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Related Concept Videos

Stability of structures01:14

Stability of structures

In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...
Stress Concentrations in Circular Shafts01:18

Stress Concentrations in Circular Shafts

Consider the elastic torsion formula, which applies to a circular shaft with a consistent cross-section. This formula assumes that the shaft's ends are loaded with rigid plates firmly attached. However, in many cases, torques are applied to the shaft through mechanisms like flange couplings or gears, which are connected by keys inserted into keyways. This application method modifies the stress distribution near the point of torque application, causing it to deviate from the distributions...
Stresses under Combined Loadings01:23

Stresses under Combined Loadings

When analyzing a bent tube with a circular cross-section subjected to multiple forces, it is crucial to determine the stress distribution in order to maintain structural integrity under varied load conditions.
The process begins by slicing the tube at critical points and analyzing the internal forces and stress components at these sections, focusing on the centroid. Normal stresses, generated by axial forces and bending moments, are either compressive or tensile and vary across the section from...
Applications of Stress01:04

Applications of Stress

Consider a structure made of a boom and a rod designed to support a load. These two components are connected by a pin and stabilized by brackets and pins. The boom and the rod are detached from their supports to assess the different stresses imposed on this structure, and a free-body diagram is drawn. Then, all the forces applied, including the load acting on the structure, are identified. The reaction forces exerted on both the boom and the rod are computed using the equilibrium equations.
The...
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...
Design Consideration01:22

Design Consideration

Designing a structure involves a series of considerations, primarily the material's ultimate strength, calculated through tests that measure changes under increased force until the material reaches its breaking point or limit. The ultimate load, where the material breaks, is divided by its original cross-sectional area, resulting in the ultimate normal stress or strength. The ultimate shearing stress is another significant factor taken into account.
The factor of safety is another key aspect...

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Related Experiment Video

Updated: May 20, 2026

A Modified Lean and Release Technique to Emphasize Response Inhibition and Action Selection in Reactive Balance
07:19

A Modified Lean and Release Technique to Emphasize Response Inhibition and Action Selection in Reactive Balance

Published on: March 19, 2020

Risk-managed safety screening via stability-constrained reachability tubes for vehicle handling.

Jinzhe Yang1, Jianzheng Liu2, Kai Tian3

  • 1Tianjin University of Science & Technology, Tianjin, China.

Scientific Reports
|May 18, 2026
PubMed
Summary

This study introduces a stability-constrained reachability tube for vehicle handling limits. It enables real-time safety checks for emergency maneuvers, considering tire friction, road grade, and crosswind conditions.

Keywords:
Finite-time reachabilityNonconvex set reconstructionOnline feasibility assessmentRisk-managed safety screeningStability-constrained reachability tubesVehicle handling envelope

Related Experiment Videos

Last Updated: May 20, 2026

A Modified Lean and Release Technique to Emphasize Response Inhibition and Action Selection in Reactive Balance
07:19

A Modified Lean and Release Technique to Emphasize Response Inhibition and Action Selection in Reactive Balance

Published on: March 19, 2020

Area of Science:

  • Robotics and Control Systems
  • Vehicle Dynamics and Safety

Background:

  • Emergency maneuvers are limited by tire saturation and stability.
  • Online querying of vehicle handling envelopes is crucial for safety.

Purpose of the Study:

  • To formulate a stability-constrained finite-time reachability tube for vehicle dynamics.
  • To enable real-time safety screening for near-limit driving scenarios.

Main Methods:

  • Developed a stability-constrained finite-time reachability tube for a planar single-track vehicle model.
  • Utilized analytic stability screening and nonconvex α-shape reconstruction for offline tube construction.
  • Derived sampling-complexity scaling based on time resolution, geometric tolerance, and environment dimension.

Main Results:

  • Proved compactness and Hausdorff-continuity of the reachability tube.
  • Demonstrated fast online feasibility screening using constructed tube slices.
  • Validated the approach on high-fidelity benchmarks including friction-only, grade-only, and wind-only variations.

Conclusions:

  • The developed reachability tube effectively bridges reachability analysis and reliability-facing safety screening.
  • The method provides conservative triage and diagnostics for extreme vehicle scenarios.
  • Enables safer operation of vehicles near their dynamic limits.