Question

A person is performing walking gait trials across a laboratory. At heel strike the hip flexion angular velocity is 0.70 rad/s, knee flexion angular velocity is 4.15 rad/s, and ankle plantar flexion angular velocity is -0.70 rad/s. Additionally, moment of inertia of the hip is 0.70 kgm², moment of inertia of the knee is 0.90 kgm², and moment of inertia of the ankle is 1.00 kgm². What is the sagittal plane angular momentum of the hip, knee, and ankle joints at heel strike?

• H_hip at heel strike: ____________________

• H_knee at heel strike: ___________________

• H_ankle at heel strike: __________________

Once this person transitions through the stance phase to toe off (e.g. propulsion) the hip flexion angular velocity increases to 3.15 rad/s, knee flexion angular velocity is 4.95 rad/s, and ankle plantar flexion angular velocity is –8.10 rad/s. If we assume gait velocity is constant during the stance phase, what is the moment of inertia of the hip (mass of femur = 8.50 kg), knee (mass of shank = 2.60 kg), and ankle (mass of foot = 0.82 kg) at toe off? Furthermore, what is the radius of gyration of the hip, knee, and ankle at toe off?

• I_hip at toe off: ____________________

• I_knee at toe off: ___________________

• I_ankle at toe off: __________________

• K_hip at toe off: ____________________

• K_knee at toe off: ___________________

• K_ankle at toe off: __________________

Answer 1

1. given,

• Hip flexion angular velocity = 0.70 rad/s
• Knee flexion angular velocity = 4.15 rad/s
• Ankle plantar flexion angular velocity = (- 0.70 rad/s)
• Moment of inertia of hip = 0.70 kgm2
• moment of inertia of knee = 0.90 kgm2
• moment of inertia of ankle = 1 kgm2
• angular momentum L = moment of inertia (I) x angular velocity()
• Angular momentum of hip, LH = 0.70 x 0.70 = 0.49 kgm2/s
• Angular momentum of knee, LK = 4.15 x 0.90 = 3.735 kgm2/s
• Angular momentum of ankle, LA = ( - 0.70) x 1 = ( - 0.70 ) kgm2/s

2. given,

• hip flexion angular velocity = 3.15 rad/s
• knee flexion angular velocity = 4.95 rad/s
• ankle plantar flexion angular velocity = ( - 8.50) rad/s
• mass of the femur = 8.50 kg
• mass of the shank = 2.60 kg
• mass of the foot = 0.82 kg
• angular velocity, = velocity / radius
• Radius = velocity / angular velocity ( given velocity during stance phase is constant, let us consider it as 1)
• Radius of gyration of hip = 1/ 3.15 = 0.317 m
• Radius of gyration of knee = 1/4.95 = 0.202 m
• Radius of gyration of ankle = 1/ ( - 8.50) = ( - 0.117) m
• moment of inertia, I = 1/2 x mass x radius of gyration2
• moment of inertia of hip = 1/2 x 8.50 x (0.317)2 = 4.25 x 0.1 = 0.425 kgm2
• moment of inertia of knee = 1/2 x 2.60 x (0.202)2 = 1.3 x 0.04 = 0.052 kgm2
• moment of inertia of ankle = 1/2 x 0.82 x ( - 0.117)2 = 0.41x 0.013 = 0.0053 kgm2