In order to execute proper design of a mechanism,
velocity analysis is of utmost importance. A designer's real interest is variation of
outlet link velocity for a specified, inlet velocity. The interesting thing about velocity analysis
is, you can determine velocity of any link, just by understanding, 2 simple concepts. Frist concept. A rigid body cannot elongate or contract,
in any direction. That means, if you take 2 points in a rigid
body, it can have 2 different velocities. But velocity components parallel to, the line
connecting the points, should be equal. If component velocity of point B is greater
than A, then link will start elongating. If the case is opposite, link will start contracting. Both these cases are impossible, since this
is a rigid body. So velocity components of both points should
be equal. This means, if we subtract velocity of A,
from velocity of B, the relative velocity vector will have no component, parallel to
the connecting line. It will get cancelled. So relative velocity vector will be perpendicular
to the connecting line. In short, concept 1 can be simplified as,
relative velocity between any 2 points in a rigid body, should be perpendicular to the
line connecting them. Second concept is applicable to mating surfaces. Mating pair of surface will never penetrate. This is the common mating point, or mating
line for both the links. This line represents common normal. The same point can have different velocity,
on different links. No penetration means, velocity component of
both the link velocities along, common normal should be equal. If velocity component of 2 is less than velocity
component of 1, then surfaces will penetrate. If opposite is the case, surfaces will detach. Both these cases are not possible for mating
surfaces. So velocity components along common normal
should be equal. Since velocity components are equal, if we
take a vector difference of V 1 and V 2, it should have no component along the common
normal. So the relative velocity should be perpendicular
to common normal. Now we will apply these 2 concepts on different
mechanisms, to do velocity analysis of them. First is a 4 bar linkage. We know input angular velocity, and we want
to find out outlet velocity. Here approach is simple, we will say that,
bar at middle cannot expand or contract. Since we know angular velocity of this link,
we can easily find out magnitude and direction of velocity of, point 1. But for point 2, we know only the direction
of velocity. Here first concept we learned, comes for help. Since this bar cannot elongate or contract,
relative velocity between these points should be perpendicular to this link. Which will lead to, magnitude of velocity
at point 2. From here, angular velocity of link can easily
be deduced. Now consider this mechanism. We know angular velocity of this cam; we want
to find out angular velocity of the second cam. This is the common normal at the time of mating. Consider the mating point, which lies on both
the cams. We know velocity direction and magnitude of
this point on first cam. But for second cam, we know only direction. Here 2nd concept we learned comes to help. Since the links cannot penetrate, relative
velocity should be perpendicular to common normal. So we can find out magnitude of, V 2, which
will lead to link angular velocity. Using same methodology, you can do velocity
analysis of any other mechanism. Hope you got a good introduction to, velocity
analysis. Thank you