An image-based approach to obtaining anthropometric measurements for inertia modeling

Marianne J R Gittoes1, Ian N Bezodis, Cassie Wilson

  • 1Cardiff School of Sport, University of Wales Institute, Cardiff, UK.

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Inertia Tensor01:24

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The concept of the inertia tensor is employed to depict the mass distribution and rotational inertia of a solid or rigid object. This tensor is expressed through a three-by-three matrix. Each component within this matrix corresponds to varying moments of inertia about specific axes.
The diagonal components of the inertia tensor matrix represent the moments of inertia concerning the principal axes of the object. These primary axes are defined as the axes where the object experiences the least...
Moments and Product of Inertia01:23

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The calculation of the moment of inertia for a differential element within a rigid body involves multiplying the element's mass by the square of the minimum distance from any one of the three-coordinate axes to the said element. This is a process that can be extended to cover the entire mass of the body by simply integrating the expression, thereby ascertaining the body's moment of inertia.
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Angular Momentum and Principle Axes of Inertia

The concept of angular momentum for a solid structure is illustrated as the cumulative result of the cross-product of the position vector of the mass element and the cross-product of the body's angular velocity with the position vector.
To put this equation into simpler terms, it can be reconfigured using rectangular coordinates. This involves choosing an alternative set of XYZ axes that are arbitrarily inclined with respect to the reference frame. The process of deriving the rectangular...
Moments of Inertia for an Area about Inclined Axes01:18

Moments of Inertia for an Area about Inclined Axes

In physics and engineering, understanding the moments of inertia for a given area with asymmetrical mass distribution is critical for proper design and analysis. When considering an arbitrary coordinate system, the moments of inertia can be obtained by integrating the moment of inertia for an infinitesimal area element.
Moment of Inertia about an Arbitrary Axis01:20

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The moment of inertia is typically associated with principal axes, but it can also be computed for any random axis. When an arbitrary axis is under consideration, the moment of inertia is determined by integrating the mass distribution of the object along that specific axis. It is crucial in applications like the design of machinery, where components rotate about various axes, and balance and stability are essential.
In this scenario, the perpendicular distance between the chosen arbitrary axis...