507 Mechanical Movements

249

Ball-and-socket joint, arranged for tubing

Ball-and-socket joint, arranged for tubing.

Only the input is driven; every other part of this model moves by physics (MuJoCo), and its ratios are measured. Run it live, change its parameters, or switch the friction off to see the output stop.

Modelled as
The socket stands fixed: a spherical shell (inner radius 4.08, 0.6 thick) open at the top for the upper tube's neck and at the bottom mouth (52°), made as 24 x 12 curved segments, its two halves bolted at the flanges. The ball (radius 4, a 32-sided polyhedron on the sphere) is on the lower tube. The tube hangs from the ball and is carried only by the socket: it rides free on two slides (across and up/down) and swings on a hinge through the ball's centre, the one driven joint (0.42 rad at 0.25 Hz, torque limited to 3 N·m).
Measured
The ball seats on the socket's lower half and stays there: it sits 0.08 to 0.10 cm down and its centre wanders 0.007 cm across over the run, with the tube swinging -0.413 to 0.403 rad. The deepest contact is 0.004 mm.
Notes
Brown gives no sizes. The upper tube and the socket are one fixed piece. The swing is in one plane, so the render reads the joint side-on; the joint is free about all axes through the ball's centre.

Film (MP4) · Still (PNG) · Spec (YAML) · Model (MJCF)

Figure 249 from Brown, 1868
Brown's figure 249 (1868)