15.6: Instantaneous Center of Zero Velocity
General plane motion, often observed in a rolling wheel, refers to a type of movement where the wheel is simultaneously rotating and translating. This complex motion can be understood by breaking it down into individual components.
To analyze this, consider two points on the wheel: point A and point B. The absolute velocity of point B can be expressed as the vector sum of the absolute velocity of point A and the relative velocity of point B with respect to point A. To simplify this analysis, one can select point A such that it has zero velocity at a given instant. This point, known as the instantaneous center of zero velocity (IC), lies on an axis perpendicular to the plane of motion. The intersection of this axis with the plane defines the location of the instantaneous axis of rotation.
At this particular moment, point B appears to move in a circular path around the IC. This can be visualized as the wheel is momentarily rotating around point A, turning in a circular motion. The velocities of different points on the wheel can then be calculated using the velocity equations, taking into account their radial distances from point A.
However, it is crucial to note that in the case of a wheel in general plane motion, the IC is not a fixed point. As the wheel moves, translates, and rotates, the IC changes accordingly. This dynamic nature of the IC reflects the complexity of the wheel's general plane motion, which involves both translation and rotation and requires a thorough understanding of kinematics for accurate analysis.
