of change of angular velocity with respect to time it is denoted by the later alpha is equal to d omega by dt. So next one now we have to get the concept of relative velocity so what is in by relative velocity suppose if we consider two bodies are moving in parallel direction suppose this is a body having the velocity of A that is nothing but the VA and this is a body B having the velocity VB in which VA is greater than VB and both are moving in parallel direction so this is a O point it is called as a pole in which now we are knowing the magnitude as well as the direction of the A point so we are getting the A point here it will gives velocity of A VA and we are knowing that the VB in magnitude as well as the in the direction this will gives the velocity of B so we can easily find out the BA vector is nothing but this is the BA vector is nothing but OA minus OB so it will gives the relative velocity of A with respect to B is equal to velocity of A minus velocity of B this is in case of if the two bodies are moving in parallel if suppose two bodies are moving in inclined direction suppose this is a body having the velocity of VA and this is a B body having the velocity of VB we are knowing the magnitude as well as in direction so this is a O pole from which we have to take the other velocity so this is your the velocity A we are knowing in magnitude as well as in the direction and this will gives the velocity of B in magnitude as well as in the direction so if I join A to B it will gives velocity of A with respect to B so it is a vector quantity if suppose I have drawn the arrow in the downward direction it will gives velocity of B with respect to A so this is a basic concept of relative velocity method next the concept of motion of a link suppose if you consider one rigid body this is a rigid body in that rigid body if you consider one link that is a AB link which is having the rotated in a clockwise direction with angular velocity omega so in that body so how the motion of the link will occurs it is rotated in the clockwise direction with angular velocity omega suppose one body is there suppose this is a O A string is there which is rotated in the circular manner so if rotated in the circular manner the velocity at the A point will be the perpendicular to that link it will gives velocity of A so always the velocity is always perpendicular to the link so by using the similar rule if it is rotated in the clockwise direction the velocity of B with respect to A is we have to draw perpendicular line to this so this is a A point so if you are drawing perpendicular to this link it will gives velocity of B with respect to A because it is perpendicular direction it is a link and this is a velocity diagram we are using the smaller letter and for the space diagram we are using the capital letter so we are getting the velocity of B with respect to A is equal to angular velocity of AB into the radius of AB because we are knowing V is equal to r omega similarly if C is any point on the link AB so we have to find out the velocity of C so at that time we are knowing that velocity of C with respect to A is equal to angular velocity of C with respect to A into AC so if you take divide both equation that is the velocity of C A divided by velocity of B A is equal to angular velocity of C A into AC divided by angular velocity of AB into AB so the angular velocity of C A and AB both are rotated with the angular velocity of omega it will get cancelled so we are getting AC by AB so we can easily find out the velocity of C A is equal to velocity of B A into AC by AB so we are knowing the velocity of B A by using this equation AC and AB are the distance from this diagram so where we can easily calculate the velocity of C A so we can locate the velocity of C A on this line now consider any link AB in which V A is known in magnitude as well as in the direction but V B known in direction only then we find the magnitude of V B suppose AB is one link we are knowing the direction of V A as well as the magnitude and V B is only we are knowing the direction we have to find out the magnitude of V B so this is the O pole from the O pole we are knowing the magnitude as well as the direction of the A so it will use the V A and we are knowing the just the direction of the B so this will use the direction we are drawn the parallel line to this V B direction and this is the AB link which is rotated in the anticlockwise direction suppose we are considering it is rotated in the anticlockwise direction now by using this concept we are knowing that the velocity of any link is perpendicular to that link so we have draw the perpendicular line so from the A points we have draw the perpendicular line like this so we are getting perpendicular line so we are getting this B point so it is nothing but the velocity of B if you are getting this like this is giving the direction it will use the velocity of B with respect to A so like this we can easily find out the velocity of B with respect to A if I had drawn the direction like this it will use the velocity of A with respect to B okay these are the basic concept of the relative velocity method so these are the two references I have taken thank you