Data and Calculations

Alexis' Arm measurements: fist wrist forearm elbow distance (cm) 32.5 20.5 8.5 0 circumference (cm) 24 15.5 20.5 24

Average circumferences fist wrist forearm 22.25cm 18cm 19.75cm

Radii based on average circumferences: r=c/2*pi fist wrist forearm 3.54cm 2.86cm 3.14cm

Lower Limit Mass of arm (taken from postage scale): .426 kg
Volume of arm: V=pi*r2h for each radius:
Upper Limit Mass of arm: 1.044 kg
Average mass of arm: 0.735kg

Calculations for moment of inertia (without small weight added):

Time constant for graph of arm movement without small weight: .141 seconds
alpha = 7.09, 2*alpha = 14.18
Period = 2.466 seconds
natural frequency = 0.406
omega-n^2 = 0.164
2*alpha and omega-n^2 can me used in the Simulink program to generate a model of the motion of an arm. This is what B and K are for this system.

Calculations for J with the weight (assume the fist's total weight is now 1 kg)


Time constant for arm and weight graph: 0.148
alpha = 6.77, 2alpha = 13.55

Period for arm and weight graph: 0.732
Natural frequency = 1.36
omega-n^2 = 1.864

B and K for the arm and weight system: