Stiffness increases the tracking behavior the displacement of the end-effector (mass m) in relation to the input (a stiff actuator). Moreover, it decreases the influence of the external force Fe, which is often a disturbance to the system.
Damping is difficult! Damping can be regarded as loss of energy. However, the positive effect of damping is that it damps oscillations and resonances.
The damping of mechanical systems is hard to predict. Rule of thumb: damping decreases with increasing frequency. Joints and other system impurities increase damping.
with viscous damping ratio
|Metals in elastic range||0.01|
|Continuous metal structures||0.02 - 0.04|
|Metal structures with joints||0.03 - 0.07|
|Plastics (hard - soft)||0.02 - 0.05|
|Sintered material (piezos)||0.05|
|Airpots (vibration isolation tables)||0.07|
1 mass m, 1 spring c, 1 damper d, input xin, external force Fe
When designing a system that has to track the input xin and that needs to be insensitive to disturbance force Fe, then design ‘light and stiff’.
When designing a system that needs to be insensitive to vibrations xin (such as ground vibrations), then design ‘heavy and weak’.
At this point the spring energy is converted into kinetic energy: hence: and thus:
(from hence: and thus: )