A Two-Dimensional Mathematical Analysis of the Knee

Katie Bedwell

Advisor: Dr. Victor Mansfield

This paper includes a two-dimensional mathematical analysis of the squat exercises and focuses on the shear and compression forces on the knee.  Data was collected on twelve female collegiate athletes using a digital video camera and the videos were analyzed with VideoPoint Software.  Squats are currently the most recommended exercise to strengthen the leg muscles, and are used both prior to knee injuries as a preventative exercise and post surgery as a reconstructive device.  However, if the exercise is performed incorrectly it is a potentially harmful exercise for the knee.  The analysis performed on each participant clearly shows that the ratio of shear to compression forces increases dramatically if the athlete puts more force on her toes instead of on her heals. Therefore, this   mathematical model can be used to pinpoint dangerous squatting techniques.