Bicycle suspension is the system, or systems, used to suspend the rider and bicycle in order to insulate them from the roughness of the terrain. Bicycle suspension is used primarily on mountain bikes, but is also common on hybrid bicycles.
Bicycle suspension can be implemented in a variety of ways, and any combination thereof:
The suspension stem is now uncommon with the ongoing trend of short stems which limit the suspension size and the "slacker" head tube angle for stability. Bicycles with only front suspension are referred to as hardtail and bicycles with suspension in both the front and rear are referred to as dual or full suspension bikes. When a bicycle has no suspension it is called rigid. Bicycles with only rear suspension are uncommon although the Brompton folding bicycle is equipped with rear only suspension.
Although a stiffer frame is usually preferable, no material is infinitely stiff and therefore any frame will exhibit some flexing. Bicycle designers intentionally make frames in such a way that the frame itself can absorb some vibrations.
Besides providing comfort to the rider, suspension systems improve traction and safety by helping to keep one or both wheels in contact with the ground.