Consider a system of two rods. Rod 1 and rod 2 are fixed to the plane frame by pin joints. Both the rods together are joined by pins. There are three pins and two rods. Both the rods together have six degrees of freedom. However, there are three pins, arresting six degrees of freedom. Hence, the degree of freedom of this system is zero. This is called a structure. No particle of a rigid structure can undergo motion.
If a force is applied to the structure, reaction forces are developed for keeping the structure in equilibrium. Can we find the reaction forces? Yes, since there are three non-parallel forces acting, they must pass through a point. In this case, the forces will pass through, common pin. By applying Lami's theorem, we can find the reaction forces.
This problem is called statically determinate, because the forces can be found by applying the equation of equilibrium.
| Equation of equilibrium |
If you make a hole a hole near one end of the rod, and through this hole, insert it in the pin, the position of the center point of the hole gets fixed. However, the rod can be rotated about this point. Thus, a pin joint arrest two degrees of freedom. Constraint means the restriction of movement. Pin restricts movement in two directions. Certain types of constraints restrict only two degrees of freedom. For example, a roller moving on a plane surface is constrained along normal direction, but not against tangential direction. The fixed support offers constraint against rotation as well as lateral movement. |