Calculate the torque transmitted by the shafts.

Step 1: Calculate the torque transmitted by the shafts. The power (P) transmitted is 60 \, kW = 60 × 10^3 \, W. The rotational speed (N) is 240 \, r/min. First, convert the rotational speed to angular velocity () in rad/s: N = 240 \, r/min = (240)/(60) \, r/s = 4 \, r/s = 2 N = 2 (4) \, rad/s = 8 \, rad/s Now, calculate the torque (T) using the formula P = T : T = (P)/() = 60 × 10^3 \, W8 \, rad/s T = (7500)/() \, N · m T ≈ 2387.32 \, N · m Step 2: Relate torque to the maximum shear stress in the claw. The claw coupling can be treated as a hollow shaft for torque transmission. The maximum shear stress (_max) in a hollow circular shaft is given by: _max = (T r_o)/(J) where r_o is the outside radius and J is the polar moment of inertia for a hollow shaft. The outside radius is r_o = d_o/2. The polar moment of inertia for a hollow shaft is J = ()/(32) (d_o^4 - d_i^4), where d_o is the outside diameter and d_i is the inside diameter. Substitute these into the shear stress formula: _max = (T (d_o/2))/()32 (d_o^4 - d_i^4) = (16 T d_o)/( (d_o^4 - d_i^4)) Step 3: Calculate the inside and outside diameters of the claw. We are given that the outside diameter of the claw is twice the inside diameter, so d_o = 2 d_i. The maximum allowable shear stress is _max = 6.4 \, MPa = 6.4 × 10^6 \, Pa. Substitute d_o = 2 d_i into the shear stress equation: _max = (16 T (2 d_i))/( ((2 d_i)^4 - d_i^4)) _max = (32 T d_i)/( (16 d_i^4 - d_i^4)) _max = (32 T d_i)/( (15 d_i^4)) _max = (32 T)/(15 d_i^3) Now, solve for d_i: d_i^3 = (32 T)/(15 _max) Substitute the values for T and _max: d_i^3 = (32 × (7500)/())15 (6.4 × 10^6) d_i^3 = (32 × 7500)/(15 ^2 × 6.4 × 10^6) d_i^3 = (240000)/(96 ^2 × 10^6) d_i^3 = (2500)/(^2 × 10^6) d_i^3 ≈ (2500)/(9.8696 × 10^6) ≈ 0.000253302 \, m^3 d_i = (0.000253302)^1/3 \, m d_i ≈ 0.06326 \, m Convert to millimeters: d_i ≈ 63.26 \, mm Now, calculate the outside diameter d_o: d_o = 2 d_i = 2 × 63.26 \, mm d_o ≈ 126.52 \, mm The inside diameter of the claw is 63.26 mm. The outside diameter of the claw is 126.52 mm. 3 done, 2 left today. You're making progress.