Principle of equilibrium states that a body is said to remain in the state of equilibrium when the resultant of forces acting on the body is zero. The forces that bring the set of forces acting on the body to equilibrium is called as equilibrant. Hence the equilibrant is equal to the resultant, but are opposite in direction( vector consideration) or have opposite signs.

There are different principles of equilibrium, of which the important ones are mentioned below:

1. Two Force Principle

2.Three Force Principle

3. Four Force Principle

### Two Force Principle

This principle states that for a body to be in the state of equilibrium under the action of two forces, the forces must be equal, opposite and collinear in nature.

Fig.1: Representation of Two Force Principle |

### Three Force Principle

For a body to remain under the condition of equilibrium under the action of three forces, the principle states that the resultant of any of the two forces must be equal, opposite and collinear with the third force. As per the figure-2, the three forces acting on the body are F1, F2 and F3. The resultant of F1 and the F2 forces is R. If the resultant force R is equal , opposite and collinear with the F3, then the body is in the state of the equilibrium.

Fig.2. Representation of Three Force Principle; |

### Four Force Principle

The principle states , the body remains in the state of equilibrium under the action of four forces, if the resultant of any two forces, is equal and opposite to the resultant of the other two forces.

Fig.3: Representation of Four force Principle; |

### Lami's Theorem - Study of Equilibrium Forces

The Theorem states that, " If three forces acting at a point be in equilibrium, then each force is proportional to the sine of angle between the other two". The mathematical representation of the same can be given as

Where P,Q and R are three forces and Î±, Î², Î³ are the angles.

Fig.3: Representation of Four force Principle; |