Step 1 :Step 1: Calculate normal stress: \(\sigma = \cfrac{P_{max}}{A} \), where \(P_{max} = 640 \mathrm{Lb} \cdot 1.66 \) and A is the cross-sectional area.
Step 2 :Step 2: Calculate torque stress: \(\tau = \cfrac{T_{max}}{J} \), where \(T_{max} = 11,400 \mathrm{in\cdot Lb} \cdot 2.5 \) and J is the polar moment of inertia.
Step 3 :Step 3: Determine maximum deflection: \(\Delta = \cfrac{PL^3}{48EI} \), where P is the axial load, L is the length, and E is the modulus of elasticity. For deflection <= 2 inches, solve for I (the moment of inertia).
Step 4 :Step 4: Determine the minimum radius based on normal stress, torque stress, and deflection criteria, and minimize the weight of the manipulator arm.