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Three-Dimensional Force System01:30

Three-Dimensional Force System

3.0K
In mechanical engineering, a three-dimensional force system is a system of forces acting in three dimensions, with forces applied along the x, y, and z coordinate axes. The three-dimensional force system is an important concept in mechanical engineering, as it allows engineers to understand and analyze the behavior of objects and structures in three dimensions. By understanding the forces acting on a system, engineers can design more efficient and effective mechanical systems that can withstand...
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General Case of Eccentric Axial Loading01:12

General Case of Eccentric Axial Loading

612
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 symmetrical bending, which are essential for designing structures to withstand different loading conditions.
Consider a member subjected to equal and opposite forces that are applied along a line that does not coincide with the member's neutral axis. In unsymmetrical...
612
Thin-Walled Hollow Shafts01:15

Thin-Walled Hollow Shafts

667
In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution of...
667
Method of Sections: Problem Solving I01:27

Method of Sections: Problem Solving I

1.2K
Consider a symmetrical roof truss structure, composed of vertical, diagonal, and horizontal members. The length of each horizontal member is 4 m. The lengths of the vertical members FB and HD are 4 m, while the length of member GC is 6 m. The loads acting at joints F, G, and H are 2 kN, while those at joints A and E are 1 kN.
1.2K
Three-Dimensional Force System:Problem Solving01:30

Three-Dimensional Force System:Problem Solving

1.5K
A three-dimensional force system refers to a scenario in which three forces act simultaneously in three different directions. This type of problem is commonly encountered in physics and engineering, where it is necessary to calculate the resultant force on the system, which can then be used to predict or analyze the behavior of the object or structure under consideration.
To solve a three-dimensional force system, first resolve each force into its respective scalar components. Do this using...
1.5K
Method of Sections: Problem Solving II01:30

Method of Sections: Problem Solving II

1.8K
Consider an arbitrary truss structure composed of diagonal, vertical, and horizontal members fixed to the wall. To calculate the force acting on members CB, GB, and GH, method of sections can be used. The loads and lengths of the horizontal and vertical members are known parameters, as shown in the figure.
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Three-Dimensional Displacement Patterns in Maxillary Molar Distalization: A Comparative Finite Element Study.

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Related Experiment Video

Updated: Mar 29, 2026

Author Spotlight: Development of a Novel Finite Element Analysis Model for Improved Orthognathic Surgical Techniques
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Author Spotlight: Development of a Novel Finite Element Analysis Model for Improved Orthognathic Surgical Techniques

Published on: October 20, 2023

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Unilateral Outer Bow Expanded Cervical Headgear Force System: 3D Analysis Using Finite Element Method.

Allahyar Geramy1, Omid Mortezai2, Masomeh Esmaily3

  • 1Professor, Dental Research Center, Dentistry Research Institute, Tehran University of Medical Sciences, Tehran, Iran; Department of Orthodontics, School of Dentistry, Tehran University of Medical Sciences, Tehran, Iran.

Journal of Dentistry (Tehran, Iran)
|December 2, 2015
PubMed
Summary
This summary is machine-generated.

Expanding unilateral headgear outer bows alters molar distalizing forces. Increased expansion leads to greater distalizing force on the affected molar and reduced force on the contralateral molar.

Keywords:
AsymmetricExtraoral Traction AppliancesFinite Element Analysis

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Area of Science:

  • Orthodontics
  • Biomechanics
  • Finite Element Analysis

Background:

  • Headgears are effective orthodontic appliances for achieving treatment goals.
  • Unilateral molar distal movement may be required during orthodontic treatment, achievable with asymmetric headgear.
  • Various unilateral headgear designs have been developed.

Purpose of the Study:

  • To analyze the force system of unilateral expanded outer bow asymmetric headgears.
  • To evaluate the biomechanical effects of varying outer bow expansion using the finite element method (FEM).

Main Methods:

  • Six 3D finite element models of the maxilla, including molars and periodontal ligaments, were created.
  • Cervical headgears with expanded outer bows were simulated with a 2 N force applied to the outer bow ends.
  • Distalizing force and net moment were evaluated using ANSYS Workbench.

Main Results:

  • Increasing outer bow expansion decreased distalizing force on the non-expanded molar (1.69 N to 1.37 N).
  • Distalizing force increased on the expanded molar (2.19 N to 2.49 N).
  • Net moment increased with greater expansion (2.26 N.mm to 4.64 N.mm).

Conclusions:

  • Unilateral outer bow expansion generates differential distalizing forces on maxillary molars.
  • The magnitude of distalizing force is directly related to the degree of outer bow expansion.