In statics, Lami’s theorem is a condition that relates the sizes of three coplanar, concurrent and non-collinear forces, that keeps a body in static balance.
Lami’s hypothesis expresses that if three forces acting at a point are in harmony, each power is corresponding to the sine of the angle between the other two forces.
Consider three forces A, B, C acting on a particle or rigid body making angles α, β, and γ with one another.
As per Lami’s theorem, the particle shall be in equilibrium if,
The angle between the power vectors is taken when all the three vectors are arising out of the particle.
Lami’s Theorem Derivation:
In the below image there is a complete derivation of Lami’s theorem.
Restrictions of Lami’s Theorem
There are different limitations of Lami’s Theorem as given below:
- Three forces should exist in Lami’s Theorem.
- All three forces should be be coplanar.
- Forces should be concurrent.
- All three forces of Lami’s Theorem should non-linear.