  A new instrument is required to accommodate the need for increased
portability and accuracy in laser power measurement above 100 W. Reflection and
absorption of laser light provide a measurable force from photon momentum
exchange that is directly proportional to laser power, which can be measured
with an electrostatic balance traceable to the SI. We aim for a relative
uncertainty of $10^{-3}$ with coverage factor $k=2$. For this purpose, we have
designed a monolithic parallelogram 4-bar linkage incorporating elastic
circular notch flexure hinges. The design is optimized to address the main
factors driving force measurement uncertainty from the balance mechanism:
corner loading errors, balance stiffness, stress in the flexure hinges,
sensitivity to vibration, and sensitivity to thermal gradients. Parasitic
rotations in the free end of the 4-bar linkage during arcuate motion are
constrained by machining tolerances. An analytical model shows this affects the
force measurement less than 0.01 percent. Incorporating an inverted pendulum
reduces the stiffness of the system without unduly increasing tilt sensitivity.
Finite element modeling of the flexures is used to determine the hinge
orientation that minimizes stress which is therefore expected to minimize
hysteresis. Thermal effects are mitigated using an external enclosure to
minimize temperature gradients, although a quantitative analysis of this effect
is not carried out. These analyses show the optimized mechanism is expected to
contribute less than $10^{-3}$ relative uncertainty in the final laser power
measurement.
