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LIFE2014

2014 年 9 月 24 日－26 日 北海道

Dynamic Analysis of Hip and Knee Joints of Lower Limb with Trans-Femoral Prosthesis○Le Van Tuan, Shibaura Institute of Technology
Kengo Onishi, Tokyo Denki University
Hiroshi Otsuka, University of Human Arts and Sciences
Yukio Agarie, Niigata University of Health and Welfare
Shinichiro Yamamoto, Shibaura Institute of Technology
Akihiko Hanafusa, Shibaura Institute of Technology
Abstract: The gait cycle forces and moments acting on the hip and knee joints of a lower limb with a trans-femoral
prosthesis were investigated. The kinematics parameters of a lower limb with a prosthesis were determined frommotion-captured system data. The reaction force was measured with a force sensor in the footplate. A 3D model of theresidual limb was created using CAD software and based on MRI data. All parts of the prosthesis were measured and afull-size 3D model was created. The 3D model of the prosthesis was exported to Matlab Simmechanics to calculate theforces and moments acting on the joints. The results of this study could be used to calculate the load transferred fromthe socket to the residual limb. They could also be used to design the structure of a prosthesis and optimize the dynamic
characteristics of such a prosthesis.
Key Words: Trans-femoral, Reaction force, Reaction moment, Lower limb prosthesis, Hip joint, Knee joint
1. Introduction
There are many people who have had to have a limb
amputated, or who were born with limb different. This isespecially prevalent in the developing countries and those thathave been at war. In Japan, the incidence of amputation is 3
per every 100,000 people (1) .
A lower limb prosthesis is designed to replace thefunctions of the missing lower limb. An understanding of thestructure’s dynamic properties and the load transfer between
the socket of the prosthesis and the residual limb is importantto the evaluation of the quality of a prosthesis.
In some previous studies, models were created to calculate
the force and moment acting on the hip and knee joints.
Examples include Xiaohong Jia et al. (2). However, thesemodels were of a trans-tibial prosthesis with one degree of
freedom, and the reaction force was assumed to act on a fixed
point on the foot, so that the position of the center of gravity(CG) of each segment was not accurate. The model of thesocket and residual limb was a pseudo model created insoftware.
In this study, the authors modeled the residual limb andprosthesis as a coupled pendulum with two links. Each part ofthe prosthesis was modeled in full size. The input kinematicparameters were derived from data acquired with a motion
capture system, a footplate force sensor, and mechanicalequations. Thus, the error in the estimation could be reduced.
These results show the forces and moments acting on the hipand knee joints in the dynamic state. This method offers
greater flexibility and the calculation requires less time.
2. Method
The subject in this study was a man with a right-side transfemoral amputation. He was aged 47, 167 cm in height, andweighed 61 kg without his prosthesis. His prosthesis
incorporated a UCLA socket, a Nabco prosthesis, and an
Ottobock foot.
The kinematic data for the lower-limb and prosthesis, aswell as the reaction forces applied to the prosthesis foot while
walking were measured using a Mac3D system (MotionAnalysis Corporation) and a force plate platform (KislerP-12-1Corporation). Two plates were placed such that both of thesubject’s feet struck them during a gait cycle. Data wasrecorded at a sampling rate of 200 Hz while the subject waswalking. The model was considered on the sagittal plane andthe socket of the prosthesis and the residual limb wereassumed as one block.

Fig. 1 Real and 3D model of lower limb with prosthesis
2.1. Established modelFig. 1 shows the actual lower limb with the prosthesis, aswell as the 3D model. The first joint is the hip joint to which
the first link, including the residual limb and part of theprosthesis above the knee joint is connected to the fixed partby a revolute joint. A 3D model of the residual limb andsocket prosthesis were created using MRI data consisting of
17 layers, each separated by 10 mm. The density of theresidual limb was obtained by averaging the density of thebone, muscle, fat, and skin. The second joint is the knee joint
where the second link below the knee joint of the prosthesis isconnected to the first link by a revolute joint. The dimensionsof the parts were taken from the actual prosthesis. The
material density of each part was calculated from d = m/V (m:mass of a part, V: volume of a part). The 3D model wasdesigned using Creo parametric 2.0 (PTC Inc.).
2.2. Kinematics parameters
The positions to which markers were attached to the lower
limb prosthesis are shown in Fig. 2. The angular rotations at
the hip (θ 1) and knee (θ 2) joints were defined as shown in thediagram. Matlab (Mathworks Inc.) was used to calculate theLIFE2014

angle, angular velocity, and angular acceleration at the hipand knee joints based on the time difference between themarkers’ coordinates.
The reaction force acts on the foot of the prosthesis at thecenter of pressure (COP). The position of the COP in the firstforce plate coordinate system is shown in Fig. 3.

2014 年 9 月 24 日－26 日 北海道force. Especially, the magnitude of the reaction force at theknee joint is almost the same as that at the ground. The
direction of the moment at point M and at the hip and knee
joints are reversed in Fig. 6. This means that, in these twocases, the reaction force vector passes the opposite side. The
maximum and minimum moment of the hip joint appear in theheel contact and toe off periods, respectively.
4. Conclusion
In this study, the forces and moments acting on the hip andknee joints were calculated for one gait cycle. From theseresults, we can calculate the forces and moments applied tothe hip and knee joints, and the load transfer between thesocket and the residual limb. These results could be used toanalyze the socket, and enable the quantitative evaluation andoptimization of prosthesis.

Fig. 2 Position of markers and angles on lower limb and footThe reaction force was moved to point M, shown in Fig. 2,with two components. The first component is the force (F1)that has same magnitude and direction as reaction force F.
The second is a moment with a magnitude defined as T = Fd.
The direction of moment T depends on the positions of A(COP) and M.
Fig. 4 Reaction force at point M and hip joints

Fig. 3 Position of COP on force plate

Fig. 5 Reaction force at point M and knee joints

The coordinates of M (M x, M y) were calculated using
equations (1) and (2), below. Here, (M 2x, M 2y) and d2 denotethe coordinates of M2 and the distance between M and M2,respectively.
M x = M 2x d2cosα(1)M y = M 2y d2sinα(2)2.3. Simulation with Simmechanics
The data determined with Creo, including the material
density, inertia moment, geometry data, and constraints wereexported to Simmechanics (MathWorks). The initial
simulation parameters consisted of the angle, angular velocity,and the angular acceleration at the hip and knee joints. The
reaction force and moments at the foot were calculated fromthe measured data.
3. Results and discussion
The forces and moments at the hip and knee joints asdetermined using Simmechanics are shown in Figs. 4, 5, and
6. In Figs. 4 and 5, the graphs of the reaction force at the hipand knee joints are almost the same as the ground reaction

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Fig. 6 Moment at point M, hip, and knee joints
References(1) Epidemiology of lower extremity amputation in centres
in Europe, North America and East Asia. N. Unwin. Br.
J. Surg. 2000, 87:328-337.
(2) Load transfer mechanics between trans-tibial prosthetic
socket and residual limb—dynamic effects. Xiaohong
Jia, Ming Zhang, Winson C.C. Lee. Journal of
Biomechanics 37 (2004), 1371–1377.