Relative Motion Analysis - Velocity

A slider-crank mechanism converts rotational motion from the crank into linear motion of the slider through a connecting rod. As external force rotates the crank, it drives the connecting rod to move, producing general plane motion. This dual conversion allows engines to transform continuous rotational input into reciprocating linear output, enabling mechanical work.

Point A on the connecting rod undergoes translational motion, while point B on the crank experiences both translational and rotational motion. Point B's rotational motion occurs relative to point A, adding complexity to the mechanism's kinematics. Understanding these dual motions is essential for analyzing slider-crank dynamics.

Different reference frames simplify analysis of complex motion. A fixed frame examines absolute translational motion of points A and B, while a translating x'y' frame attached to point A isolates the rotational motion of point B relative to point A. This separation allows engineers to study each motion component independently.

The absolute linear velocity of point B equals the vector sum of the absolute linear velocity of point A and the relative velocity of point B with respect to point A. The relative velocity component arises from rotational motion and is always perpendicular to segment AB, enabling precise kinematic calculations.

The relative velocity of point B with respect to point A represents the velocity contribution from rotational motion. This term is always directed perpendicular to the connecting rod segment AB. It captures how point B moves around point A as the mechanism rotates, distinct from translational motion.

General plane motion combines both translational and rotational components simultaneously. Unlike pure translation where all points move identically, or pure rotation about a fixed axis, general plane motion allows different points to have different velocities. The slider-crank mechanism exemplifies this combined motion.

The relative velocity is perpendicular to segment AB because it results from rotational motion of point B around point A. In rigid body rotation, velocity is always perpendicular to the radius vector connecting the rotation center to the point. This geometric relationship ensures the connecting rod maintains constant length.