Modeling the Roll-Slip Nonlinear Dynamics of the Knee

Open Access
Gagliardi, Virginia Marie
Area of Honors:
Bachelor of Science
Document Type:
Thesis Supervisors:
  • Joseph Paul Cusumano, Thesis Supervisor
  • William O Hancock, Honors Advisor
  • Margaret June Slattery, Faculty Reader
  • knee
  • knee joint
  • prosthetics
  • dynamics of the knee
  • roll-slide
  • roll-slip
  • oscillator
A better understanding of the cause and effect of various knee injuries as well as the design and optimization of more environmentally-adaptive knee prostheses are becoming a great need throughout all of society, yet the fundamental dynamics within the knee joint itself are not well-understood. The aim of this study was to mathematically model the roll-slip nonlinear dynamics of the knee joint in order to observe and to quantify the motions of the knee. A spring-mass-damper, rolling disk on flat surface model was analyzed mathematically using MATLAB®. The results obtained showed preliminary insight into the dynamics occurring within the knee joint. Specifically, as the static coefficient of friction increased within the knee, slipping decreased leading to increased steady state response and average power amplitudes. Therefore, a static coefficient of friction that is approximately equal to the kinetic coefficient of friction within the knee provides appropriate levels of slipping and decreased wear on the system. Adequate slipping is a key dynamical component in the motion of the knee; too little or too much slipping within the knee would result in increased instability and could potentially lead to injury of the soft tissues within the joint.