Spherical Joint

A three-degree-of-freedom joint that lets one part rotate about a fixed point in any direction, but not translate.

A spherical joint, also called a ball joint or ball-and-socket joint, has one part's ball-shaped head seated inside another part's socket: the two can rotate about the ball's center in any direction, but can't translate relative to each other, giving 3 rotational degrees of freedom — functionally similar to a human shoulder or hip, and often written S in mechanism notation. Passive ball joints are used extensively in the linkages of parallel mechanisms like the Stewart platform. Real robot arms rarely drive a spherical joint with a single motor; instead, they approximate one with three revolute joints whose axes intersect at a point, as in a spherical wrist. In simulation, MuJoCo offers a ball joint type, representing rotation with a unit quaternion, so it takes up 4 numbers in qpos but only 3 in qvel; URDF has no spherical joint type at all, so it's usually approximated by chaining three revolute joints together.

ExampleSetting a humanoid robot's shoulder as a ball joint in MuJoCo lets a single quaternion describe the upper arm's orientation; exporting that to URDF for ROS requires splitting it into three separate revolute joints — shoulder pitch, roll, and yaw.

Also called

Ball Joint, Ball-and-Socket Joint

Related

Revolute Joint · Spherical Wrist · Parallel Mechanism · Degrees of Freedom (DoF) · MuJoCo (Multi-Joint dynamics with Contact) · Unified Robot Description Format

Sources

Modern Robotics (Lynch & Park), Ch.2.2 Joints
MuJoCo XML Reference: body/joint type
urdfdom_headers: joint.hpp (URDF joint types)