This paper presents a comprehensive analysis of the uncertainties in joint torque estimates derived through inverse dynamics. The analysis considered most of the quantifiable sources of inaccuracy in the input variables for inverse dynamics solutions (i.e., errors in body segment parameter estimates, joint center of rotation locations, force plate measurements, motion capture system measurements, and segment angle calculations due to skin movement artifacts). Estimates of inaccuracies were synthesized from existing literature and from a complementary set of experimental data. The analysis was illustrated and tested via an inverse dynamic analysis of gait, in which kinematic and force plate data from 10 adult subjects were recorded and used to calculate the planar (flexion/extension) torques at the ankle, knee, hip, elbow, shoulder, and bottom of torso. The results suggested that the uncertainties in torque estimates derived through inverse dynamics can be substantial (6–232% of the estimated torque magnitude); the time-varying uncertainty patterns do not resemble the torque profiles, and the magnitudes are smaller for more distal joints; the main contributors to these uncertainties were identified to be the inaccuracies in estimated segment angles and body segment parameters. The empirical test also showed that the uncertainty predicted by a more conservative (smaller) set of inaccuracy estimates was comparable to the statistical (3σ) bound of the error. Implications in terms of how inverse dynamics solutions should be interpreted and improved, along with the limitations of the current work, are discussed.

Keywords: Error analysis; Inverse dynamics; Uncertainty

Article Outline

1. Introduction

2. Methods

2.1. Anthropometric linkage representation

2.2. Equations of motion

2.3. Error analysis

2.4. Determination of the inaccuracy magnitudes (Δxi)

2.4.1. Body segment parameters

2.4.2. Segment angle and skin motion artifact

2.4.3. Location of joint center of rotation

2.4.4. Force plate measurements