# NASA EMU - Torque Modeling

Mathematical Model: Two approaches were used for modeling the torques required to bend the space suit's joints. The first modeling method is to fit a hysteresis model to the experimental torque and angle data. The hysteresis model allows a reduced coefficient set to reproduce the torque-angle relationships for the space suit joints, but this descriptive modeling technique does not lead to an understanding of how space suit design parameters affect mobility. Three mathematical techniques for modeling hysteretic systems, the Krasnoselski-Pokrovski model, the Preisach model, and the Tao and Kokotovic model, were evaluated for possible use. The Preisach model was chosen because it can produce output curves simplar in shape to the space suit torque vs. angle curves and its identification process is relatively simple.

Mathematical Model Results Elbow flexion torque data compared to hysteresis model output for three subjects. (Circles are experimental data, solid line is the model, dotted line is confidence interval)

Physical Model: The second modeling approach is based on structural mechanics and other physical processes. The physical modeling effort addresses space suit design issues by using structural mechanics analysis techniques to predict joint angle-torque relations from joint geometry and materials. Two physics-based models of pressurized fabric cylinder bending were compared to the experimental data. The beam model treats the inflated cylinder as a beam with a fabric wall that stretches, maintaining a constant internal volume. The mobility of the space suit joint is determined by elastic behavior of the fabric wall. Alternatively, the membrane model treats the fabric shell as an inextensible membrane. Bending deflections of the cylinder result in shape and volume changes, and the work required to bend the joint is entirely due to compression of the gas inside. Modeling and simulation capabilities also include a dynamic simulation of the robotic space suit tester. The simulation includes an accurate representation of the robot's 24 degrees of freedom, and allows simulation of motions with user-specified control laws. With this capability, insight into realistic human motor control can be gleaned.

Physics Based Model Results Comparison between the beam model, membrane model, and experimental data for knee joint.