Rayrai Example: Spherical Joint Friction

Overview

Coulomb friction of spherical joints (Joint Damping and Friction). Three spherical pendulums ($m=1kg$ at $d=0.5m$) are released on the same conical swing, tilted $1.1rad$, and differ only in the friction ${\tau }_c$ of their spherical joints:

Bob	<dynamics friction>	Friction cone	What happens
blue	none	–	swings on
orange	$0.2Nm$	$2.3°$	spirals down slowly and stops
red	$0.6Nm$	$7.0°$	spirals down quickly and stops

The friction torque is the same in every direction and opposes the bob's rotation, so the swing loses energy at every turn instead of stopping one direction first. A bob can stop wherever gravity's torque, $mgd\sin \theta$ at the tilt $\theta$, is at most ${\tau }_c$: anywhere inside the ring drawn in its color. It stops off the vertical, and stays there. The example prints where and when each bob came to rest, and releases the pendulums again every 12 seconds.

Run

./build-examples/examples/rayrai_spherical_joint_friction

CMake target: rayrai_spherical_joint_friction. Source: examples/src/rayrai/dynamics/rayrai_spherical_joint_friction.cpp. On Windows, run rayrai_spherical_joint_friction.exe instead.

API pattern

The friction is the standard URDF attribute of the spherical joint:

<joint name="ball" type="spherical">
    <parent link="socket"/>
    <child link="bob"/>
    <dynamics friction="0.6"/>
</joint>

The joint's generalized velocity is the bob's angular velocity in its own frame. A joint held by friction keeps only round-off of it:

auto* pendulum = world->addArticulatedSystem(urdf);
pendulum->setState(gc, gv);  // gc: quaternion w, x, y, z; gv: angular velocity
world->integrate();
const bool atRest = pendulum->getGeneralizedVelocity().e().norm() < 1e-9;