Lami’s Theorem

In statics, Lami’s theorem is an equation that relates the magnitudes of three coplanar, concurrent, and non-collinear forces that keep a body in static equilibrium.

Lami’s theorem states that if three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two forces.

Consider three forces A, B, and C, acting on a particle or rigid body, making angles α, β and γ with each other.

According to Lami’s theorem, the particle shall be in equilibrium if

When all three vectors emerge from the particle, the angle between the force vectors is taken.

Conditions for Applicability of Lami's theorem:

• The three forces must be coplanar.
• The forces should act on a single point.
• The system must be in static equilibrium (net force equals zero).

Applications of Lami's theorem:

• Used to solve problems in mechanics involving three forces in equilibrium.
• Commonly applied in structural analysis, crane and pulley systems, and mechanical linkages.