Quasi-Static Assumption

Assuming motion is slow enough that inertial forces can be ignored, so every instant can be analyzed as a force balance.

The quasi-static assumption is a common simplification in robot manipulation analysis: velocities and accelerations are assumed small enough that inertial forces (the mass-times-acceleration term) can be neglected, so at every instant the external and contact forces are in balance, and the full dynamics equation collapses into static equilibrium — every force and torque sums to zero. Lynch and Park's textbook Modern Robotics uses it throughout its chapter on grasping and manipulation to analyze tasks like supporting, gripping, and pushing. Its benefit is that dynamics never needs to be integrated over time: it's enough to check, at each contact, whether it's sticking or slipping, and whether the contact force stays inside the friction cone (the range of directions friction allows). Slow pushing, peg-in-hole insertion, and grasp-stability analysis are mostly built on this assumption. The cost is that it breaks down once motion speeds up: flinging, throwing, and fast flipping — dynamic manipulation tasks — require going back to full rigid-body dynamics.

ExampleThe “ruler trick”: balance a long ruler horizontally on two index fingers, then slowly bring the fingers together. The ruler slides on one finger, then the other, then both, but its center of mass always stays between the two fingers, so it never falls — quasi-static force balance predicts exactly which finger slips and when. Move the fingers too fast, and the analysis breaks down, and the ruler falls.

Also called

Quasistatic Approximation

Related

Statics · Rigid-Body Dynamics · Coulomb Friction · Friction Cone · Non-prehensile Manipulation · Slip

Sources

Modern Robotics: Mechanics, Planning, and Control (Lynch & Park), Ch.12 Grasping and Manipulation
Robotic Manipulation (Russ Tedrake, MIT): Force Control