Having lots of fun making centrifugally formed tops lately. This new gray/black "bracelet top" is one of my best -- partly for its long, wobble-free spins, and partly for a very nice feel during hand starts. The lion's share of its mass and rotational inertia resides in the floppy light and dark gray rotor, originally a gag bracelet for my wife.
The link design (left photo below) allows the bracelet to take on any in-plane shape with negligible resistance.
In this 82 g version, a bracelet of total length
L = 384 mm mounts on 3 equally spaced spokes of length
R = 64 mm. Best launch speeds and spin times are respectively ~1,000 RPM and ~90 s by hand and 1,520 RPM and 110 s with an electric starter. The structure could probably handle a lot more speed, but I have yet to push that envelope.
Centrifugal force is amazingly efficient at expanding, shaping, stiffening, and balancing the bracelet. At high speed (left), the bracelet blurs into a circular ring. But photos at lower speeds (right) hint at the true equilibrium shape, and it's definitely not circular. This shape forms at speeds well below critical and depends only on the bracelet / spoke length ratio
B =
L /
R.
Here, I chose
R = 64 mm first for structural reasons and then optimized
L to minimize wobble. The result:
L = 384 mm and
B = 6.00. Compare that
B to the
B = 5.20 of a bracelet just long enough to form a straight-sided equilateral triangle, the
B = 5.44 of a Rouleaux triangle, and the
B = 2
pi = 6.28 of a true circle. Smooth spins at
B > 6.28 are rare -- presumably due to bracelet waves between spokes.
Smaller blue/gray version with
R = 56 mm and
L = 336 mm -- here stopped gently enough to retain the bracelet's equilibrium shape. This is also the gray/black's equilibrium shape, as
B = 6.00 in both cases.
This version shows some vibration wobble, as its core (combined stem+hub+spoke+tip assemblies) isn't as stiff.