Modelling, Mathematical Description, Measurements and Control of the Selected Animal and Human Body Manipulation and Loc
The investigations in the area of Biomechanics of Engineering and Rehabilitation Engineering started at the Technical University of Warsaw in 1961. In the last 24 years several projects were carried out by the interdisciplinary Team of Biomechanics. The l
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A. Morecki Technical University of Warsaw, Poland
INI'RODUCTICN The investigations in the area of Biomechanics of Engineering and
Rehabilitation Engineering started at the Technical University of Warsaw in 1961. In the last 24 years several projects were carried out by the interdisciplinary Team of Biomechanics. The list of the main new results obtained in this period of time is as follows: - mathematical models of isolated muscles included the basic characteristics; - mathematical models of muscle cooperation in statical and dynamical conditions of the upper extremity of a man; - statical and dynamical models concerning the problems of biped and fourlegged locanotion; - design and control of anthrop:>rnorphic, bionic and so called "alive" A. Morecki (ed.), Biomechanics of Engineering © Springer-Verlag Wien 1987
A. Morecki
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rm.nipulators for supporting or substituting the lost _functions of upper human extremities. These notes will present some latest results obtained in the area of human muscle models included-discus-sion on the influence of some parameters on muscle characteristics. Some remarks on dynamic-rrodelling of relationship between EMG and muscle force will be given. Special attention will be given to the dynamic measurer-rents and control of limbs rrovement in man, animals and robots. Next, some problems of rrodelling in athletic rroverrent will be discussed. Manipulation and locorrotion problems will be presented on examples of animal locomotion, walking machines and artificial hands. Finally special problems concerning the dynamical oooperation of muscles and mathematical rrodel of a man under vibration will
re discussed. HUMAN AND ANIMALS MUSCLE MJDELS
Two muscle models, namely generalized rheological rrodel of isolated muscle and modyfied Hill's two component muscle model will be
bri~fly
discussed. In formulating the generalized model we proceed from a common accepted assumption, namely that a force F, which depends on muscle leng l, developed by the muscle during tetanic contraction under constant stimulation, is the sum of the passive component Fp , independent of stimulation, and the active component Fa , dependent of the stimulation value . (Fig. l.la) . A generalized diagram of the rheological model of the muscle is presented in Fig. l.lb1 where the following denotations have been accepted: 1,2,3- componential units of the model; E0 ,E1 ,E2'-E 3 - Young modulus val-
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Animal and Human Body Manipulation Movements
b
a
2 ~-~ I I I
F
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1- r;,
I
Fo
'
/
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10
Unstimulated in static conditions
-
1
I Unstimulated in dynamic conditions
2
1 + 2
3
3
2 + 3
1 + 2 + 3
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Stimulated in static conditions
1 Stimulated
in
~YQ~~
conditions
--
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Animal and Human Body Manipulation Movements
Given below is the set of differential equations describing the model:
nln2 r:l r:2 • - o + - - 02 02 +E- + E 2 1 2 ElE2
(n 1+n 2 )E +
E3d(om-o 3) (om-o 3) (E3 +Es) + dt
where
o
2 m = ES £
with
£1
El +E2
EE 1 2
• nln2£ (1.1)
n3ES~ + ESE3£
= ±0,4.
The f
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