Using Inverse Dynamics to Prevent Ankle Injuries


Ankle injuries are one of the most common injuries that occur in NFL linemen. If these injuries persist, the number of games missed can accumulate and the injuries can potentially end a player’s career. Research is currently being done to figure out how these injuries occur in order to design more efficient equipment such as ankle braces and modified cleats. One common method of injury involves the linemen planting the tip of their foot on the ground with great force. The force that is applied translates over to the ankle which causes the injury. Can we use engineering principles to approximate how much force is applied to the ankle? Yes we can, with the use of inverse dynamics. Inverse dynamics calculates forces and moments at one body segment by using the forces and moments of an adjacent body segment as well as the position, velocity, and acceleration of the connected body segments. By using inverse dynamics, one can solve for the amount of force that is applied to the ankles and potentially create new technology, such as insoles for the cleats, which can absorb some of the force that is applied and thus reduce the risk of injury.


Known Values and Assumptions:

Height = 1.956 m (6 foot 5 inches)* → length of foot (d) = (1.956)(0.0425)** = 0.08313 m

Mass = 141.521 kg (312 pounds)* → mass of foot (m) = (141.521)(0.0143)** = 2.024 kg

Force due to gravity (Fg) = m(9.81) = (2.024)(9.81) = 19.855 m/s^2

Normal force (FN) and force of friction (FFr)***, which are applied at the tip of the foot.

Angle between foot and playing surface (θ) = 15°[1]

Linear acceleration (a) and angular acceleration (α)****

Moment of Inertia (I)

Center of mass = (0.50)(d) = 0.0416 m

*Average height and weight of an NFL lineman during the 2015 season[2]

**Body segment weight and length[3]

***Exact value of FN and FFr can be used if force plate data is available

****Exact value of a and α can be used if motion capture data is available

Unknown Values to be Solved For:

x-direction force applied to the ankle (Fx, ankle)

y-direction force applied to the ankle (Fy, ankle)

Moment about the ankle (Mankle)

Equations to be Used:

∑Fx = max

∑Fy = may

∑M = Iα

Figure 1: Free-Body Diagram of the forces acting on the foot and ankle of an NFL lineman


Step 1: calculate moment of inertia

Radius of gyration constant for the foot (Kfoot)[4] = 0.475 m

Radius of gyration of the foot (kfoot)= (Kfoot)(d)[4] = (0.475)(0.08313) = 0.0395 m^2

I = (m)(kfoot) = (2.024)(0.0395) → I = 0.0799 kg*m^2

Step 2: solve for forces in the x and y direction

∑Fx = ma→ (2.024)(a*cos(15)) = Fx, ankle – FFrFx, ankle = FFr+ 1.955*a

∑Fy = may → (2.024)(a*sin(15)) = FN – 19.855 – Fy, ankleFy, ankle = F– 19.855 – 0.524*a

Step 3: solve for moments

∑M = Iα → (I)(α) = Mankle + (dy)*(Fx, ankle – FFr) + (dx)*(F– Fy, ankle)


d= y-distance between ankle or tip of foot to center of mass

d= x-distance between ankle or tip of foot to center of mass

∑M = Iα → (0.0799)(α) = Mankle + (0.0416*sin(15))*(Fx, ankle – FFr) + (0.0416*cos(15))*(F– Fy, ankle)

∑M = Iα → Mankle =(0.0799)(α) – (0.011)*(Fx, ankle – FFr) + (0.040)*(F– Fy, ankle)

The solution seems reasonable in the sense that forces are being added on to the ankle. The extent to which the forces are added will depend on multiple factors such as the angle between the cleats and playing surface as well as the height and weight of the athlete being tested. One limitation in this solution was not using exact values of angular and linear acceleration as well as the normal and frictional force. If one is able to accurately obtain these measurements via motion capture and force plate data, they can plug the values into the solutions above to determine exact values of the forces and moments acting on the ankle. For future studies it may be interesting to look at how the other lower limbs, such as the knees and hips, react to translated forces which can accumulate and potentially lead to a greater risk of non-contact injury.






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