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Principle of virtual work
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In equilibrium, virtual work of applied forces vanishes.
ΣF·δr = 0A system is in equilibrium if the virtual work of the applied forces is zero for any small virtual displacement compatible with constraints: ΣF·δr = 0.
A lever balances when F₁δ₁ = F₂δ₂.
Constraint forces drop out, which makes this powerful.
In more detail
The principle of virtual work says that for a system in equilibrium, the total virtual work done by applied forces is zero for any small virtual displacement consistent with the constraints.
Real-world uses
- Engineers analyse structures and mechanisms using virtual work to find forces.
- Robotics uses virtual work to find joint torques for a desired end-effector force.
- Engineers analyse statics problems, such as a truss, by requiring that the virtual work of the forces is zero for any small allowed movement.
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Frequently asked questions
What is a virtual displacement?
An imagined small displacement that the constraints allow, used only in the mathematics.
Why is it useful?
It removes unknown constraint forces from the analysis, which can simplify a problem.
When do I use virtual work?
When you want the equilibrium condition directly, without finding every internal force in a structure.
Related topics in Work, Energy & Power
Renewable energy · Conservation of energy in collisions · Virial theorem · Work–energy with variable mass · Hamiltonian as total energy · Lagrangian mechanics intro