Kinematic Analysis of Planar Biomechanical Models using Mixed Coordinates

Abstract

Inverse Kinematics Analysis (IKA) is a powerful tool to study mechanical and biological systems, since it can be used to adjust the position and orientation of each segment of the model to the experimental data, enabling to achieve reliable and consistent model positions. Optimization-based methods have been successfully applied to perform IKA in intricate biomechanical systems. However, these methods tend to be more complex requiring more computational power and CPU times. This work presents an alternative methodology based on the use of Fully Cartesian Coordinates (FCC) and Mixed Coordinates (MC), alongside with a weighted least square approach to solve the IKA problem. The proposed methodology was applied in the study of a gait movement for a planar full body biomechanical model. The Root Mean Square Error (RMSE) between the experimental and computed positions was calculated both for the proposed method and for a forward kinematic analysis (FKA) carried out with pre-calculated angular drivers, resulting in smaller average differences in the former case (IKA: 0.018 m FKA: 0.019 m). Based on the obtained results it is possible to conclude that the proposed methodology is an accurate, efficient, and reliable approach to perform the IKA of biomechanical models, assuring the kinematic consistency between experimental data and the biomechanical model, and, at the same time, avoiding the usual drawbacks of the use of angular drivers or complex optimization techniques.