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Research Papers

The Effects of the Inertial Properties of Above-Knee Prostheses on Optimal Stiffness, Damping, and Engagement Parameters of Passive Prosthetic Knees

[+] Author and Article Information
Yashraj S. Narang

School of Engineering and Applied Sciences,
Harvard University,
Cambridge, MA 02138
e-mail: ynarang@seas.harvard.edu

V. N. Murthy Arelekatti

Department of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: murthya@mit.edu

Amos G. Winter, V

Mem. ASME
Assistant Professor
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: awinter@mit.edu

Manuscript received April 27, 2015; final manuscript received July 12, 2016; published online November 3, 2016. Assoc. Editor: Paul Rullkoetter.

J Biomech Eng 138(12), 121002 (Nov 03, 2016) (10 pages) Paper No: BIO-15-1199; doi: 10.1115/1.4034168 History: Received April 27, 2015; Revised July 12, 2016

Our research aims to design low-cost, high-performance, passive prosthetic knees for developing countries. In this study, we determine optimal stiffness, damping, and engagement parameters for a low-cost, passive prosthetic knee that consists of simple mechanical elements and may enable users to walk with the normative kinematics of able-bodied humans. Knee joint power was analyzed to divide gait into energy-based phases and select mechanical components for each phase. The behavior of each component was described with a polynomial function, and the coefficients and polynomial order of each function were optimized to reproduce the knee moments required for normative kinematics of able-bodied humans. Sensitivity of coefficients to prosthesis mass was also investigated. The knee moments required for prosthesis users to walk with able-bodied normative kinematics were accurately reproduced with a mechanical system consisting of a linear spring, two constant-friction dampers, and three clutches (R2=0.90 for a typical prosthetic leg). Alterations in upper leg, lower leg, and foot mass had a large influence on optimal coefficients, changing damping coefficients by up to 180%. Critical results are reported through parametric illustrations that can be used by designers of prostheses to select optimal components for a prosthetic knee based on the inertial properties of the amputee and his or her prosthetic leg.

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References

Figures

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Fig. 1

Two-dimensional, four-segment link structure to model the prosthetic leg of a unilateral amputee wearing a transfemoral prosthesis. The model consisted of a trunk segment, an upper leg segment (residual limb and socket), a lower leg segment (shank), and a foot segment. The connections between each segment were modeled as revolute joints.

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Fig. 2

Gross effects of altering inertial properties on the knee moment required for a prosthetic leg to move with normative kinematics. Symbol Treq* designates the required knee moment normalized to body mass. The masses of all segments of the leg are scaled to the specified percentages of able-bodied values, and the moments of inertia (about the centers of mass of the segments) are scaled in proportion.

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Fig. 4

Three energy-based phases of gait. Normalized knee power versus time graph (solid blue curve) is shown for a prosthetic leg with a typical inertial configuration (upper leg mass = 50% of able-bodied value, and lower leg and foot mass = 33% of able-bodied values [20,25]) moving with normative kinematics. Symbol Pk* designates knee power normalized to body mass. Phase 1 is a negative and positive work phase (Wneg/Wpos=0.77), which can be partially replicated with a spring element, and phases 2 and 3 are purely negative work phases (Wpos = 0), which can be accurately replicated with dampers. Normalized knee power versus time graph (dashed red curve) is also shown for able-bodied values of segment masses [22] (upper leg mass = 100% of able-bodied value, and lower leg and foot mass = 100% of able-bodied values).

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Fig. 3

Schematic of general passive mechanical model used to model the knee. Symbol θ designates the knee joint angle.

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Fig. 5

Behavior of simplified mechanical model over the gait cycle. The model was optimized to reproduce knee moment, Treq, of a prosthetic leg with a typical inertial configuration (mass of upper leg = 50% of able-bodied value, and masses of lower leg and foot = 33% of able-bodied values). (a) Illustration of optimized engagement (θeng) and disengagement (θdis) angles of the clutch for each component. (b) Comparison of knee moment normalized to body mass for normative kinematics (Treq*) and produced by the mechanical model (Tmod*). Agreement between Treq* and Tmod* is R2=0.90. Labels k1 and b0 designate the linear spring coefficient and constant damping coefficient for a given phase. Note that the difference between Tmod* and Treq* around 45% of the gait cycle is a consequence of a negative work, Wneg, to positive work, Wpos, ratio of less than one during phase 1, meaning that more energy is generated than dissipated (Fig. 4). Thus, a single passive mechanical component cannot perfectly reproduce Treq during phase 1. (c) Comparison of knee power (normalized to body mass) required for normative kinematics and knee power produced by the mechanical model. Knee power is calculated as the product of knee moment (modeled or required) and able-bodied angular velocity of the knee joint. Agreement between required knee power and modeled knee power is R2=0.91. Hatched areas show where the modeled knee power is insufficient and is less than the generative knee power required for normative gait kinematics.

Grahic Jump Location
Fig. 6

Parametric illustrations showing the effects of leg segment masses on optimal MMC. Labels mul*, mll*, and mf* designate upper leg mass, lower leg mass, and foot mass normalized to the masses of corresponding able-bodied segments, respectively. Labels phase 1: k1, phase 2: b0, and phase 3: b0 designate the linear stiffness coefficient during phase 1, the constant damping coefficient during phase 2, and the constant damping coefficient during phase 3, respectively, all normalized to body mass. Section 3.2 explains the method to determine MMC in this figure. Dashed lines and arrows correspond to an example leg and optimum MMC with 75% upper leg, 50% lower leg, and 60% foot masses compared to able-bodied values.

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