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Related Concept Videos

Rolling Without Slipping01:09

Rolling Without Slipping

People have observed the rolling motion without slipping ever since the invention of the wheel. For example, one can look at the interaction between a car's tires and the surface of the road. If the driver presses the accelerator to the floor so that the tires spin without the car moving forward, there must be kinetic friction between the wheels and the road's surface. If the driver slowly presses the accelerator, causing the car to move forward, the tires roll without slipping. It is essential...
Rolling Resistance: Problem Solving01:17

Rolling Resistance: Problem Solving

Rolling resistance, also known as rolling friction, is the force that resists the motion of a rolling object, such as a wheel, tire, or ball, when it moves over a surface. It is caused by the deformation of the object and the surface in contact with each other, as well as other factors like internal friction, hysteresis, and energy losses within the materials. Rolling resistance opposes the object's motion, requiring additional energy to overcome it and maintain movement. In practical...
Rolling With Slipping01:14

Rolling With Slipping

Rolling with slipping is a physical phenomenon that occurs when a rolling object experiences both rotational and linear motion but also experiences frictional forces that cause slipping. This phenomenon can occur in various situations, such as when a tire rolls on a wet road or a ball rolls on a rough surface.
An object's rolling motion is characterized by its rotation around its axis, while linear motion refers to the object's translational motion along a surface. Frictional forces can affect...
Rolling Resistance01:21

Rolling Resistance

When a solid cylinder rolls steadily on a rigid surface, the normal force applied by the surface on the cylinder is perpendicular to the tangent at the contact point. However, since no materials are entirely rigid, the surface's reaction to the cylinder involves a range of normal pressures.
For instance, imagine a hard cylinder rolling on a comparatively soft surface. The cylinder's weight compresses the surface beneath it. As the cylinder moves, the material in front of it slows down due to...
Rotational Motion about a Fixed Axis01:26

Rotational Motion about a Fixed Axis

A rigid body's rotation around a fixed axis makes every point within it trace a circular path around a specific line or point. The term given to this type of spinning is defined by the angular position, symbolized by the angle θ. This angle is gauged from a static reference line to the revolving object. From this angular position, any variation is referred to as angular displacement, denoted by dθ. The extent of this displacement can be calculated in degrees, radians, or revolutions, where one...
Non-uniform Circular Motion01:22

Non-uniform Circular Motion

In uniform circular motion, the particle executing circular motion has a constant speed, and the circle is at a fixed radius. However, not all circular motion occurs at a constant speed. A particle can travel in a circle and speed up or slow down, showing an acceleration in the direction of motion. In that case, the motion is called non-uniform circular motion, and an additional acceleration is introduced, which is in the direction tangential to the circle. 
For example, such accelerations...

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Related Experiment Video

Updated: Jul 7, 2026

Tracking Individual Running Metrics in Mice Using a Voluntary Wheel Running Protocol that Minimizes Social Isolation
04:48

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Tracking control of a rolling disk.

C Frangos1, Y Yavin

  • 1Dept. of Stat., Rand Afrikaans Univ., Johannesburg.

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|February 5, 2008
PubMed
Summary

This study introduces path controllability for a rolling disk, developing control laws to precisely track desired paths on a horizontal plane using tilting and pedaling torques.

Area of Science:

  • Robotics and Control Systems
  • Mechanical Engineering
  • Applied Mathematics

Background:

  • Controlling the motion of rolling objects presents challenges due to complex dynamics.
  • Achieving precise path tracking for a disk on a 2D plane requires sophisticated control strategies.
  • Existing methods may not fully address the non-holonomic constraints of a rolling disk.

Purpose of the Study:

  • To introduce and define the concept of path controllability for a disk rolling without slipping on a horizontal plane.
  • To develop novel control laws for trajectory tracking of the disk.
  • To enable the disk to follow arbitrary paths in the (X, Y)-plane.

Main Methods:

  • Formulation of the disk's dynamics considering rolling without slipping constraints.

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  • Introduction of the path controllability concept specific to the disk's motion.
  • Derivation of control laws based on the path controllability analysis.
  • Simulation or experimental validation of the proposed control strategy.

    • Main Results:

    • Demonstration that the disk is path controllable under the proposed framework.
    • Successful calculation of control laws enabling precise path tracking.
    • The disk can be guided along specified trajectories in the (X, Y)-plane.

    Conclusions:

    • The path controllability concept provides an effective framework for controlling rolling disk motion.
    • The derived control laws ensure accurate tracking of desired paths.
    • This research advances the control capabilities for underactuated mechanical systems like rolling disks.