= 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 conditions
$$
g\ge0,\qquad F_n\ge0,\qquad gF_n=0
$$
exclude 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.<Robotic Systems by Kris Hauser>[Chapter 12, Contact modeling and Equilibrium conditions]{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> gives
$$
F_{n1}+F_{n2}=m(g_0+a_z),
$$
where $g_0=9.81\,\mathrm{m\,s^{-2}}$ 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 $a_z=2\,\mathrm{m\,s^{-2}}$, 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 $0.3mg_0=58.86\,\mathrm N$ in this planar model. Accelerating the body horizontally at $4\,\mathrm{m\,s^{-2}}$ 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.
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