0
RESEARCH PAPERS

# Optimal Combination of Minimum Degrees of Freedom to be Actuated in the Lower Limbs to Facilitate Arm-Free Paraplegic Standing

[+] Author and Article Information
Joon-young Kim

Department of Mechanical and Industrial Engineering,  University of Toronto, 5 King’s College Road, Toronto, ON, M5S 3G8, Canada;  Toronto Rehabilitation Institute, Lyndhurst Centre, 520 Sutherland Drive, Toronto, ON, M4G 3V9, Canadajoonyoung.gim@gmail.com

James K. Mills

Department of Mechanical and Industrial Engineering,  University of Toronto, 5 King’s College Road, Toronto, ON, M5S 3G8, Canadamills@mie.utoronto.ca

Albert H. Vette

Institute of Biomaterials and Biomedical Engineering,  University of Toronto, 164 College Street, Toronto, ON, M5S 3G9, Canada;  Toronto Rehabilitation Institute, Lyndhurst Centre, 520 Sutherland Drive, Toronto, ON, M4G 3V9, Canadaa.vette@utoronto.ca

Milos R. Popovic1

Institute of Biomaterials and Biomedical Engineering,  University of Toronto, 164 College Street, Toronto, ON, M5S 3G9, Canada;  Toronto Rehabilitation Institute, Lyndhurst Centre, 520 Sutherland Drive, Toronto, ON, M4G 3V9, Canadamilos.popovic@utoronto.ca

Denervated muscles cannot be activated using conventional FES technology. They also degenerate over time and convert rapidly into fat and connective tissue.

Note that 3D implies a model articulation in 3D space with three positional and three rotational DOF ($x$, $y$, and $z$; roll, pitch, and yaw).

1

Corresponding author.

J Biomech Eng 129(6), 838-847 (Mar 16, 2007) (10 pages) doi:10.1115/1.2800767 History: Received May 22, 2006; Revised March 16, 2007

## Abstract

Arm-free paraplegic standing via functional electrical stimulation (FES) has drawn much attention in the biomechanical field as it might allow a paraplegic to stand and simultaneously use both arms to perform daily activities. However, current FES systems for standing require that the individual actively regulates balance using one or both arms, thus limiting the practical use of these systems. The purpose of the present study was to show that actuating only six out of 12 degrees of freedom (12-DOFs) in the lower limbs to allow paraplegics to stand freely is theoretically feasible with respect to multibody stability and physiological torque limitations of the lower limb DOF. Specifically, the goal was to determine the optimal combination of the minimum DOF that can be realistically actuated using FES while ensuring stability and able-bodied kinematics during perturbed arm-free standing. The human body was represented by a three-dimensional dynamics model with 12-DOFs in the lower limbs. Nakamura’s method (Nakamura, Y., and Ghodoussi, U., 1989, “Dynamics Computation of Closed-Link Robot Mechanisms With Nonredundant and Redundant Actuators  ,” IEEE Trans. Rob. Autom., 5(3), pp. 294–302) was applied to estimate the joint torques of the system using experimental motion data from four healthy subjects. The torques were estimated by applying our previous finding that only 6 (6-DOFs) out of 12-DOFs in the lower limbs need to be actuated to facilitate stable standing. Furthermore, it was shown that six cases of 6-DOFs exist, which facilitate stable standing. In order to characterize each of these cases in terms of the torque generation patterns and to identify a potential optimal 6-DOF combination, the joint torques during perturbations in eight different directions were estimated for all six cases of 6-DOFs. The results suggest that the actuation of both ankle flexion∕extension, both knee flexion∕extension, one hip flexion∕extension, and one hip abduction∕adduction DOF will result in the minimum torque requirements to regulate balance during perturbed standing. To facilitate unsupported FES-assisted standing, it is sufficient to actuate only 6-DOFs. An optimal combination of 6-DOFs exists, for which this system can generate able-bodied kinematics while requiring lower limb joint torques that are producible using contemporary FES technology. These findings suggest that FES-assisted arm-free standing of paraplegics is theoretically feasible, even when limited by the fact that muscles actuating specific DOFs are often denervated or difficult to access.

<>

## Figures

Figure 3

Internal validity test for Case VI in Fig. 2. The thick gray lines indicate the inputs and outputs of the inverse dynamics, and the thin black lines indicate those of the forward dynamics. Note that the validation test was performed for all six cases of 6-DOFs.

Figure 4

Joint angles and joint torques of subject S1 at the actuated 6-DOFs due to the perturbation given in direction D1. The mean values with one standard deviation from three trials are shown as a function of time.

Figure 6

Joint angles and joint torques of subject S1 at the actuated 6-DOFs due to the perturbation given in direction D3. The mean values with one standard deviation from three trials are shown as a function of time. Since the torque characteristics at HAA were identical for all three cases, only Case I is shown.

Figure 7

Joint angles and joint torques of subject S1 at the actuated 6-DOFs due to the perturbation given in direction D2. The mean values with one standard deviation from three trials are shown as a function of time. Since the torque patterns were composed of the patterns during the A∕P and M∕L perturbations (Figs.  46), only Case I is shown.

Figure 8

Torque sums of the joint torques at all active DOFs, shown for each of the six 6-DOF systems (Cases I–VI) and all directions of perturbation (D1–D8). Note that subjects S2 and S4 show overall torque sums for seven perturbation directions only as these subjects lost balance during the D5 perturbations. Recall that Cases I and II represent Group A, Cases III and IV represent Group B, and Cases V and VI represent Group C.

Figure 1

3D dynamic model of the human body during double-support stance (17). The DOF of the joints are as follows: ankle inversion∕eversion (lAIE, rAIE), ankle dorsiflexion∕plantarflexion (lADP, rADP), knee flexion∕extension (lKFE, rKFE), hip abduction∕adduction (lHAA, rHAA), hip flexion∕extension (lHFE, rHFE), and hip rotation (lHRT, rHRT). The system was perturbed in eight different directions, D1–D8.

Figure 2

Six cases of 6-DOFs such that the passive Jacobian matrices are not singular (17). Note that due to the symmetry of the two legs, each case also represents the 6-DOF combination of its mirror image. For example, Case I also stands for the combination of lKFE, lHFE, rADP, rKFE, rHAA, and rHFE as active DOFs.

Figure 5

The average torque sums for each A∕P DOF and each group that were generated due to the A∕P perturbations. The average torque sum with standard deviation (N m s) from four subjects (12 trials) is shown, i.e., the torque generated due to the perturbation in the D1 (upper arrow and torque value) and D5 (lower arrow and torque value) directions. Notice the difference of the arrow directions.

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections