upper bound must be a set of mass values that can be handled given the physical reality of space  available at each balance mass location. They could also turn off certain masses that are difficult to access due to some practical envelope constraints. The linear problem given by Equation (12) is solvable  using MATLAB’s linear programming function “linprog” using the same software that collects dynamometer sensor data and encoder position as the test unit spins atop of the dynamometer. Calibration of the Dynamometer Setup The calibration entails three parts. In the first part, the dynamometer is shown to have the necessary  sensitivity to accurately make the necessary measurements needed to process the imbalance data. The  noise floor of the dynamometer is identified and compared to the requirements on forces and moments that are derived to meet GMI’s static and dynamic balancing requirements.  In the second part of the calibration, the forces measured by the dynamometer are checked using two  separate data acquisition systems and two loading methods. This was performed to isolate and quantify the sources and magnitudes of systematic and random measurement errors. Finally, the third part in the  calibration program evaluates data collected from auxiliary risk mitigation tests which used the GMI SMA(Spin Mechanism Assembly) and simulated payloads with off-axis known masses precisely located on a  rotating disk (see Figure 4). These mitigation tests were planned to assess the performance of the tools  to be used in the actual balancing of GMI. Three test cases were performed. The first one has a moderate  imbalance, while the second test case is intended to achieve extreme static and dynamic imbalances. Finally, the third test case is intended to produce a balanced state from which we demonstrate the capability of the system to meet the required level of balance measurements for GMI.  Specified and Derived Requirements The two GMI balancing requirements are expressed in terms of the product /g80/g72/g148/g3/g19/g17/g19/g22/g21/g3kg-m (2.77 lb-in)  for static imbalance and /g45/g85/g93/g3/g148/g30.055 kg-m2/g3(187 lb-in2) for dynamic imbalance. We derive two equivalent  requirements that provide the equivalent limits on the static and dynamic imparted forces and moments  that GMI needs to meet in order for the balancing effort to be successful. These requirements are shown to be for the radial /g73/g82/g85/g70/g72/g3/g148/g3/g19/g17/g19/g27 lb (0.36 N) and the radial /g80/g82/g80/g72/g81/g87/g3/g148 10 in-lb (1.1 N-m). In addition, a requirement on the noise floor is set so that accurate and reliable measurements of the balanced state are performed. The noise floor of the dynamometer is checked against 1/10 thof the requirement levels,  padded by a 50% uncertainty levied to account for unknown error contributions to the measurements. The  /g81/g82/g76/g86/g72/g3/g73/g79/g82/g82/g85/g3/g76/g86/g3/g73/g82/g88/g81/g71/g3/g87/g82/g3/g69/g72/g3/g148/g3/g19/g17/g19/g19/g23/g3/g79/g69/g3(0.018 N) for reliable measurements to occur.      Using the expression for the radial load from Equation (1) and using an angular frequency of 0.533 Hz (32  rpm), the magnitude of the radial load is related to the imbalance /g80/g72/g3via/g3 22 2   0.032 (2  0.533) 0.36  (0.08 lb)r rfme f me N /g90/g83/g90/g32/g159 /g32/g32 /g32 Furthermore, de-rating this level by 50% to account for unknowns in the setup, we need to bring the radial  load to less than 0.04 lb (0.18 N) if we want to show that GMI is statically balanced. Thus, we need to  have a noise floor level less than 0.004 lb (0.018 N). In order to address the dynamic balance  requirement, we use Equation (3). We have the magnitude of the radial moment given by: /g11/g1222 2 22 2 22 2 2     +      0.055( 2 0.533) 0.032(9.81 16.455 0.0254(2 0.533) )yz y yz y r rz r xz x xz x rr zif i f gg gMJ f if i f MJm e g M/g90/g90 /g90/g90/g90 /g90 /g90/g90/g83 /g83/g16/g16/g16 /g16/g173/g189 /g173/g189 /g173/g189 /g173/g189/g176/g176 /g176/g176 /g176/g176 /g176/g176/g167/g183 /g167/g183 /g167/g183/g32 /g14 /g14/g39/g100 /g14/g39 /g32 /g14 /g14/g39/g174/g190 /g174/g190 /g174/g190 /g174/g190/g168/g184 /g168/g184 /g168/g184/g14/g14/g14 /g14/g169/g185 /g169 /g185 /g169/g185 /g176/g176 /g176/g176 /g176/g176 /g176/g176/g175/g191 /g175/g191 /g175/g191 /g175/g191 /g100/g14 /g14 /g39/g32 /g117/g14 /g14/g117 /g117 /g11/g12   1.08   10 r Nm in lb/g100/g16 (< 10 in-lb) 309