Stance phase

The stance phase of a robot leg is the portion of a gait during which its foot is in the intended ground contact. It permits force transfer between the robot and its surroundings. Contact can occur with little load, and contact alone does not imply that the foot remains fixed without slipping. The swing phase instead transfers the foot toward another contact.

In an ideal rigid, nonadhesive contact model, let $g$ be the foot's normal gap above the ground and $F_n$ its normal contact force. The conditionsexclude penetration and tensile ground reaction. An open gap requires zero normal reaction; a zero gap permits a compressive reaction but does not require it to be strictly positive. The primary contact model distinguishes these unilateral constraints from the force/torque equations for equilibrium.^[ref]

For an original level-ground example, take a $20\mathrm{kg}$ robot supported by two stance feet, neglecting other external vertical forces. Newton's second law giveswhere $g_0=9.81\mathrm{m}{\mathrm{s}}^{-2}$ is gravitational acceleration and $a_z$ is upward center of mass acceleration. With equal sharing and $a_z=0$, each foot carries $98.1\mathrm{N}$. With $a_z=2\mathrm{m}{\mathrm{s}}^{-2}$, each carries $118.1\mathrm{N}$. Equal sharing is an additional symmetry assumption, not a consequence of knowing there are two contacts.

A simple Coulomb friction model constrains tangential force by $|F_t|\le \mu F_n$. At zero vertical acceleration and $\mu =0.3$, the two feet's combined horizontal-force capacity is at most $0.3m{g}_0=58.86\mathrm{N}$ in this planar model. Accelerating the body horizontally at $4\mathrm{m}{\mathrm{s}}^{-2}$ would require $80\mathrm{N}$ and violate that bound. A stance-time schedule alone cannot remove this force limit. Individual contact geometry and torque balance can impose further constraints even when the combined bound passes.

For a periodic cycle, contact duration $T_s$ gives duty cycle $\beta =T_s/T$. A proposed test records stance timing and forces separately, using calibrated sensors under the contacts together with body-motion measurements. It checks load transfer and slipping as well as touch timing. A support polygon is useful in an explicitly static planar model; dynamic stance additionally requires the changing force and momentum balance.