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Virtual Work for a System of Connected Rigid Bodies01:06

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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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Related Experiment Video

Updated: Dec 25, 2025

Characterization of the Sense of Agency over the Actions of Neural-machine Interface-operated Prostheses
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Rendering of Constraints With Underactuated Haptic Devices.

Daniel Lobo, Miguel A Otaduy

    IEEE Transactions on Haptics
    |March 24, 2020
    PubMed
    Summary

    This study reveals unnatural ghost forces in underactuated haptic devices due to simplified rendering assumptions. A new strategy minimizes these forces, improving haptic rendering accuracy.

    Area of Science:

    • Robotics
    • Human-Computer Interaction
    • Haptics

    Background:

    • Previous proxy-based rendering algorithms for underactuated haptic devices rely on oversimplified assumptions.
    • These methods often neglect crucial factors like device configuration and user intent, leading to inaccuracies.

    Purpose of the Study:

    • To theoretically investigate and quantify unnatural ghost forces in underactuated haptic rendering.
    • To develop a novel rendering strategy that minimizes ghost forces and enhances force reproduction accuracy.

    Main Methods:

    • Theoretical analysis to identify and characterize ghost forces in proxy-based rendering.
    • Design and implementation of a new rendering strategy featuring anisotropic coupling.
    • Validation through synthetic experiments and a real-world experimental setup.

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    Main Results:

    • Unnatural ghost forces were theoretically identified and quantified under typical proxy-based rendering conditions.
    • The novel anisotropic coupling strategy effectively minimizes ghost forces.
    • The proposed method achieves a better match between forces rendered by underactuated and fully actuated devices.

    Conclusions:

    • Existing proxy-based rendering methods for underactuated haptics are flawed due to oversimplifications.
    • The developed anisotropic coupling strategy offers a significant improvement for realistic haptic force rendering.
    • This work advances the fidelity of haptic feedback in underactuated systems.