2D kinematics of a rigid body

Rigid body

A solid body that doesn’t deform.

Degrees of freedom

In the motion of a rigid body in 2D kinematics, there are degrees of freedom.

• Movement along direction
• Movement along direction
• Rotation about direction

In 3D, there are degrees of freedom: movement and rotation along each direction.

Translation

Movement that changes the position of an object. Translation can be done through a rectilinear or curvilinear path. Axes of the body always stays parallel.

Rotation

Circular movement of an object about a fixed axis that is perpendicular to the plane.

General 2D motion

Mixture of translation and rotation.

Here:

• - Angular velocity of relative to
• - Velocity of relative to
• - Acceleration of relative to
• - Position vector of relative to . It’s constant.

In general motion, each particle of the body has a different velocity at every instance.

Instantaneous centre of rotation

The point that has velocity at a particular instant of time. This point might be changing throughout the motion. Denoted by .

It can be imagined that the object is momentarily having a pure rotation about this centre .

can be found by drawing a line perpendicular at the velocity vectors at 2 different points and finding their intersection point.

Centrode

The locus of instantaneous centres during the motion.