Relative Motion Analysis - Velocity

A stroke engine has a slider-crank mechanism that converts rotational motion from the crank into linear motion of the slider or vice versa.

As the crank rotates due to external force, it causes the connecting rod to move, resulting in a general planar motion.

Point A from the connecting rod and point B from the crank undergo translational motion. Furthermore, point B also undergoes rotational motion with respect to point A.

The absolute translational motion of points A and B can be studied using a fixed frame.

Similarly, the rotational motion of point B, with respect to point A,  can be analyzed using a translating x'y' frame attached to point A.

The absolute linear velocity of point B is then expressed as the vector sum of the absolute linear velocity of point A and the relative velocity of point B with respect to point A.

Here, the last term represents the relative velocity of point B due to the rotational motion having the direction perpendicular to the segment AB.