In order to calculate the forces acting on the joints of the robot arm, a free body diagram(FBD) must be drawn to analyse the forces involved. There are two types of forces acting on the arm. Firstly weight, mass times the gravitational acceleration. The force is a desire of the mass to move downward but is stationary. The second type of force here is torque. Torque is a force applied at a radial distance from a point. A torque can be described as a moment about a point but moments are normally used to describe non-circular mechanics.
Our robot will have only 2 DOF. The forces acting on the members of the arm are the weight of the arm links, the weight of the motors, and the weight of the object being lifted. These forces apply moments M1 and M2 as seen in the diagram.

It is important to consider the requirements of the system when designing the arm. If the arm needs to carry a heavy load and it needs to be moved very fast, the design of the arm will look a lot different than a robot that needs to be slow and precise in its movements. This is a FBD of a robotic arm that does not move; as the arm moves the force of the weights is still acting downward but more or less torque is applied to the joints. The study of moving forces is dynamics and will not be covered in this analysis.

The moments acting on the arm are:
↺ M1 = L1/2*W1 + L1*W2 + (L1+L2/2)*W3 + (L1+L3)*W4
↺ M2 = L2/2*W3 + L3*W4