Experimental Brain Research

, Volume 167, Issue 3, pp 352–361 | Cite as

Determining natural arm configuration along a reaching trajectory

  • Tao Kang
  • Jiping He
  • Stephen I. Helms Tillery
Research Article


Owing to the flexibility and redundancy of neuromuscular and skeletal systems, humans can trace the same hand trajectory in space with various arm configurations. However, the joint trajectories of typical unrestrained movements tend to be consistent both within and across subjects. In this paper we propose a method to solve the 3-D inverse kinematics problem based on minimizing the magnitude of total work done by joint torques. We examined the fit of the joint-space trajectories against those observed from human performance in a variety of movement paths in 3-D workspace. The results showed that the joint-space trajectories produced by the method are in good agreement with the subjects’ arm movements (r 2>0.98), with the exception of shoulder adduction/abduction (where, in the worst case, r 2 ∼0.8). Comparison of humeral rotation predicted by our algorithm with other models showed that the correlation coefficient (r 2) between actual data and our predictions is extremely high (mostly >0.98, 11 out of 15 cases, with a few exceptions, 4 of 15, in the range of 0.8–0.9) and the slope of linear regression is much closer to one (<0.05 distortion in 12 out of 15 cases, with only one case >0.15). However, the discrepancy in shoulder adduction/abduction indicated that when only the hand path is known, additional constraint(s) may be required to generate a complete match with human performance.


Arm movements Minimum work Reaching Joint trajectory Inverse kinematics 



The project is supported in part by a grant from DARPA (MDA972-00-1-0027) and by NIH contract NS-9-2321.


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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • Tao Kang
    • 1
  • Jiping He
    • 1
    • 2
  • Stephen I. Helms Tillery
    • 1
  1. 1.The Biodesign Institute and Harrington Department of BioengineeringArizona State UniversityTempeUSA
  2. 2.BioInformatics and BioControl LaboratoryHuazhong University of Science and TechnologyWuhanChina

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