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