Velocity Analysis

Velocities and acceleration in machines can be determined either analytically or graphically. With the invention of computers, it has become much easier to make use of analytical methods.

However, graphical analysis is more direct and is accurate to an acceptable degree and thus cannot be neglected.

Concept of a rigid body

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 as shown.
But since this is a rigid body, velocity components parallel to the line connecting the points should be equal.

If the component velocity of point B is greater than A, then the link will start elongating. If the case is opposite link starts to contract. Both these cases are impossible since this is a rigid body. Hence, the velocity components of both must be equivalent.

This means, if we subtract the velocity of A from the velocity of B, the relative velocity vector will have no component, parallel to the connecting line. It will get canceled. So relative velocity vector will be perpendicular to the connecting line.

Strictly speaking, all motions are relative since an arbitrary set of axes or planes is required to define motion. Usually, the earth is taken to be a fixed reference plane and all the motions relative to it are termed as absolute motions.

If a train moves in a particular direction, the motion of the train is referred to as the absolute motion of the train or motion of the train relative to the earth. Now, suppose a man moves on the train. Then, the motion of the man will be described in two different ways with different meanings:

  1. The motion of the man relative to the train: It is equivalent to the motion of the man assuming the train to be stationary.
  2. The motion of the man or absolute motion of the man relative to the earth: Motion of the man relative to the train + Motion of the man relative to the earth.

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