2D Rigid Body Motion is the
Sum of the Translation and
Rotation Velocities

Two dimensional motion includes both a translation and rotation components. To solve problems, it is usually easier to break rigid body motion into these two components.

To derive the 2D relative velocity equation, first relate two arbitrary points on a rotating body,

     rB = rA + rB/A

Differentiating with respect to time gives

     drB /dt = drA /dt + drB/A /dt

vB = vA + vB/A

Typical Rotating 3-link
Structure Motion

The relative velocity equation can be separated into linear motion and angular motion,


The rotation equation can also be written as

     vB = vA + ω × rB/A

     vB = vA + ωret

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