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A Modified Dynamic Model of the Human

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8
This article can be downloaded from http://www.ijmerr.com/currentissue.php
Int. J. Mech. Eng. & Rob. Res. 2013S M Nacy et al., 2013
A MODIFIED DYNAMIC MODEL OF THE HUMANLOWER LIMB DURING COMPLETE GAIT CYCLE
S M Nacy
1
*, S S Hassan
1
and M Y Hanna
1
*Corresponding Author:
S M Nacy,
nacys2@asme.org
A modified method for identifying dynamic model of the human lower limb during complete gaitcycle was developed in this paper. The model was based on two dimensional modeling of thehuman lower limb; the equations of motion were derived using Euler-Lagrange method andenergy approach. The lower limb is simulated as a three link robotic manipulator (thigh, shankand foot), the force plate reaction forces were performed as external forces acted on the contactpoint between foot and the ground. The foot is simulated as two right angle triangles where thepoint of contact and the angle of contact of the foot were varied as a function of time from heelstrike point to the toe off point of the foot. Therefore in this analysis we have the variation of four angles namely thigh, knee, ankle and foot. Also we considered the variation of the foot lengthand the angle between the line of action and the vertical line from ankle joint with the variation of the reaction forces from heel strike to toe off points along the gait cycle.
Keywords:
Dynamic model, Human lower limb, Euler-lagrange method
INTRODUCTION
The gait cycle is defined as the time intervalbetween two successive occurrences of oneof the repetitive events of walking (Michael,2007). The gait cycle is divided into the stancephase (the foot is on the ground), and the swingphase (the foot is moving forward through theair), as shown in Figure 1.Gait analysis is the study of thebiomechanics of human movement aimed atquantifying factors governing the functionality
ISSN 2278 – 0149 www.ijmerr.comVol. 2, No. 2, April 2013© 2013 IJMERR. All Rights ReservedInt. J. Mech. Eng. & Rob. Res. 2013
1
University of Baghdad, Iraq.
of lower extremities; also the simulation of thehuman lower limb motion during complete gaitcycle is very useful for analysis of the forcesand moments acted on the human lower limb joints (Obinata
et al.
, 2004; Shabnam
et al.
,2008; and Han and Wang, 2011). Duringwalking, a normal healthy individual executesthe most stable gait patterns, so it makessense to capture those gait patterns and usethem for the analysis of the gait cycle which isrequired to obtain the above target. However,in spite of the several models developed to
Research Paper
9
This article can be downloaded from http://www.ijmerr.com/currentissue.php
Int. J. Mech. Eng. & Rob. Res. 2013S M Nacy et al., 2013
increase our understanding of normal gait, fewgait models have been provided and most of them have been limited to swing phase (Luis
et al.
, 2009; Marko and Fabio, 2009; Jian
et al.
, 2010; and Han and Wang, 2011).Mathematical modeling can be effectively usedto study the kinematics, dynamics and other characteristics of the human lower limb(Faramand
et al.
, 2006; Roozbeh, 2008; andHong-Liu
et al.
, 2009). The purpose of thepresent study is to employ the mathematicalmodeling approach to analyze the kinematicsand dynamics of human lower limb duringcomplete gait cycle including both swing andstance phases and also taking intoconsideration the variation of the groundreaction forces and their points of contact withthe foot which include many variables.
MATHEMATICAL ANALYSES
A human body can be modeled as a serialmanipulator with rigid links; therefore, the
Figure 1: Gait PhasesFigure 2: Model of the Lower Limb
(a) Model of the Lower Limb with ThreeDegree of Freedom and the Foot Model(b) Model of the Lower Limb as Three LinkManipulator
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This article can be downloaded from http://www.ijmerr.com/currentissue.php
Int. J. Mech. Eng. & Rob. Res. 2013S M Nacy et al., 2013
equations of motion can be obtained. In thisstudy, the human lower limb is assumed as athree rigid link manipulator (i.e., the thigh link,the shank link and the foot link) as illustrated inFigure 2. In order to build the equations of motion, the Euler Lagrange equations areused and the energy approach was adopted,in addition to that, the equations werespecialized by applying the Denavit Hatenberg(DH) convention (Mark
et al.
, 1992).First of all, the manipulator have three jointswhich are the hip joint, the knee joint and theankle joint, these three joints make threeangles (
1
,
2
,
3
). These three angles makethe three generalized coordinates (
q
1
,
q
2
,
q
3
).The positive direction for these angles isviewed in Figure 2b (Andrew
et al.
, 2005; andMarko and Fabio, 2009).The (DH) convention is applied to themanipulator and the obtained (DH) parametersare shown in Table 1.In order to calculate the value of
D
(
q
),
C
(
q
,
q
') and
g
(
q
), we need to know thevariation of the three angles (i.e., hip, kneeand ankle angles), the human joint lower limb angles were obtained from Ref.(Michael, 2007), in these curves thevariation of lower limb joint throughcomplete gait cycle were viewed.The inertia matrix and their secondderivative of the generalized coordinatescome from two parts of the kinetic energy of the three link manipulator, which are thetransitional part and the rotational part of thekinetic energy.(
K
.
E
)
T
= 1/2
m
1
V
c
1
T
V
c
1
+ 1/2
m
2
V
c
2
T
V
c
2
+ 1/2
m
3
V
c
3
T
V
c3
...(2)(
K
.
E
)
R
= 1/2
q
'
T
(
JW
c
1
T
R
1
I
1
R
1
T
JW
c
1
+
JW
c
2
T
R
2
I
2
R
2
T
JW
c
2
+
JW
c
3
T
R
3
I
3
R
3
T
JW
c
3
)
q
'The obtained
D
(
q
) matrix is:The christoffel symbols
C
(
q
.
q
') which aredefined as:
ni i ijk kj
qqc C
1
k ij j ki i
ni kj
qd qd qd
///2/1
1
...(4)The obtained
C
(
q
.
q
') matrix is:
Link
a
i
i
d
i
?
i
1L
1
00?
1
2L
2
00?
2
3L
3
00?
3
Table 1: (DH) Parameters
The manipulator dynamic equation of motion using matrix form is:
D
(
q
)
q''
+
c
(
q
.
q
')
q
' +
g
(
q
) =
0
that is:
321333231232221131211321333231232221131211
qqqC C C C C C C C C qqqDDDDDDDDD
030201
qg
...(1)

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