The red arrows on the surface of the gear tooth are the forces applied by the intermeshing gear. The gear tooth experiences these bending stresses each time the tooth is engaged as the gear spins. Fatigue is what causes a paper clip to break when bent back and forth and is an important failure mode in mechanical engineering.
Mechanical engineers design mechanisms to transmit power.
The drum has pockets so that the chain can not slip. Toothed belts, such as the belt which moves the ink jet in a computer printers or the timing belt in an automobile, are 20th century innovations based on the same principle using grooves in the sheave to prevent the belt from slipping. The most common mechanism to transmit or transform mechanical power is a gear set, as shown in this CAD drawing. At Lafayette College, sophomore mechanical engineering students build this gear box in ME 210. In fact, students produce the fly wheel, shown at the top of the upper drawing, from the CAD drawing file using Lafayette's CNC milling machine and lathe.