Friction Models

Friction is the force that resists sliding. Simple models treat it as a constant push back, or as growing with speed. Real surfaces also stick: it takes more force to start sliding than to keep sliding. That difference causes the jerky stick-slip motion behind squeaky doors and jittery robot joints.

Friction model Static friction μs Kinetic friction μk Viscous coefficient Pulling speed

Three models

$$\text{Coulomb: } F = \mu_k N\,\operatorname{sign}(v) \qquad \text{Viscous: } F = b\,v \qquad \text{Stiction: } \lvert F_{\text{applied}}\rvert < \mu_s N \Rightarrow v = 0$$

Real contacts combine them, often with a smooth drop from static to kinetic friction at low speed, called the Stribeck effect.

What to notice

With stiction, the block sits still while the spring stretches and the force climbs. When the force reaches the static limit, the block breaks free, jumps forward because kinetic friction is lower, and sticks again. The force plot becomes a sawtooth. With only Coulomb or viscous friction, the block slides smoothly. The bigger the gap between static and kinetic friction, and the softer the spring, the worse the stick-slip.

Robot joints with stiction make controllers struggle with small, precise moves, since the joint either does not move or jumps. Controllers often add friction compensation, and good joints use bearings and lubrication to keep stiction low.