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Related Concept Videos

Virtual Work01:20

Virtual Work

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The principle of virtual work states that if a body is in static and dynamic equilibrium, then the sum of all the virtual work done by all external forces and couple moments for any given virtual displacement must be zero.
In static equilibrium, a body can experience an imaginary or virtual movement, such as displacement or rotation. The virtual work done by a force is equal to the dot product of force and virtual displacement in the direction of the force. When it comes to virtually rotating a...
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Virtual Work for a System of Connected Rigid Bodies01:06

Virtual Work for a System of Connected Rigid Bodies

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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.
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Velocity and Position by Graphical Method01:34

Velocity and Position by Graphical Method

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Velocity and position can be calculated from the known function of acceleration as a function of time. The total area under the acceleration-time graph and the velocity-time graph gives the change in velocity and position, respectively. In the case of an airplane, its acceleration is tracked using the inertial navigation system. The pilot provides the input of the airplane's initial position and velocity before takeoff. The inertial navigation system then uses the acceleration data to...
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Kinetic Friction01:26

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Consider a truck trying to pull a stationary car. As the truck exerts a force on the car, static friction is created at the point of contact between the two surfaces. This frictional force resists the car's movement and keeps it at rest. However, when the applied force by the truck surpasses the limiting static frictional force, an interesting phenomenon occurs. The frictional force at the interface reduces to a lower value, known as the kinetic frictional force. At this point, the car...
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Three-Dimensional Force System01:30

Three-Dimensional Force System

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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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Kinematic Equations for Rotation01:30

Kinematic Equations for Rotation

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In mechanics, when one observes a rigid body in rotational motion with constant angular acceleration, it is possible to establish equations for its rotational kinematics. This process resembles how linear kinematics are dealt with in simpler motion studies.
For instance, imagine a point A on a rigid body engaged in circular motion. The translational velocity of this particular point can be calculated by taking the time derivatives of the displacement equation, which essentially measures the...
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Related Experiment Video

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In Vivo Quantification of Hip Arthrokinematics during Dynamic Weight-bearing Activities using Dual Fluoroscopy
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Graphic kinematics, visual virtual work and elastographics.

Allan McRobie1, Marina Konstantatou1, Georgios Athanasopoulos1

  • 1Cambridge University Engineering Department, Trumpington St, Cambridge CB2 1PZ, UK.

Royal Society Open Science
|June 3, 2017
PubMed
Summary

This study introduces a graphical method combining graphic statics and Williot diagrams for analyzing truss structures. It enables visualization of statics, kinematics, and elastic behavior in 2D and 3D pin-jointed trusses.

Keywords:
Maxwell reciprocal diagramsRankine reciprocal diagramsWilliot diagramsgraphic staticskinematicsvirtual work

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Area of Science:

  • Structural Engineering
  • Computational Mechanics
  • Applied Mathematics

Background:

  • Graphic statics provides a graphical method for analyzing forces in structures.
  • Williot diagrams are used to determine displacements in structures.
  • Integrating these methods can offer new insights into structural behavior.

Purpose of the Study:

  • To develop a unified graphical approach for analyzing both statics and kinematics of pin-jointed trusses.
  • To extend this graphical method to both two- and three-dimensional structures.
  • To introduce novel diagrams for visualizing elastic behavior and structural mechanisms.

Main Methods:

  • Combining reciprocal form and force diagrams with Williot displacement diagrams.
  • Dissecting force diagrams into component cells and translating them to form displacement diagrams.
  • Utilizing parallelograms (2D) and parallelopipeds (3D) to represent Virtual Work contributions.
  • Identifying mechanisms by translating force cells and obtaining elastic solutions via aspect ratios.

Main Results:

  • A topologically equivalent displacement diagram to the structure's form diagram is defined.
  • Contributions to Virtual Work are visualized as geometric shapes separating force and displacement.
  • Structural mechanisms are identified through specific force cell translations.
  • Elastic solutions are derived by adjusting the aspect ratios of geometric representations.

Conclusions:

  • The proposed graphical method offers a comprehensive description of statics and kinematics for pin-jointed trusses.
  • New 'elastographic' diagrams (deformed Maxwell-Williot and Rankine-Williot) are presented, integrating structural deflection with member forces.
  • This approach enhances the understanding of structural behavior and facilitates the analysis of complex truss systems.