Name: rolling wheel motion and the instant center
Uploaded: 2024-03-07T13:22:24.000Z
Duration: 1 min 20 s
Channel: JoVE

Consider a wheel in general planar motion. The absolute velocity of point B is expressed as the vector sum of the absolute velocity of point A and the relative velocity of point B with respect to point A.
If point A is chosen such that it has a zero velocity at a given instant, then the velocity expression for point B gets simplified. Here, point A is called an instantaneous center of zero velocity or IC.
This point 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.
Here, point B appears to move momentarily in a circular path around the instantaneous center of zero velocity.
The velocities of different points on the wheel can be calculated using the velocity equations with the corresponding radial distances with respect to point A.
For a wheel undergoing general planar motion, the instantaneous center of zero velocity point is not fixed but changes with the motion of the wheel.

instantaneous center of zero velocity

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&#39;s general plane motion, which involves both translation and rotation and requires a thorough understanding of kinematics for accurate analysis.

Consider a wheel in general planar motion. The absolute velocity of point B is expressed as the vector sum of the absolute velocity of point A and the ...

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JoVE Core

Mechanical Engineering

Unit 1

Planar Kinematics of a Rigid Body

KEY TERMS AND CONCEPTS

rolling wheel motion and the instant center

General plane motion can be seen in a rolling wheel. The wheel rotates and translates at the same time. To study this motion, the velocity of one point can be written as the vector sum of the velocity of another point and the relative velocity between them.

A useful simplification is to choose a point that has zero velocity at a given instant. This point is called the instantaneous center of zero velocity, or IC. The IC lies on an axis perpendicular to the plane of motion. Where that axis meets the plane gives the instantaneous axis of rotation.

At that moment, another point on the wheel moves as if it were circling the IC. The motion can look like the wheel is briefly rotating around the zero-velocity point. The velocity of points on the wheel can then be found from their distance from that point.

The IC does not stay in one place for a wheel in general plane motion. As the wheel rolls, translates, and rotates, the IC changes as well. This makes the instantaneous center a moving reference for kinematics analysis.

Rolling Wheel Motion and the Instant Center

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General plane motion can be seen in a rolling wheel. The wheel rotates and translates at the same time. To study this motion, the velocity of one point can be written as the vector sum of the velocity of another point and the relative velocity between them. A useful simplification is to choose a point that has zero velocity at a given instant. This point is called the instantaneous center of zero velocity, or IC. The IC lies on an axis perpendicular to the plane of motion. Where that axis...

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key terms and concepts

Learn how a rolling wheel combines rotation and translation, and how the instantaneous center of zero velocity helps analyze point velocities in plane motion.

Rolling Wheel Motion and the Instant Center | JoVE K12

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Rolling Wheel Motion and the Instant Center

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