Purdue University Graduate School
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A Simple Biomechanical Analysis of the Ankle

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posted on 2023-08-09, 12:32 authored by Lindee Brie CalvertLindee Brie Calvert

Our healthcare system is experiencing a substantial economic burden, and one of the contributing factors is ankle injury - particularly ankle sprains - and the resulting chronic conditions like ankle instability and osteoarthritis. Ankle sprains commonly occur in sports such as basketball, where sudden, lateral changes in direction are common. As a shoe provides the foundational support for an athlete, a simple slipping/tipping analysis was performed to derive a stability criterion that relates impact forces and shoe geometry. The criterion was populated with geometric measurements from seven currently-available basketball shoes and impact forces seen in lateral maneuvers from several published studies to generate multiple cases to observe if the shoes were safe. Of the 35 cases (seven different shoes applied in six different loading conditions) there were six cases where the shoe passed the stability criterion and was considered safe. Given that the impact forces in lateral movements likely will not change, the geometry of the shoes should be considered to reduce the chance of tipping of the shoe (i.e. rolling of the ankle) and risk of injury to the athlete.

Another contributing factor to the healthcare system's economic burden is limb loss, and the negative effects of ill-fitting and ill-functioning prosthetic devices. Examples of these secondary complications are osteoarthritis and tissue breakdown, which are thought to result from uneven joint loading and asymmetric gait. In light of this, a prosthetic ankle was developed that employs a three degree of freedom system modeled with a ball-in-socket joint. The range of motion of this joint can be custom-bounded by the system of nubs and cavities, along with shims that can be inserted around the joint shaft, to control dorsiflexion, plantarflexion, inversion, eversion, and medial/lateral rotation in the transverse plane. A joint like this, which enables the user to have a more natural gait, will help reduce the onset of conditions like osteoarthritis, ultimately reducing the demand on resources from the healthcare system.

Another effort to mitigate the burden on the healthcare system is seen through the development of a wearable resistance device that is designed to help prevent injury by strengthening musculoskeletal and neuromuscular systems during sport-specific movements. While traditional gym training is beneficial for an athlete's overall health and fitness, it tends to lack in adequately preparing the athlete for sport-specific movements. Thus, a wearable resistance system is beneficial in that it can provide resistance training during sport to enhance and strengthen an athlete's neuromuscular and musculoskeletal systems. In this study, five recreational runners performed running trials on an instrumented treadmill with and without the wearable resistance system. Force plate and surface electromyography (sEMG) data were collected to observe changes in the muscle activation in both legs. Additionally, sEMG data was examined to detect any effect on left/right symmetry in each subject.

These studies can all be enhanced with the incorporation of a newly-developed skeletal muscle force model that provides more accurate estimates of individualized muscle forces to better predict surrounding musculoskeletal tissue and joint contact loading. It is founded in dimensional analysis and uses electromyography and the muscle force-length, force-velocity, and force-frequency curves as inputs. The constitutive equation gives way to a unique application of inverse-dynamics that avoids the issue of indeterminacy when reaction moments and ligament loading are minimized in a joint. The ankle joint is used as an example for developing the equations that culminate into a system of linear equations. Seventeen subjects (8 males, 9 females) performed five different exercises geared towards activating the primary muscles crossing the ankle joint. The moments about the ankle joint due to the calculated muscle forces were compared to the sum of the moments due to all other sources and the kinematic terms in the second Newton-Euler equation of rigid body motion. Average percent errors for the \(\vec{B}\) components for each subject ranged from 4.2\% to 15.5\% with a total average percent error across all subjects of 8.2\%. Not only is this muscle force model physiologically relevant, but it can be calibrated and used to predict joint contact loading and loading in the surrounding tissues. Thus, it will be beneficial for use in designing biomechanics equipment for athletes like basketball players, or in designing prosthetic devices that function more like a natural joint. Furthermore, this model can be used in conjunction with the wearable resistance device to validate it's effects on the strengthening of neuromuscular and musculoskeletal systems over time.


Degree Type

  • Doctor of Philosophy


  • Mechanical Engineering

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Eric Nauman

Advisor/Supervisor/Committee co-chair

Jeff Rhoads

Additional Committee Member 2

Russell Main

Additional Committee Member 3

Scott Lawrance

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