Support Reactions in Three Dimensions

A variety of supports are employed in mechanical engineering based on their application.  These support reactions in a three-dimensional force system prevent the system from translating and rotating.

Consider a robotic arm lifting a weight. Here, joint A is a ball and socket joint. The arm is free to rotate about any axis as there is no moment to restrict the rotation in the ball and socket joint. However, it restricts translational motion because of the three reaction forces along the three dimensions.

Alternately joint B on the arm is a single smooth pin support. This support creates three reaction forces and two couple moments and allows the rotational motion along the axis of the pin.

The base of the robotic arm is fixed support, having reaction forces and moments along all three directions.

Another type of support is hinge support, used commonly in a door. Three reaction forces at the support restrict the translational motion of the door, while two moments restrict the rotation of the door.