General Plane Motion

General plane motion is simply a superposition of translation and fixed axis rotation.

Absolute Motion

Relative Motion

Relative Velocity

Instantaneous Center of Zero Velocity

Relative Acceleration

Taking the time derivatives of the relative position equations, we get

which is valid for any two particles A and B.

However, if particles A and B are two points in the same rigid body, then the distance between them is constant and point B appears to travel a circular path around point A (as seen with respect to point A).

Therefore, the relative acceleration can be written as

where the superposition principal says that the acceleration of point B of a rigid body is equal to the translational accelation, a_A, of the entire rigid body with point A plus the fixed axis rotation of the rigid body about an axis through A.

The tangential component is perpendicular to the relative position vector r_A/B and points in the direction that rotates the body.

The normal component is directed along the relative position vector and points toward A, the point about which the relative motion occurs.

Notice that when two rigid bodies are pinned (constrained) together, the point connecting the bodies will have the same velocity and acceleration on both bodies. Therefore, the velocities and accelerations of the two bodies can be related by looking at this common point.

The instantaneous center of zero velocity for a rigid body in general plane motion is not fixed, so the acceleration of this point is usually not zero. Therefore, this point must not be used to calculate accelerations.

An instantaneous center of zero acceleration can be found for a rigid body just as for velocities, but it is usually not useful in the solution of simple problems.