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Related Concept Videos

Centroid for the Paraboloid of Revolution01:16

Centroid for the Paraboloid of Revolution

The paraboloid of revolution is an axially symmetric surface generated by rotating a parabola around its axis. This shape has several applications in mechanical engineering due to its advantageous structural properties, such as strength against stress concentration points and rotational symmetry.
The centroid for the paraboloid of revolution is the point where all the mass of the paraboloid is concentrated. This centroid is important for engineering applications, as it determines how forces are...
Eccentric Axial Loading in a Plane of Symmetry01:16

Eccentric Axial Loading in a Plane of Symmetry

Eccentric axial loading occurs when an axial load is applied away from the centroidal axis of a structural member. This scenario is common in engineering, where structural elements may not be directly aligned due to various design or functional requirements.
Ellipses01:30

Ellipses

An ellipse is formed when a right circular cone is intersected by an inclined plane that does not cut through its base. This intersection yields a closed, symmetric curve characterized by distinctive geometric properties. Most notably, an ellipse is defined as the collection of all points in a plane for which the combined distances to two fixed points—called the foci—remain constant.The ellipse features two principal axes: the major and the minor axes. The major axis is the longest diameter,...
Spherical Coordinates01:23

Spherical Coordinates

Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
Theorems of Pappus and Guldinus: Problem Solving01:12

Theorems of Pappus and Guldinus: Problem Solving

Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a cylinder...
General Case of Eccentric Axial Loading01:12

General Case of Eccentric Axial Loading

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 bending,...

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Related Experiment Video

Updated: May 20, 2026

In Vivo Quantification of Hip Arthrokinematics during Dynamic Weight-bearing Activities using Dual Fluoroscopy
07:43

In Vivo Quantification of Hip Arthrokinematics during Dynamic Weight-bearing Activities using Dual Fluoroscopy

Published on: July 2, 2021

Patient-specific acetabular shape modelling: comparison among sphere, ellipsoid and conchoid parameterisations.

Pietro Cerveri1, Alfonso Manzotti, Guido Baroni

  • 1a Dipartimento di Bioingegneria - Politecnico di Milano , via Golgi 39, I-20133 Milano , Italy.

Computer Methods in Biomechanics and Biomedical Engineering
|July 14, 2012
PubMed
Summary

The human acetabular cup

Related Experiment Videos

Last Updated: May 20, 2026

In Vivo Quantification of Hip Arthrokinematics during Dynamic Weight-bearing Activities using Dual Fluoroscopy
07:43

In Vivo Quantification of Hip Arthrokinematics during Dynamic Weight-bearing Activities using Dual Fluoroscopy

Published on: July 2, 2021

Area of Science:

  • Orthopedic biomechanics
  • Medical imaging analysis
  • Computational geometry

Background:

  • Acetabular cup geometry is traditionally modeled as a hemisphere.
  • Recent literature suggests patient-specific and alternative geometries.
  • The sphericity assumption's accuracy requires further investigation.

Purpose of the Study:

  • To evaluate the limitations of the sphericity assumption in acetabular cup modeling.
  • To compare sphere, ellipsoid, and rotational conchoid parameterizations for acetabular surfaces.
  • To analyze fitting accuracy for the overall acetabular shape and the lunate surface independently.

Main Methods:

  • Hip surface models reconstructed from CT scans of Caucasian cadavers and patients.
  • Automated extraction of acetabular surfaces.
  • Nonlinear gradient-based and evolutionary computation for geometric fitting.
  • Statistical analysis of fitting errors.

Main Results:

  • Minor fitting errors (<1 mm) across all three geometries (sphere, ellipsoid, conchoid).
  • Sphere fitting significantly differed from ellipsoid and conchoid for the overall acetabular shape (Case A).
  • Ellipsoid and conchoid showed no significant difference for Case A, but did for the lunate surface only (Case B).

Conclusions:

  • The overall acetabular cup morphology can be accurately parameterized by ellipsoid or conchoid shapes, outperforming the sphere.
  • For the lunate surface alone, the ellipsoid provides superior fitting results compared to the sphere and conchoid.
  • These findings refine geometric modeling of the acetabulum for improved clinical applications.