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Related Concept Videos

Rigid Body Equilibrium Problems - II01:21

Rigid Body Equilibrium Problems - II

A rigid body is in static equilibrium when the net force and the net torque acting on the system are equal to zero.
Consider two children sitting on a seesaw, which has negligible mass. The first child has a mass (m1) of 26 kg and sits at point A, which is 1.6 meters (r1) from the pivot point B; the second child has a mass (m2) of 32 kg and sits at point C. How far from the pivot point B should the second child sit (r2) to balance the seesaw?
Rigid Body Equilibrium Problems - I00:49

Rigid Body Equilibrium Problems - I

A rigid body is said to be in static equilibrium when the net force and the net torque acting on the system is equal to zero. To solve for rigid body equilibrium problems, do the following steps.
Virtual Work for a System of Connected Rigid Bodies01:06

Virtual Work for a System of Connected Rigid Bodies

Virtual work is a powerful method used to solve problems involving several connected rigid bodies. When the system is in equilibrium, virtual work is zero. This allows the calculation of the resulting forces when a system undergoes a virtual displacement. When attempting to analyze such a system, first, use a free-body diagram, where an independent coordinate represents the configuration of the links, and mark its deflected position resulting from the positive virtual displacement.
Next,...
Planar Rigid-Body Motion01:22

Planar Rigid-Body Motion

Understanding the movement of a rigid body in planar motion involves recognizing that every particle within this body is traversing a path that maintains a consistent distance from a specific plane. This concept is fundamental in the study of physics and mechanical engineering, and it allows us to comprehend better how objects move in space.
Planar motion is typically divided into three distinct categories. The first is rectilinear translation, demonstrated by a subway train that moves along...
Angular Momentum: Rigid Body01:11

Angular Momentum: Rigid Body

The total angular momentum of a rigid body can be calculated using the summation of the angular momentum of all the tiny particles rotating in the same plane. Considering all the tiny particles rotating in the x-y plane, the direction of angular momentum of all such particles and that of the rigid body would be perpendicular to the plane of the rotation along the z-axis.
This calculation can get complicated when tiny particles within the rigid body are not rotating in the same plane but have...
Radius of Gyration of an Area01:12

Radius of Gyration of an Area

The second moment of area, also known as the moment of inertia of area, is a crucial factor in understanding an object's resistance against bending deformation, or stiffness. To accurately estimate the second moment of area along any axis, one needs to concentrate all areas associated with that object into a thin strip, which should be placed parallel to that particular axis.

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Automatic multiple-zone rigid-body refinement with a large convergence radius.

Pavel V Afonine, Ralf W Grosse-Kunstleve, Alexandre Urzhumtsev

    Journal of Applied Crystallography
    |August 4, 2009
    PubMed
    Summary

    An automatic procedure for rigid-body refinement was developed to balance speed and accuracy. This method, implemented in phenix.refine, uses a multiple-zone protocol for efficient crystallographic model building.

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    Area of Science:

    • Crystallography
    • Structural Biology
    • Computational Chemistry

    Background:

    • Rigid-body refinement is a crucial technique in structural biology for refining atomic coordinates of molecular groups moving cohesively.
    • Current methods often face challenges in balancing computational efficiency with the ability to converge from large initial errors.

    Purpose of the Study:

    • To develop an automated, efficient, and robust procedure for rigid-body refinement.
    • To optimize the protocol for practical applications in structural determination, considering both speed and convergence radius.

    Main Methods:

    • Extensive analysis of trial refinements across 12 classes of rigid-body displacements with varying error magnitudes.
    • Utilized both least-squares and maximum-likelihood target functions to evaluate refinement strategies.
    • Developed and empirically optimized a multiple-zone protocol based on test refinement results.

    Main Results:

    • Identification of optimal parameterization for a multiple-zone protocol through extensive empirical testing.
    • Demonstrated a practical compromise between runtime requirements and convergence radius for rigid-body refinement.
    • The developed protocol effectively handles various magnitudes of initial atomic coordinate errors.

    Conclusions:

    • The newly established multiple-zone protocol offers an efficient and reliable approach to rigid-body refinement.
    • This automated procedure enhances the process of crystallographic model building and refinement.
    • The protocol is integrated into the widely used phenix.refine software, making it accessible for researchers.