Research Papers

Model-Based Analysis of the Stiffness of the Wrist Joint in Active and Passive Conditions

[+] Author and Article Information
Andrea Zonnino

Human Robotics Laboratory,
Department of Biomedical Engineering,
University of Delaware,
Newark, DE 19713
e-mail: zonni@udel.edu

Fabrizio Sergi

Human Robotics Laboratory,
Department of Biomedical Engineering,
University of Delaware,
Newark, DE 19713
e-mail: fabs@udel.edu

1Corresponding author.

Manuscript received March 6, 2018; final manuscript received January 18, 2019; published online February 27, 2019. Assoc. Editor: Beth A. Winkelstein.

J Biomech Eng 141(4), 041006 (Feb 27, 2019) (10 pages) Paper No: BIO-18-1121; doi: 10.1115/1.4042684 History: Received March 06, 2018; Revised January 18, 2019

The control of joint stiffness is a fundamental mechanism used to control human movements. While many studies have observed how stiffness is modulated for tasks involving shoulder and elbow motion, a limited amount of knowledge is available for wrist movements, though the wrist plays a crucial role in manipulation. We have developed a computational framework based on a realistic musculoskeletal model, which allows one to calculate the passive and active components of the wrist joint stiffness. We first used the framework to validate the musculoskeletal model against experimental measurements of the wrist joint stiffness, and then to study the contribution of different muscle groups to the passive joint stiffness. We finally used the framework to study the effect of muscle cocontraction on the active joint stiffness. The results show that thumb and finger muscles play a crucial role in determining the passive wrist joint stiffness: in the neutral posture, the direction of maximum stiffness aligns with the experimental measurements, and the magnitude increases by 113% when they are included. Moreover, the analysis of the controllability of joint stiffness showed that muscle cocontraction positively correlates with the stiffness magnitude and negatively correlates with the variability of the stiffness orientation (p < 0.01 in both cases). Finally, an exhaustive search showed that with appropriate selection of a muscle activation strategy, the joint stiffness orientation can be arbitrarily modulated. This observation suggests the absence of biomechanical constraints on the controllability of the orientation of the wrist joint stiffness.

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Grahic Jump Location
Fig. 1

Representation of the musculoskeletal system (left) and the musculotendon unit (right) used in the simulations

Grahic Jump Location
Fig. 2

Block diagram of the framework used to calculate the passive (A) and active (B) joint stiffness. The analyses presented in this manuscript always assumed a null desired joint torque (τ=0).

Grahic Jump Location
Fig. 3

Measurements of the passive stiffness of the wrist (left). Model-based estimates of the passive stiffness when different groups of muscles are included (right). All values are obtained with the wrist in the neutral posture. Units of stiffness in the polar plot are Nm/rad. PM1-5 are the five passive models (see Sec. 2.5.1).

Grahic Jump Location
Fig. 4

Map of the passive stiffness of the wrist joint in multiple postures

Grahic Jump Location
Fig. 5

Polar histogram representing the distribution of the orientation of the passive stiffness of the wrist joint in the joint angle domain considered. Note that the distribution is symmetric about the origin so peaks at 120 deg and 300 deg represent the same group of ellipses, as well as the peaks at 90 deg and 270 deg.

Grahic Jump Location
Fig. 6

Set of admissible stiffness values established via systematic search when all muscles (left) can cocontract, or when only the wrist muscles (center), or only the finger and thumb muscles (right) can cocontract. The values refer to the neutral posture and to a null desired net torque. The smallest ellipse represents the passive stiffness, while the black represents the stiffness that corresponds to the activation vector that minimize GAL, selected within the subset A(0). Units of stiffness in the polar plot are N·m/rad. In each of the three polar plots only 500 ellipses, equally spaced in terms of GAL have been represented.

Grahic Jump Location
Fig. 7

(Top) the plot represents the relationship between the magnitude of the achievable joint stiffness and the GAL; the small dots represent the set of achievable stiffness value (decimated 1000 times), while the line is the fit obtained from linear regression. (Bottom) the plot represents the relationship between the orientation of the achievable joint stiffness and seven equally spaced groups of GAL; the bars represent the mean value of orientation for the ellipses within each group, while the error bars show the standard deviation within each group. The big dots in the Y-axis represent the values obtained in the passive condition.

Grahic Jump Location
Fig. 8

The plots represent the distribution of the achievable magnitude (top) and orientation (center), and eccentricity (bottom), when different groups of muscles cocontract. Please note the logarithmic scale used for the vertical axis, which allows one to appreciate the presence of a small number of feasible solutions for several values of magnitude, orientation, and eccentricity.



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