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Related Concept Videos

Angle of Twist: Problem Solving01:13

Angle of Twist: Problem Solving

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An electric motor applies a torque of 700 N·m to an aluminum shaft, triggering a stable rotation. Two pulleys, B and C, are subjected to torques of 300 N·m and 400 N·m, respectively. The modulus of rigidity is provided as 25 GPa. With the knowledge of the length and diameter of each segment, the twist angle between the two pulleys can be computed. First, a section cut is made between pulleys B and C, and the cut cross-section is analyzed using a free-body diagram. Given that the...
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Angle of Twist - Elastic Range01:13

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Consider a cylindrical shaft with a length denoted by L and a consistent cross-sectional radius referred to as r. This shaft undergoes a torque at the free end. The highest shearing strain within the shaft is directly proportional to the twist angle and the radial distance from the shaft axis. When the shaft behaves elastically, this shearing strain can be articulated using variables such as the applied torque, radial distance, the polar moment of inertia, and the modulus of rigidity. By...
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Unsymmetric Bending01:18

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Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from those in symmetrical bending, and are essential for designing structures to withstand different loading conditions. In unsymmetrical bending, the neutral axis—where stress is zero—does not necessarily align with the geometric axes of the cross-section. The...
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Unsymmetric Bending - Angle of Neutral Axis01:15

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Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
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Related Experiment Video

Updated: Aug 25, 2025

Magnetic Tweezers for the Measurement of Twist and Torque
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The generalized super-twisting algorithm with adaptive gains.

Ida-Louise G Borlaug1, Kristin Y Pettersen1, Jan Tommy Gravdahl1

  • 1Centre for Autonomous Marine Operations and Systems, Department of Engineering Cybernetics Norwegian University of Science and Technology (NTNU) Trondheim Norway.

International Journal of Robust and Nonlinear Control
|October 17, 2022
PubMed
Summary
This summary is machine-generated.

A new adaptive generalized super-twisting algorithm (GSTA) with dynamic gains ensures fast, stable control for autonomous underwater vehicles. This advanced GSTA improves tracking accuracy without increasing energy use.

Keywords:
autonomous underwater vehicleexperimental resultsroboticssliding mode control (variable structure systems)

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Area of Science:

  • Control Systems Engineering
  • Robotics
  • Ocean Engineering

Background:

  • Complex systems often face time- and state-dependent perturbations and uncertain control coefficients.
  • Achieving global finite-time convergence and stability in such systems is a significant control challenge.

Purpose of the Study:

  • To propose a novel adaptive generalized super-twisting algorithm (GSTA) for systems with time- and state-dependent uncertainties.
  • To demonstrate the algorithm's effectiveness in ensuring global finite-time convergence and stability.
  • To validate the adaptive GSTA's performance in controlling an articulated intervention autonomous underwater vehicle (AIAUV).

Main Methods:

  • Development of a novel adaptive generalized super-twisting algorithm (GSTA) with dynamically adapted control gains.
  • Utilization of a nonsmooth strict Lyapunov function to establish conditions for global finite-time stability.
  • Implementation and testing on an articulated intervention autonomous underwater vehicle (AIAUV) using a singularity-robust multiple task-priority method for trajectory generation.

Main Results:

  • The adaptive GSTA guarantees global finite-time convergence of system states.
  • Tracking errors for the AIAUV were shown to converge to zero in finite time.
  • Comparative analysis demonstrated that the adaptive GSTA outperformed the standard GSTA and adaptive-gain super-twisting algorithm in tracking accuracy.

Conclusions:

  • The proposed adaptive GSTA is well-suited for controlling AIAUVs, providing superior tracking performance.
  • Adding adaptive gains to the GSTA enhances tracking capabilities without increasing energy consumption.
  • The study validates the theoretical advantages of GSTA combined with practical adaptive gains for robust control applications.