  We studied the anelastic aftereffect of a flexure being used in a Kibble
balance, where the flexure is subjected to a large excursion in velocity mode
after which a high-precision force comparison is performed. We investigated the
effect of a constant and a sinusoidal excursion on the force comparison. We
explored theoretically and experimentally a simple erasing procedure, i.e.,
bending the flexure in the opposite direction for a given amplitude and time.
We found that the erasing procedure reduced the time-dependent force by about
30%. The investigation was performed with an analytical model and verified
experimentally with our new Kibble balance at the National Institute of
Standards and Technology employing flexures made from precipitation-hardened
Copper Beryllium alloy C17200.
  Our experimental determination of the modulus defect of the flexure yields
1.2E-4. This result is about a factor of two higher than previously reported
from experiments. We additionally found a static shift of the flexure's
internal equilibrium after a change in the stress and strain state. These
static shifts, although measurable, are small and deemed uncritical for our
Kibble balance application at present.
  During this investigation, we discovered magic flexures that promise to have
very little anelastic relaxation. In these magic flexures, the mechanism
causing anelastic relaxation is compensated for by properly shaping and loading
a flexure with a non-constant cross-section in the region of bending.
