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Gait & Posture

Volume 27, Issue 4, May 2008, Pages 578-588

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Copyright © 2007 Elsevier B.V. All rights reserved.

Uncertainties in inverse dynamics solutions: A comprehensive analysis and an application to gait

Raziel Riemer, Elizabeth T. Hsiao-Wecksler and Xudong Zhang

Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

Received 17 July 2006;  revised 23 July 2007;  accepted 29 July 2007.  Available online 21 September 2007. 



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

2.4.5. Motion marker noise and segmental accelerations

2.5. Synthesis of the inaccuracy magnitudes (Δxi)

2.6. Gait experimental data acquisition

2.7. Data analysis

3. Results

4. Discussion


Appendix A. Error conservation in inverse dynamics

Appendix B. Evaluation of proposed approach by a comparison of the top-down and bottom-up results


Gait & Posture

Volume 27, Issue 4, May 2008, Pages 578-588

Result list | previous < 9 of 31 > next 





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