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Università degli Studi di Perugia
Facoltà di Medicina e Chirurgia
biomeccanica
del sistema muscolo-scheletrico
Prof. Andrea Biscarini
Capitolo 1:
INTRODUZIONE
1.1 - La biomeccanica: definizione e campo di indagine
1.2 - La biomeccanica del sistema muscolo scheletrico
Capitolo 2:
RICHIAMI DI MECCANICA DEI SISTEMI
2.1 - Braccio e momento di una forza
2.2 - Le leve: definizione, regola di equilibrio
2.3 - Leve vantaggiose e svantaggiose
2.4 - Leve di primo, secondo e terzo tipo
2.5 - Leve di forza e leve di velocità
2.6 - Calcolo della forza agente sul fulcro
2.7 - Le leve: proprietà dinamiche
Capitolo 3:
FORZE ESTERNE
3.1 - Classi di forze esterne
3.2 - Momento delle forze esterne
3.3 - Misura delle forze esterne
Capitolo 4:
FORZA MUSCOLARE
Aspetti geometrici:
4.1 - Punto di applicazione, direzione, verso
4.2 - Braccio della forza muscolare
4.3 - Angolo di trazione
Intensità e regolazione della forza muscolare:
4.4 - Curva lunghezza-tensione
4.5 - Curva forza-velocità
4.6 - Livello di attivazione
4.7 - Parametri dell’architettura del muscolo
4.8 - Momento della forza muscolare
Valutazione della forza muscolare:
4.9 - Elettromiografia
4.10 - Modelli biomeccanici
Capitolo 5:
CARICHI ARTICOLARI
1.1 - La biomeccanica: definizione e campo di indagine
1.2 - La biomeccanica del sistema muscolo scheletrico
Capitolo 6
ASPETTI FUNZIONALI
6.1 - Ciclo allungamento-accorciamento
6.2 - Biomeccanica dei muscoli poliarticolari
6.3 - Co-contrazione
Capitolo 7
APLLICAZIONI
7.1 - Strength training equipment (leg extension modificato)
7.2 - Supporti per la riabilitazione del ginocchio in acqua
7.3 - Cardio equipment (cardio wave)
7.4 - Squat al multipower
Capitolo 1:
INTRODUZIONE
1.1 - La biomeccanica: definizione e campo di indagine
1.2 - Biomeccanica del sistema muscolo-scheletrico
1.1 La biomeccanica: definizione e campo di indagine
Definizioni generali:
“Biomechanics is the science that study
structures and functions of biological systems
using the knowledge and methods of mechanics.”
(Hatze, 1971)
Definizioni specifiche:
“Biomechanics is the science that examines
forces acting upon and within a biological structure
and the effects produced by such forces.”
(Hay, 1973)
Società:
International Society of Biomechanics
European Society of Biomechanics
International Society of
Biomechanics in Sports
American Society
of Biomechanics
Canadian Society
of Biomechanics
Riviste:
Journal of Biomechanics
Clinical Biomechanics
Impact Factor 2.4
Impact Factor 1.5
Journal of
Applied Biomechanics
Journal of
Biomechanical Engineering
Impact Factor 0.5
Impact Factor 1.7
Campo di indagine:
Fundamental Topics - Biomechanics of the musculoskeletal, cardiovascular, and respiratory systems,
mechanics of hard and soft tissues, biofluid mechanics, mechanics of prostheses and implant-tissue
interfaces, mechanics of cells.
Cardiovascular and Respiratory Biomechanics - Mechanics of blood-flow, air-flow, mechanics of the soft
tissues, flow-tissue or flow-prosthesis interactions.
Cell Biomechanics - Biomechanic analyses of cells, membranes and sub-cellular structures; the relationship
of the mechanical environment to cell and tissue response.
Dental Biomechanics - Design and analysis of dental tissues and prostheses, mechanics of chewing.
Functional Tissue Engineering - The role of biomechanical factors in engineered tissue replacements and
regenerative medicine.
Injury Biomechanics - Mechanics of impact and trauma, dynamics of man-machine interaction.
Molecular Biomechanics - Mechanical analyses of biomolecules.
Orthopedic Biomechanics - Mechanics of fracture and fracture fixation, mechanics of implants and implant
fixation, mechanics of bones and joints, wear of natural and artificial joints.
Rehabilitation Biomechanics - Analyses of gait, mechanics of prosthetics and orthotics.
Sports Biomechanics - Mechanical analyses of sports performance.
1.2 Biomeccanica del sistema muscolo-scheletrico
Definizione:
“Biomechanics of the musculo-skeletal system is the science that examines
forces acting on the musculo-skeletal system
(external loads, muscular forces and joint load)
and the effects produced by such forces
(movements, deformations, biological change in tissues).”
Tre tipi di forze:
• Forze esterne
• Forze muscolari
• Carichi articolari
Capitolo 2:
RICHIAMI DI MECCANICA DEI SISTEMI
2.1 - Braccio e momento di una forza
2.2 - Le leve: definizione, regola di equilibrio
2.3 - Leve vantaggiose e svantaggiose
2.4 - Leve di primo, secondo e terzo tipo
2.5 - Leve di forza e leve di velocità
2.6 - Calcolo della forza agente sul fulcro
2.7 - Le leve: proprietà dinamiche
2.1 Braccio e momento di una forza
Definizione
Dato un corpo rigido vincolato a ruotare attorno ad un asse fisso,
e una forza agente sul corpo e appartenente a un piano perpendicolare a tale asse,
si definisce momento della forza rispetto all’asse
il prodotto del modulo della forza per il suo braccio.
Il braccio è la minima distanza fra l’asse di rotazione e retta di applicazione della forza.
M a   Fb
asse di rotazione
corpo rigido

F
Dimensioni ed unità di misura
M a   FL  MLT 2 L  ML2T 2 
Nm  kg m2 s 2
C
corpo rigido

F
C
corpo rigido

F
Il braccio della forza (ed il momento)
aumenta all’aumentare della distanza
fra punto di applicazione della forza e
centro di rotazione
Il braccio della forza (ed il momento)
aumenta all’aumentare quanto più la
forza è perpendicolare alla retta fra il
punto di applicazione della forza e il
centro di rotazione
Il braccio della forza (e il momento) è nullo quando la retta di applicazione della forza passa per il centro di rotazione C
2.2 Le leve: definizione, regola di equilibrio, classificazione
Leve
Corpo rigido vincolato ad asse fisso (fulcro) sollecitato da due forze (dette forza F e resistenza R) che producono
momenti assiali di segno opposto (rotazioni di verso opposto).


Braccio della
resistenza, bR

F

R  mg
retta di applicazione
della resistenza
Regola d’equilibrio
M a(est )  0
Se
bF  10bR
bF F  bR R  0
 F
1
R
10
bF F  bR R
F
bR
R
bF
(per equilibrare la resistenza basa una forza 10 volte più piccola).
E’possibile equilibrare/spostare un carico elevato con una forza minima

F
bF
bR

R
2.3 Leve vantaggiose e leve svantaggiose
Leve vantaggiose
Braccio della forza è maggiore del braccio della resistenza
Per equilibrare la resistenza è sufficiente una forza il cui modulo è minore di quello della resistenza
bF F  bR R
vantaggiose
bF  bR
bR
 FR

F
bF

R
Leve svantaggiose
Braccio della forza è miniore del braccio della resistenza
Per equilibrare la resistenza è necessaria una forza il cui modulo è maggiore di quello della resistenza
bF F  bR R
svantaggiose
bF  bR
 FR

R
bR
bF

F
2.4 Leve di primo, secondo e terzo tipo
Leve di primo tipo
Fulcro in posizione intermedia fra forza e resistenza
Le leve di primo genere possono essere vantaggiose o svantaggiose
1° tipo

R
Esempio di leva anatomica di primo tipo
Estensione dell’articolazione atlanto-occipitale

F
Leve di secondo tipo
Resistenza in posizione intermedia fra forza e fulcro
Le leve di secondo genere sono in generale vantaggiose

F
2° tipo
Esempio di leva anatomica di secondo tipo
Estensione della caviglia nel sollevamento del peso del corpo

R
Leve di terzo tipo
Forza in posizione intermedia fra resistenza e fulcro
Le leve di terzo genere sono in generale svantaggiose

F
3° tipo
Esempio di leva anatomica di terzo tipo
Flessione dell’articolazione del gomito

R
2.5 Leve di forza e leve di velocità
Le leve anatomiche sono in maggioranza svantaggiose. Ciò appare un controsenso. In realtà una leva svantaggiosa dal
punto dinamico(delle forze) è vantaggiosa dal punti di vista cinematico (degli spostamenti e delle velocità) e viceversa.
R
bR  nbF
F
e DsR  nDsF
n
 FDsF  RDsR  LF  LR
 R
DsR
DsF
Il lavoro compiuto dalla forza e la resistenza è lo stesso.
E’ necessaria una grande forza per spostare una piccola
resistenza, ma lo spostamento della resistenza è grande
rispetto a quello del punto di applicazione della forza.

F
2.6 Calcolo della forza agente sul fulcro (reazione vincolare)


Braccio della
resistenza, bR

F

R  mg

F
retta di applicazione
della resistenza


Regola d’equilibrio
 (est )
R
0
  
F  R  0

 
  ( F  R)
R
2.7 Le leve: proprietà dinamiche
Momento di inerzia:
Data un asse a, si definisce momento di inerzia di un sistema rispetto all’asse a, e si indica con il simbolo Ia ,
la somma dei prodotti delle masse dei punti del sistema per i quadrati delle rispettive distanze dall’asse.
Sistema particellare
I a  m1d12  m1d12    mN d N2

Sistema continuo
I a  lim Dm1r12  Dm2 r22    DmN rN2
Dmi 0
  r 2 dm
M
d1
m1
d2
di
m2
ri
mi
dN
mN
Dmi

Equazione del moto:


Braccio della
resistenza, bR

F

R  mg
retta di applicazione
della resistenza
M a(est )  I
bF F  bR R  I
F
bR R  I
bF
 = accelerazione angolare
 = velocità angolare
bF F  bR R    0   aumenta
 =cost: movimento isocinetico
bF F  bR R    0   costante
In particolare:
bF F  bR R    0   diminuisce
=0: equilibrio statico
Capitolo 3:
Forze esterne agenti sul sistema
muscolo-scheletrico
3.1 - Classi di forze esterne
3.2 - Momento delle forze esterne
3.3 - Misura delle forze esterne
3.1 Classi di forze esterne
•
•
•
•
Pesi liberi o vincolati
Forze elastiche
Resistenze di mezzi fluidi
Razioni vincolari di appoggio (“ground reaction”)
Le forze esterne, sono note a priori (pesi liberi o vincolati, forze elastiche) o possono essere misurate
(resistenze di mezzi fluidi, reazioni vincolari). Possono quindi essere considerate note in modulo
direzione e verso.
Forza peso
g = 9.81 m/s2 alle nostre latitudini
g = 9.78 m/s2 all’equatore
g = 9.83 m/s2 ai poli
Intensità: prodotto della massa del corpo per l’accelerazione di gravità;
Direzione e verso : verticale discendente.


P  mg
Esempio (pesi liberi):
Esercizi con manubri.

mg

mg

mg
Implicazioni biomeccaniche:
Durante un esercizio con pesi liberi la resistenza
mantiene direzione ed intensità invariate.
Esempio (pesi vincolati al moto di leve):
Esercizi al la leg extension.

R

R

R
Implicazioni biomeccaniche:
Durante un esercizio quasi-statico alla leg extension la resistenza
mantiene intensità R invariata ma cambia la sua direzione.
Esempio (pesi vincolati a cavi):
Esercizi ai cavi.

R

R

R
Implicazioni biomeccaniche:
Durante un esercizio quasi-statico ai cavi la resistenza mantiene
intensità R invariata (R=mg) ma cambia la sua direzione.

mg

OP  r  rrˆ
Forza elastica di centro O
Forza sempre diretta verso un punto fisso O (detto centro
della forza elastica) in modulo proporzionale alla distanza
di P da O
O
r̂

Fel
r


Fel  kOP  kr  krrˆ
P
k = costante elastica
Esempio (bande elastiche):
Forza esercitata da una molla compressa o
allungata, o da una banda elastica
allungata rispetto alla configurazione a
riposo (assenza di sollecitazione).
banda elastica a riposo
banda elastica allungata
O
banda elastica allungata
O
Implicazioni biomeccaniche:
Durante un esercizio con bande elastiche
varia sia la direzione che l’intensità della
resistenza.
P
P
Resistenze di mezzi fluidi
Quando un corpo si muove all’interno di un fluido esercita una forza sulle particelle del fluido. Le
particelle, per il terzo principio, esercitano sul corpo forze uguali e contrarie: la somma di queste forze
costruisce la resistenza offerta dal mezzo fluido al moto del corpo.

F  Af (v)vˆ
f (v )  v
0  v  2 m/ s
(regime viscoso)
f (v )  v 2
2  v  200 m / s
(regime idraulico)
 = densità del fluido
 = coefficiente di forma
A = superficie investita
Esempio:
I due corpi rappresentati
hanno lo stesso valore di
A ma differenti valori di .
fluido

v
Implicazioni biomeccaniche:
Durante un esercizio in acqua l’intensità della resistenza può essere
modulata variando la velocità dell’esercizio e la superficie esposta.

v
A
Ground reaction
Forza esercitata dal piano di appoggio sulla zona di contatto fra piede e piano di appoggio. Per il terzo
principio della dinamica è uguale ed opposta alla forza esercitata dal piede sul piano
3.2 Momento delle forze esterne
Estensione del ginocchio con cavigliera
bR
bR

mg

mg
M R  bR Mg

mg
La resistenza mg resta costante,
il braccio della resistenza bR cresce,
quindi il momento della resistenza cresce
Estensione del ginocchio con leg-extension
bR
bR
bR

R
M R  bR R

R

R
La resistenza R resta costante e pari al peso del pacco di piastre selezionate,
il braccio della resistenza bR resta costante,
quindi il momento della resistenza resta costante
Estensione del ginocchio con elastici
bR

Fel
M R  bR Fel
bR
bR

Fel

Fel
La resistenza elastica aumenta all’aumentare della lunghezza dell’elastico,
il braccio della resistenza bR diminuisce,
Momento della resistenza????
3.3 Misura delle forze esterne
Pedane di forza
Pedane baropodometriche
Capitolo 4:
FORZA MUSCOLARE
Aspetti geometrici:
4.1 - Punto di applicazione, direzione, verso
4.2 - Braccio della forza muscolare
4.3 - Angolo di trazione
Intensità e regolazione della forza muscolare:
4.4 - Curva lunghezza-tensione
4.5 - Curva forza-velocità
4.6 - Livello di attivazione
4.7 - Parametri dell’architettura del muscolo
4.8 - Momento della forza muscolare
Valutazione della forza muscolare:
4.9 - Elettromiografia
4.10 - Modelli biomeccanici
Capitolo 4:
FORZA MUSCOLARE
Aspetti geometrici:
4.1 - Punto di applicazione, direzione, verso
4.2 - Braccio della forza muscolare
4.3 - Angolo di trazione
Intensità e regolazione della forza muscolare:
4.4 - Curva lunghezza-tensione
4.5 - Curva forza-velocità
4.6 - Livello di attivazione
4.7 - Parametri dell’architettura del muscolo
4.8 - Momento della forza muscolare
Valutazione della forza muscolare:
4.9 - Elettromiografia
4.10 - Modelli biomeccanici
4.1 Punto di applicazione, direzione e verso
Parametri noti (studi anatomici):
• Punto di applicazione: inserzione (e origine)
• Direzione: tangente alla linea inserzione - origine nel punto di inserzione (e di origine)
• Verso: inserzione → origine (origine → inserzione)
•
•
Braccio della forza rispetto all’asse di rotazione articolare
Angolo di trazione rispetto all’asse meccanico del segmento anatomico su cui il muscolo si inserisce

F

F

F
4.2 Braccio della forza muscolare
Definizione
Il braccio della forza muscolare
è la minima distanza fra la retta di applicazione della forza muscolare
ed il centro di rotazione articolare

F

F
Importanza
Il momento assiale M della forza muscolare è
definito come il prodotto del braccio della forza
muscolare per l’intensità della forza muscolare:
M = ± aF F
Determina l’accelerazione angolare a del
segmento anatomico in accordo alla seconda
equazione cardinale della dinamica dei sistemi:
I = M
M = momento assiale della forza
I = momento di inerzia
 = accelerazione angolare
Braccio della forza
muscolare
Forza muscolare

F
aF
Variazione del braccio della forza muscolare
Il braccio della forza muscolare varia al variare dell’angolo articolare
Esempio
Il braccio della forza del quadricipite femorale varia al variare dell’angolo di flessione del ginocchio.
Forza del
quadricipite
femorale
Braccio

F
aF
Esempio
Braccio dei muscoli flessori ed estensori del gomito.
4.3 angolo di trazione
Definizione
Angolo individuato della forza muscolare e l’asse meccanico longitudinale del segmento
anatomico su cui il muscolo si inserisce
Forza muscolare
Angolo di
trazione

F
j
Variazione dell’angolo di trazione
L’angolo di trazione varia al variare dell’angolo articolare
Esempio: quadricipite femorale
Angolo individuato dal tratto rettilineo di tendine rotuleo che si inserisce sulla tibia e
l’asse meccanico longitudinale della tibia
Forza del
quadricipite
femorale
Angolo di
trazione

F
j
Importanza
Determina la componente rotatoria e componente stabilizzatrice della forza muscolare

F
j
Componente stabilizzatrice e de-stabilizzatrice
Nel caso del bicipite brachiale la componente stabilizzatrice, ad elevati angoli di flessione del gomito,
diviene de-stabilizzatrice (lussante)

F
Gomito: Angolo di flessione 70°

F
Gomito: Angolo di flessione 135°
Funzione meccanica della rotula
Funzione meccanica dei condili mediali e dei malleoli
Capitolo 4:
FORZA MUSCOLARE
Aspetti geometrici:
4.1 - Punto di applicazione, direzione, verso
4.2 - Braccio della forza muscolare
4.3 - Angolo di trazione
Intensità e regolazione della forza muscolare:
4.4 - Curva lunghezza-tensione
4.5 - Curva forza-velocità
4.6 - Livello di attivazione
4.7 - Parametri dell’architettura del muscolo
4.8 - Momento della forza muscolare
Valutazione della forza muscolare:
4.9 - Elettromiografia
4.10 - Modelli biomeccanici
4.4 Curva lunghezza-tensione
Curva lunghezza tensione del sarcomero e sua interpretazione
La forza che il sarcomero è in grado di produrre dipende dalla sua lunghezza. Si possono individuare 4 regimi:
e
1
d
c
f
g
b
h
0
i
1.25
a
1.65
2.05
2.65
Lunghezza del sarcomero (mm)
4.05
0.025
1.2
1.6
1.2
0.025
mm
0.2
a
4.05
b
c
2.65
d
2.45
e
2.05
f
g
1.65
h
i
1.25
Forza delle fibre muscolari
•
Since sarcomeres are arranged in series, the force that a muscle fiber can generate is independent of the
number of sarcomeres, i.e. provided that sarcomere length is not-changing, the force produced by each
sarcomere will be equal. The force produced by the muscle fiber will be equal to the sarcomere force.
LFIBER = NSARC LSARC
•
FFIBER = FSARC
Because the maximum force which can be produced by a sarcomere depends on sarcomere length, the
maximum force which can be produced by a muscle fiber will depend on its length. The relationship
between maximum force and muscle fiber length will depend on the number of sarcomeres that make up
the fiber.
FMAX depends on: LSARC = LFIBER / NSARC
•
Sarcomeres may not be uniform and homogeneous. Sarcomere diameter, myofilament length and
myofilament density may vary along the length of the muscle fiber. This will result in different lengthtension relations for different sarcomeres.
Curva lunghezza tensione del muscolo
When a muscle fiber is stretched beyond a certain point, the structural proteins acting in parallel with
contractile proteins begin to be stretched. The force produced by these parallel elastic structures then
increases rapidly with muscle length. Consequently, the total sarcomere force (active + passive) is
generally a monotonically increasing function of length, despite the fact that myofilament overlap
decreases at long lengths.
Esempio: muscoli che attraversano il
gomito
Estimated operating ranges of the
elbow flexors over 100° of elbow
flexion and of the extensors over 90°
flexion. Estimated fascicle excursions
were normalized by optimal fascicle
length (l0M) and super-imposed on a
normalized force-length curve based
on the sarcomere lengths measured
from the five extended specimens.
The variation in force-generating
capacity during elbow flexion is
expressed as a proportion of peak
isometric force (F0M). Results shown
are averages of the 10 extremities in
this study. Both muscle moment arm
and optimal fascicle length determine
how much of the isometric forcelength curve each muscle uses.
4.5 Curva forza-velocità
Fase eccentrica (allungnamento)
•
When a muscle fiber is activated to produce a steady force while being held isometric and is then
stretched at constant velocity, the resulting force is greater than the isometric force (Fig. 2.1).
•
For low velocities of stretch the force increases with velocity, but as the velocity increases further the force
levels off or drops slightly, reaching a maximum of between 1.2-1.8 times the isometric force (Fig 2.3).
Interpretation
The increase in force with muscle lengthening
velocity is probably largely due to stretching of
attached cross-bridges (Fig. 1.6).
Cross-bridges, which are being stretched, will
generate a greater average force during their
period of attachment than crossbridges which are
isometric.
The higher the lengthening velocity, the greater
the amount of stretch that will occur during the
period of attachment and hence, the greater the
average force during the period of cross-bridge
attachment.
When the lengthening velocity becomes too high,
cross-bridges are stretched beyond the limits that
can be supported by the binding force between
actin and myosin, resulting in forcible detachment.
This limits the maximum force during muscle
lengthening.
Fase concentrica (accorciamento)
•
When a muscle fiber is held isometric and is then released and allowed to shorten at a constant
velocity, the contractile force produced by the muscle fiber drops to a lower relatively constant value.
The higher the shortening velocity the lower the force (Fig. 2.2).Conversely, by decreasing the load on a
muscle fiber, its shortening velocity can be increased.
•
If contractile force is plotted against shortening velocity a hyperbolic relation is obtained where force is
inversely proportional to velocity, decreasing continuously from its isometric value to zero at maximum
shortening velocity (Fig. 2.3).
Interpretation
There are several possible reasons why muscle force drops as the velocity of shortening increases.
•
First, there are fewer cross-bridges attached during shortening and their number decreases as the
velocity of shortening increases. It has been suggested that this is a consequence of an increase in the
rate of cross-bridge detachment during muscle shortening and a decrease in the rate of attachment.
Both of these rates may be functions of velocity.
•
Second, shortening likely reduces the tension in attached myosin cross-bridges (Fig. 1.6). Crossbridges, which are shortening, will generate a smaller average force during their period of attachment
than cross-bridges which are isometric. The higher the shortening velocity, the greater the amount of
shortening that will occur during the period of attachment and hence, the lower the average force
during the period of crossbridge attachment.
•
Third, some cross-bridges may be compressed as the result of shortening before they detach. These
cross-bridges would generate negative force, thereby reducing the overall tension developed by the
fiber. The higher the shortening velocity the more quickly cross-bridges would compress, resulting in
a greater number of cross-bridges generating negative force before detachment.
Maximum velocity of muscle fiber shortening
•
The maximum velocity of muscle fiber shortening occurs when there is no load on the muscle fiber.
•
Conversely, when the muscle fiber is shortening at maximum velocity it does not generate any
contractile force.
The maximum shortening velocity of a muscle fiber depends
•
on the number of sarcomeres that make up the muscle fiber
•
their average length of sarcomeres that make up the muscle fiber
Velocity of muscle fiber shortening and fiber length
•
The velocity of muscle fiber shortening (V) is the sum of the shortening velocities of the individual
sarcomeres (vsarc). Each sarcomere has a maximum shortening velocity. Therefore, the maximum
shortening velocity of the muscle fiber will be equal to the sum of the maximum shortening velocities of
the sarcomeres. The greater the number of sarcomeres the higher the maximum velocity.
Long fiber: number of sarcomeres nlong ; length llong = nlonglsarc
t
t + Dt
fiber shortening (slong)
Short fiber: number of sarcomeres nshort ; length lshort = nshortlsarc
t
t + Dt
sarcomere shortening (ssarc)
Vlong 
slong
Dt

nlongssarc
Dt
 nlongvsarc
fiber shortening (sshort)
s
n s
Vshort  short  short sarc  nshortvsarc
Dt
Dt
Vlong
Vshort

nlong
nshort

llong
lshort
Velocity of muscle fiber shortening and sarcomere length
At sarcomere lengths that are long
enough to stretch the parallel elastic
structures of the muscle fiber,
passive tension acts as a driving
force on the contractile system and
increases the speed of shortening
above its maximum value at zero
load.
For very short sarcomere lengths,
the maximum shortening velocity
decreases in parallel with the
isometric tension (Fig. 2.4).
4.6 Livello di attivazione
Motor unit: functional unit of neuro-muscular systems
•
A muscle consists of thousands of muscle fibers organized into motor units. Each motor unit comprises
a group of muscle fibers, often several hundred, which are innervated by a single motoneuron. The
muscle fibers belonging to one motor unit may be distributed throughout a large region of the muscle,
i.e., they need not be adjacent to one another.
•
A motor unit is activated in an all-or-none fashion by a single action potential, which travels from the
motoneuron along the axon to the muscle fibers. The neural action potential leads to an action
potential in each muscle fiber innervated by that motoneuron.
Twitch
•
A single muscle action potential produces a brief contraction of the muscle fiber called a twitch. The
duration of the twitch depends on the muscle fiber type. The duration of both the contraction and
relaxation phases of the twitch are longer for slow-twitch (type I) than fasttwitch (type II) fibers (Fig.
2.8).
•
In skeletal muscle the range of contraction times (time to peak) is from 7.5 ms for fast (extraocular
muscle: IR- internal rectus); 40 ms for intermediate (G - gastrocnemius); to 90 ms for slow (S - soleus)
muscle fibers. Most skeletal muscles have a mixture of different types of fibers: slow; fast oxidative
glycolytic (rare); or fast glycolytic. However, all fibers in a given motor unit are of the same type - the
type being determined to some extent, by the nature of the motoneurone. Small tonically active
motoneurones prompt development of slow fibre types; large, phasic motoneurones favour fast
glycolytic fibres.
Frequency of activation (firing rate)
•
Motor unit force is a function of the frequency of activation (firing rate) of the innervating motoneuron.
Firing rate is defined as number of action potentials per second.
•
The force produced by each muscle fiber, innervated by the motoneuron, increases with firing rate
because of the accumulation of intracellular calcium (Ca+2). Each action potential depolarizes the muscle
membrane, which results in more Ca+2 being released from the terminal cisternae, diffusing through the
intracellular space and activating more actin-binding sites.
1 second
T
time
Action
potential
T: period
n: Frequency of activation.
Numbers of action potential
per second
Mechanical summation (temporal summation)
•
The intracellular calcium concentration produced by a single action potential, increases and decreases more
rapidly than the isometric twitch force. Therefore, the amount of force added by a second action potential
occurring immediately after the first will depend on the time interval between them, i.e., on the amount of
intracellular calcium at the time of occurrence. The additional force contribution by a second action potential
drops steeply as a function of the interval between two successive action potentials.
Fast
units
Slow
units
Twitch sequences of fast and slow motor units. Numbers to the right of each trace indicate the time interval in ms, between
successive action potentials.
Tetanus
•
If a motor unit is activated at a steady frequency, the force will initially rise and then oscillate about a new
mean value at the frequency of activation, producing what is called an unfused tetanus. Both the mean
force and the initial rate of force development will increase as firing rate increases. The higher the firing
rate the smaller the oscillation with respect to the mean force. At high firing rates, there is no noticeable
oscillation in force. This smooth steady force is called tetanus. Because type I motor units have longer
twitch contraction times than type II units they reach tetanus at lower frequencies.
Fast
units
Slow
units
Unfused and fused tetanus of fast and slow motor units. Numbers to the right of each trace indicate the time interval in ms,
between successive action potentials. At low stimulation rates (long intervals between action potentials) tetanus is unfused
Characteristic frequencies
•
Humans can voluntarily activate motor units briefly at instantaneous firing rates of about 100 Hz during
brief forceful contractions.
•
The maximum firing rates that they can sustain during steady contractions are considerably lower and
generally do not exceed 30 Hz. However, these rates are sufficiently high that several action potentials
can occur before the twitch force from the first action potential has dropped to zero. Whereas the
muscle action potential has a duration of less than 10 ms, the twitch duration for skeletal muscle fibers
is of the order of 100-200 ms. Action potentials which arrive before the twitch force has dropped to its
pre-activation level produce additional force by causing more Ca+2 to be released.
n = 30 Hz
T = 1/ 30 s = 0.033 s = 33 ms
n = 100 Hz
T = 1/ 100 s = 0.01 s = 10 ms
Motor unit time-tension curve
Single stimulus
Twitch
Double stimulus
Slow train
Fast train
Summation
Un-fused tetanus
Fused tetanus
Motor unit recruitment: size principle
•
When a muscle is activated voluntarily under isometric conditions, motor units tend to become
active in a fixed order.
•
The recruitment order is correlated with the amount of force that a motor unit can produce.
•
Motor unit force is related to the number of muscle fibers and the size of the muscle fibers that it
comprises.
•
The motor unit that produces the smallest force is recruited first. It remains active and the next
motor unit is recruited as the total muscle force increases. The motor units that produce the largest
forces are the last to be recruited. As total muscle force increases, each newly recruited unit
contributes an increment in force, which is a similar percentage of the total muscle force. In this way
force can be increased smoothly.
Muscular force regulation:
•
frequency of activation
•
recruitment strategy of
different motor units
4.7 Parametri dell’architettura del muscolo
La forza muscolare dipende anche dai parametri dell’architettura del muscolo:
•
•
•
•
•
Sezione fisiologica del muscolo
Angolo di pennazione
Lunghezza delle fibre muscolari (numero di sarcomeri in serie)
Lunghezza del tendine
Braccio della forza muscolare
Pennation angle
•
•
•
The arrangement of the muscle fibres has an important role to play. The muscle fibre direction is not always
in the same direction as the line of pull of the muscle.
When the line of action of the muscle does not match the line of action of the fibres then the muscle is
known as pennate.
There are a number of sub-classifications but the important property of these pennate muscles is the angle
of pennation: the angle between the two lines of action.
Fig.1. The internal architecture of skeletal muscles: (A) non-pennate; (B, E, F) unipennate; (C) bipennate.
Physiological cross-section
•
•
•
The maximum force a muscle can generate depends on its physiological cross-section area (PCA): area of the
fibers perpendicular to fiber direction.
In a non-pennate muscle this is simply the area of a slice taken in the middle of a muscle perpendicular to the
line of pull (fig.1A).
In a pennate muscle this would miss some of the muscle fibers (fig.2). In this case the cross-sectional area would
need to be taken perpendicular (at right angles) to the average fiber direction so as to include all the fibers in the
muscle (fig.1B,1C).
Fig.2
Fig.1: PCA for fusiform (A), unipinnate (B) and bipinnate (C) muscles.
•
Relation between physiological cross-section and pennation angle:
PCSA increases with increasing the pennation angle
Fiber length
•
•
•
Long fibers have more sarcomeres in series
Long fibers are capable of shortening over a greater distance
Long fibers have greater maximum velocity of shortening
if 30000 sarcomeres shorten 1 mm
if 20000 sarcomeres shorten 1 mm
total fiber shortens 3 cm
total fiber shortens 2 cm
•
Relation between fiber length and pennation angle:
Fiber length decreases with increasing the pennation angle
Fiber
length
Fiber
length
PCSA
PCSA
PCSA
Schematic representation of muscle with different architecture:
muscles with short fibers, large pennation angle and a large PCA;
muscles with long fibers , small pennation angle and a small PCA.
Muscle length
Length-tension and force-velocity curves for muscles with different architectural properties:
• Long fibers
• Short fibers
• Large PCSA
• Small PCSA
Length-tension and force-velocity curves for muscles with different architectural properties:
• Long fibers and Small PCSA
• Short fibers and Large PCSA
Long fibers,
Small PCA
Muscle Shorthening
Muscle Force
Muscle Force
Short fibers,
Large PCA
Short fibers, Large
PCA
Long fibers,
Small PCA
Muscle Velocity
Example: Muscles that cross the elbow
Biceps brachii
(BIC, long and short heads),
brachialis
(BRA)
brachioradialis
(BRD)
extensor carpi radialis longus
(ECRL)
pronator teres
(PT)
and triceps brachii
(TRI, long and lateral heads)
W.M. Murray et al.
Journal of Biomechanics
33 (2000) 943-952
Tendon slack length
Diagram illustrating the relationships between
optimal muscle-fiber length (LOM) tendon slack
length (LST) and the minimum and maximum
physiological lengths of a muscle (LminM) and
(LmaxM) and a musculotendon actuator, (LminMT)
and (LmaxMT) respectively. For the purpose of
illustration, pennation angle is assumed to be
zero.
• When tendon slack length is large, musclefiber length is small; thus, muscle excursion
will be small.
• When tendon slack length is small, musclefiber length is large, and muscle excursion
will be large
B. A. Garner and M. G. Pandy. Annals of Biomedical Engineering, Vol. 31, pp. 207–220, 2003
B. A. Garner and M. G. Pandy. Annals of Biomedical Engineering, Vol. 31, pp. 207–220, 2003
B. A. Garner and M. G. Pandy. Annals of Biomedical Engineering, Vol. 31, pp. 207–220, 2003
Braccio della forza muscolare
minima distanza fra la retta di applicazione della forza muscolare
ed il centro di rotazione articolare
Muscle force
moment arm

F
aF
Joint center of
rotation
Muscle
force
Example
Biceps brachii

F

F
Effect of muscle moment arm on muscle shortening
With increasing muscle moment arm the muscle shortens further for a given range of motion
(say from 20° to 120°) of joint angles and utilizes a greater portion of the force-length curve
small muscle moment arm
large muscle moment arm
ROM
ROM
muscle
shortening
muscle
shortening
Effect of muscle moment arm on joint angular velocity and range of motion
With increasing muscle moment arm joint angular velocity increases
small muscle moment arm
large muscle moment arm
large
ROM
small
ROM
lengthen muscle
contracted muscle shortening
Example:
Muscles that cross the elbow
Estimated operating ranges of the
elbow flexors over 100° of elbow
flexion and of the extensors over 90°
flexion. Estimated fascicle excursions
were normalized by optimal fascicle
length (l0M) and super-imposed on a
normalized force-length curve based
on the sarcomere lengths measured
from the five extended specimens.
The variation in force-generating
capacity during elbow flexion is
expressed as a proportion of peak
isometric force (F0M). Results shown
are averages of the 10 extremities in
this study. Both muscle moment arm
and optimal fascicle length determine
how much of the isometric forcelength curve each muscle uses.
Example: upper limb
B. A. Garner and M. G. Pandy. Annals of Biomedical Engineering, Vol. 31, pp. 207–220, 2003
4.8 Momento della forza muscolare
Momento assiale M della forza muscolare
prodotto del braccio della forza muscolare
per l’intensità della forza muscolare:
M = ± aF F
Braccio della forza
muscolare
Forza muscolare

F
aF
Centro di rotazione
articolare
Regola di equilibrio:
In esercizi con sovraccarico, in condizioni di equilibrio articolare, il momento della forza muscolare è uguale
in modulo al momento della forza esterna.
M a(est )  0
bF F  bR R  0
bF F  bR R
F
bR
R
bF
Sistema meccanico = avambraccio + manubrio

F

F
bF

R
bR

R
Forza muscolare
Carico esterno = peso
dell’avambraccio e del manubrio
applicato nel cenrto di massa del
sistema avambraccio + manubrio
Equazione del moto:
Determina l’accelerazione angolare a
del segmento anatomico in accordo
alla seconda equazione cardinale della
dinamica dei sistemi:
M a(est)  I
bF F  bR R  I
 = accelerazione angolare
I = Momento di inerzia
F

F
bF
bR R  I
bF
La forza muscolare dipende anche dall’accelerazione articolare
bR

R
bF F  bR R    0   aumenta
 =cost: movimento isocinetico
bF F  bR R    0   costante
In particolare:
bF F  bR R    0   diminuisce
=0: equilibrio statico
 = velocità angolare)
Architecture parameters, joint angular velocity and moment generating capacity
•
•
•
•
•
PCA (number of fibers in parallel)
Fiber length (number of sarcomeres in series)
Pennation angle (arrangement of the fibers)
Moment arm
Tendon length
can be thought of as being designed for:
•
Moment generating capacity
- short fibres, large pennation angle, large PCA
- large moment arm
•
Joint angular velocity
- long fibres, small pennation angle, small PCA
- small moment arm
•
Compromise between two capacities
- short fibres, large pennation angle, large PCA (more fibres in parallel)
- small moment arm
or
- long fibres, small pennation angle, small PCA (more fibres in series)
- large moment arm
Example of collection of architectural parameters
W.M. Murray et al. / Journal of Biomechanics 33 (2000) 943-952
Capitolo 4:
FORZA MUSCOLARE
Aspetti geometrici:
4.1 - Punto di applicazione, direzione, verso
4.2 - Braccio della forza muscolare
4.3 - Angolo di trazione
Intensità e regolazione della forza muscolare:
4.4 - Curva lunghezza-tensione
4.5 - Curva forza-velocità
4.6 - Livello di attivazione
4.7 - Parametri dell’architettura del muscolo
4.8 - Momento della forza muscolare
Valutazione della forza muscolare:
4.9 - Elettromiografia
4.10 - Modelli biomeccanici
4.9 Elettromiografia
Elettromiografia di superficie
Scatola
interconnessione
Software
Elettrodi
Unità
centrale
Risultati dell’indagine elettromiografica
Valori sincronizzati nel tempo dell’attività elettrica dei principali muscoli agonisti, sinergici,
stabilizzatori, antagonisti.
4.10 Modelli biomeccanici
Estensione del ginocchio: muscoli agonisti
RF
Vas
vastus medialis (VasMed), vastus intermedius (VasInt), vastus lateralis (VasLat), rectus femoris (RF).
Estensione del ginocchio: muscoli antagonisti, …
GRA
TLF &
SAR
BFSH
BFLH
MEM
TEN
Gas
vastus medialis (VasMed), vastus intermedius (VasInt), vastus lateralis (VasLat), rectus femoris (RF), biceps femoris
long head (BFLH), biceps femoris short head (BFSH), semimembranosus (MEM), semitendinosus (TEN), medial
gastrocnemius (GasMed), lateral gastrocnemius (GasLat), and tensor fascia latae (TFL). Also included in the model
but not shown are sartorius (SAR) and gracilis (GRA).
Modello biomeccanico
The muscles of the leg is modeled by thirteen actuators (34):
vastus medialis (VasMed), vastus intermedius (VasInt), vastus
lateralis (VasLat), rectus femoris (RF), biceps femoris long head
(BFLH), biceps femoris short head (BFSH), semimembranosus
(MEM), semitendinosus (TEN), medial gastrocnemius
(GasMed), lateral gastrocnemius (GasLat), and tensor fascia
latae (TFL). Also included in the model but not shown are
sartorius (SAR) and gracilis (GRA).
Capitolo 5:
CARICHI ARTICOLARI
5.1 - Carico articolare: forze di contatto e tensione dei legamenti
5.2 - Determinazione del carico articolare
5.1 Carico articolare: forze di contatto e tensione dei legamenti
Il carico articolare è la risultante delle
•
Forze di contatto di compressione che si esplicano fra
segmenti anatomici adiacenti attraverso le superfici
articolari di contatto. Si oppongono alle sollecitazioni
di compressione
•
Forze attivate dalla tensione dei legamenti. Si
oppongono alle sollecitazioni di trazione e di
scorrimento.
Esempio:
Forze di contatto
tibiofemorali
Superficie di contatto
tibiofemorale
Forze di contatto (di
compressione)
tibiofemorali
Esempio
Legamenti che contribuiscono al carico articolare
dell’articolazione tibiofemorale
The ligaments of the tibiofemoral joint can be modeled by 14
elastic bundles: anterior (aACL) and posterior (pACL) bundles of
the anterior cruciate ligament; the anterior (aPCL) and posterior
(pPCL) bundles of the posterior cruciate ligament; the anterior
(aMCL), central (cMCL), and posterior (pMCL) bundles of the
superficial medial collateral ligament; the anterior (aCM) and
posterior (pCM) bundles of the deep medial collateral ligament;
the lateral collateral ligament (LCL); the popliteofibular ligament
(PFL); the anterolateral structures (ALS); and the medial (Mcap)
and lateral (Lcap) posteriorcapsule.
* Kevin B. Shelburne, Michael R. Torry, Marcus G. Pandy
Med. Sci. Sports Exerc., Vol. 37, No. 11, pp. 1948–1956, 2005.
5.2 Determinazione del carico articolare
Parametri noti:
•
Punto di applicazione:
Superfici articolari di contatto
Punti di inserzione dei legamenti
•
Verso
Dalla superficie articolare verso il segmento anatomico adiacente
Dall’inserzione del legamento verso l’origine
Incognite:
•
Intensità
•
Direzione
•
Misure in vivo mediante strain gauge impiantati
nell’articolazione
•
Modelli biomeccanici
Problema della dinamica diretta
“Note le forze attive (carichi esterni e forze muscolari),
ricavare il moto e le reazioni vincolari”
Noti:
•
•
•
Carichi esterni
Parametri anatomici: bracci a angoli di trazione delle forze
Intensità delle forze muscolari (misure elettromiografiche, modelli meccanici del muscolo)
Ricavare:
•
•
Cinematica: traiettorie, velocità ed accelerazioni angolari
Intensità, direzione dei carichi articolari
Problema della dinamica inversa
“Noto il moto del sistema ed alcune forze attive (carichi esterni),
ricavare le altre forze attive (forze muscolari) e le reazioni vincolari”
Noti:
•
•
•
Carichi esterni
Parametri anatomici: bracci a angoli di trazione delle forze muscolari
Cinematica: traiettorie, velocità ed accelerazioni angolari
Ricavare:
•
•
Intensità delle forze muscolari
Intensità, direzione dei carichi articolari
L’analisi cinematica nel problema della dinamica inversa
Risultati dell’analisi cinematica
Velocità angolari e accelerazioni angolari articolari in funzione dell’angolo articolare
Capitolo 6:
ASPETTI FUNZIONALI
6.1 - Ciclo allungamento-accorciamento
6.2 - Muscoli poliarticolari
6.3 - Co-contrazione
6.1 Stretch-shorten cycle
Definition:
A common pattern (scheme) of muscle activation in which an activated muscle first lengthens (is stretched) before it shortens.
Importance:
It occurs in most movements that we perform, for example:
− in the knee extension and ankle plantarflexor muscle after footstrike in runing
− in the knee extensor muscles during kicking
− In the trunk and arm muscles during throwing
− In the hip, knee, and ankle extensor muscles during the countermovement jump and long-jump takeoff.
Advantages:
1. It can enhance the positive work done by muscle during the shortening contraction.
2. It can lower the metabolic cost of performing a prescribed amount of positive work.
Mechanisms underlying the enhancement of performance with the stretch-shorten cycle:
− Time to develop force (1): increased time that the muscle has to become fully activated when there is an initial
lengthening contraction, and consequet increase in the muscle force at the beginning of the shortening contraction.
− Elastic energy (1,2): storage of elastic energy in tendon (and muscle connective tissue) during the lengthening contraction,
and subsequent use of this energy in the shortening contraction. This capability is greatest in muscles with long tendons.
− Force potentation (1): force from individual cross-bridges is enhanced as a consequence of the preceding stretch.
− Reflexes (1): the stretch reflex may be evoked by the forced lengthening of the muscle at the beginning of the stretchshorten cycle.
Open questions:
− Incomplete description of muscle function during the task: the change in whole-muscle (muscle fibers and tendon) length
do not necessary coincide with or parallel the change in length experienced by the muscle fibers.
− In slow eccentric contractions and in muscle with long tendons, the increase in the whole-muscle length may be
accomplished by a fiber shortening (and a greater tendon lengthening).
6.2 Two-joint muscles
Definition:
A muscle whose attachment sites span two joints.
Importance:
There are a significant number two joints muscles (biceps brachii, rectus femoris, gastrocnemius)
Advantages:
•
Two-joint muscle couple the motion at the two joints that they cross.
Thus, two-joint muscle may refine the coordination.
•
The shortening velocity of two-joint muscle may be less than that of its one-joint synergists.
Thus, the two-joint muscle are higher on the force-velocity relation compared with the one-joint muscle and hence are capable
of exerting a force that is a greater proportion of the isometric maximum within the joint ROM.
•
Two-joint muscle can redistribute muscle torque, joint power, and mechanical energy throughout a limb
Activation of one-joint muscles 1 and 3 produce extensor torque at knee and hip
Co-activation of two-joint muscle 5 results in a reduction in the net torque at the
hip but an increase in the net torque at the knee.
Thus, two-joint muscle 5 is described as redistributing some of the extensor torque
and power from the hip to the knee.
6.3 Co-activation
Definition:
Concurrent activation of the muscles around a joint, usually involving the agonist and antagonist muscles.
Importance:
It is frequently used in many different activities.
Advantages:
•
Increases the stiffness and hence the stability of a joint .
− lift heavy loads
− lift loads about which the lifters are uncertain
− learn novel tasks
•
Transfer of power from one joint to another
− coactivation at the hip joint can result in an increase of the torque at the knee joint: coactivation of a
single-joint hip extensor (e.g., gluteus maximus) and a two-joint hip flexor (e.g., rectus femoris) has the
net effect of increasing the extensor torque at the knee joint.
•
Perform a movement requiring a high degree of accuracy
− fine movements of the finger require complex patterns of co-activation.
•
Economize movements that involve changes in direction (e.g., extension to flexion).
− It is more economical to modulate the level of tonic activity in an agonist-antagonist set of muscle than
to alternately turn then on and off.
− Activation of the stretch-shorten cycle.
•
Protect the joint at extreme joint angles
Disvantages:
Reduction of the net muscle torque.
Capitolo 7:
APPLICAZIONI
7.1 - Strength training equipment (leg-extension modificato)
7.2 - Supporti per la riabilitazione del ginocchio in acqua
7.3 - Cardio equipment (cardio wave)
7.4 - Squat al multipower
7.1 Strength training equipment
Ottimizzazione della forza muscolare
Most selectorized equipments provide a fine
control and optimization of the muscular force,
through the entire range of motion (ROM), by
including a cam in their mechanics, and
selecting properly:
• the shape and the dimension of the cam,
• the spatial configuration of the cam around its
axis of rotation in a given reference working
position,
• the radius of the first re-directional pulley
(connected by the cable to the cam), the
position of this pulley with respect to the cam.
selected weight stack
first re-directional pulley
cable
knee
cam
hip
resistance rod
selected weight stack
q
resistance pad
shank

R
Progettazione del profilo della cam
Typically, the system is configured to reproduce the user’s strength curve, such that the greatest (least)
amount of resistance torque is felt at the user’s strongest (weakest) point in the ROM.
This kind of calibration may be obtained by replacing the weight stack with an isokinetic dynamometer and
modifying the geometrical parameters of the cam/pulley system until a constant torque is provided by the
dynamometer within the entire ROM during maximal effort trials.
first re-directional pulley
cable
knee
cam
Isokinetic
dynamometer
hip
resistance rod
q
resistance pad
shank

R
first re-directional pulley
cable
knee
cam
Isokinetic
dynamometer
hip
resistance rod
q
resistance pad
shank

R
Ottimizzazione dei carichi articolari
Unfortunately,
a general procedure
for the optimization
(minimization)
of the joint load
is lacking.
Progetto di ricerca
Calcolo delle componenti di (compressione, trazione e taglio) delle sollecitazioni articolari mediante modelli
biomeccanici.
Minimizzazione delle componenti delle sollecitazioni articolari.
Progetto meccanico per la realizzazione di attrezzature per il potenziamento o la riabilitazione che
minimizzano la sollecitazione articolare complessiva o la sollecitazione su specifiche strutture articolari.
open kinetic chain exercises
Leg extension
Leg extension equipment
Schema meccanico

FPT


Sistema = gamba + piede


F
Forza muscolare

angolo di trazione
q
angolo articolare

R Carico esterno

 Carico articolare
q

R
x
Determinazione della forza muscolare
La forza muscolare può essere determinata mediante la seconda equazione cardinale
I aq  FbF  RbR
Braccio della forza
muscolare (bPT)

F

1 
FF 
I a q  RbR
bF

Esercizi quasi-statici o isocinetici
FbF  RbR
Braccio del carico
esterno (bR)

R
bR  bF
bR
F
R
bF
 F  R
Determinazione del carico articolare
Nota la forza muscolare, il carico articolare può essere determinato mediante prima equazione cardinale
A

TF
  

maG  R  F  FT


 

TF  FT  R  F  maG

F
Esercizi quasi-statici o isocinetici


 
TF  FT  R  F
T
T
= componente di taglio
del carico articolare
A

R

R
= componente assiale
del carico articolare

TF

F
Componente di taglio della sollecitazione sull’ articolazione tibiofemorale
PCL stress
ACL stress
aR

R
aR

R

R
t  mS lGS q  mS g sin(q   GS )
sin(    GS ) 

dy 
d2y 2

I

I

a
m
q

a
m
q

a
m
g

m
gl
sin(
q


)

m
gl
sin(
q


)


M
C W
C W
C W
M
GM
GM
S
GS
GS 
 S
aPT
dq 
dq2


1

aR


dy 
d2y 2
I

a
m
q

a
m
q

a
m
g

m
gl
sin(
q


)


M
C
W
C
W
C
W
M
G
G

M
M 
dq 
dq2


PCL
stress
ACL
stress
90° flex
full ext.
90° flex
full ext.
Minimizzazione della componente di taglio della sollecitazione sull’ articolazione tibiofemorale
t  mS lGS q  mS g sin(q   GS )
sin(    GS ) 

dy 
d2y 2

q

a
m
g

m
gl
sin(
q


)

m
gl
sin(
q


)
q  aC mW
C
W
M
G
G
S
G
G
 I S  I M  aC mW
M
M
S
S 
aPT
dq 
dq2


1

aR


dy 
d2y 2
I

a
m
q

a
m
q

a
m
g

m
gl
sin(
q


)


C W
C W
C W
M
GM
GM 
 M
dq 
dq2


Calcolo del valore di aR per cui t = 0
aR

R
(a R ) OPT
dy 
d2y 2

q  aC mW g  mM glGM sin(q   GM )
 I M  aC mW
q  aC mW
dq 
dq 2


sin(    GS ) 

dy 
d2y 2
q  aC mW g  mM glGM sin(q   GM )  mS glGS sin(q   GS )  mS lGS q  mS g sin(q   GS )
q  aC mW
 I S  I M  aC mW
2
a PT
dq 
dq


Tensione del tendine rotuleo, ovvero, forza complessiva del quadricipite femorale
FPT
1

aPT


dy 
d2y 2
I

I

a
m
q

a
m
q

a
m
g

m
gl
sin(
q


)

m
gl
sin(
q


)


M
C W
C W
C W
M
GM
GM
S
GS
GS 
 S
dq 
dq2


E’ indipendente da aR
aR
E’possibile minimizzare il carico articolare
(spostamento del punto di applicazione della resistenza)
senza interferire con l’ottimizzazione della forza muscolare (progettazione del profilo della cam)

R
Componente assiale della sollecitazione sull’ articolazione tibiofemorale
n  mS lGS q 2  mS g cos(q  GS )
cos(   GS ) 

dy 
d2y 2

I

I

a
m
q

a
m
q

a
m
g

m
gl
sin(
q


)

m
gl
sin(
q


)

M
C W
C W
C W
M
GM
GM
S
GS
GS 
 S
aPT
dq 
dq2


E’ indipendente da aR
ed approssimativamente coincide
con la tensione del tendine rotuleo
aR

R
Compressione assiale esterna
Pad mobile e compressione assiale esterna
open kinetic chain exercises
Underwaer knee extension
Supporti per la riabilitazione del ginocchio in acqua

FPT
j
hip
j: traction angle
knee
Lx
Lz
z
z: flexion-extension axis
x: longitudinal
shank axis
q : joint angle
q
x
Conclusions
… In conclusion, this work highlights that aquatic exercises can
be safely and usefully utilized in the rehabilitation program
following ACL surgery. However, the shape, the dimensions, the
density, the surface roughness and the location of the resistive
device must be carefully selected, according to the indications
established in the present study.
closed kinetic chain exercises
Squat
Squat techniques
barbell
Barbell back squat
Barbell front squat
Barbell hack squat
dumbell
Dumbell squat
Dumbell front squat
Trap bar squat
cable
Cable squat
Cable squat (with belt)
Lever (plate loaded)
Lever front squat
Lever full squat
Lever (selectorized)
Lever squat
Lever V-squat
Lever hack squat
Lever V-squat
Weighted
weighted squat
weighted sissy squat
Body weight
Sissy squat
Sissy squat
on apparatus
weighted sissy squat
on apparatus
Smith
smith squat
smith front squat
Sled
sled squat
Sled hack squat
smith hack squat
smith wide squat
Squat guidelines
Squat is effective
Squatting is a fundamental exercise for strengthening the lower body and core muscles. It is an integral part of
training and conditioning programmes in sports and fitness, and is also commonly prescribed in knee
rehabilitation settings.
Squat is safe
There is a general agreement that correctly performed squats are safe exercises when executed with appropriate
load, adaptation, and supervision (see Escamilla, 2001, for a review). Injuries attributed to the squat may result
not from the exercise itself, but from improper technique, pre-existing structural abnormalities, fatigue or
excessive training. Nevertheless, injury may also occur if the knee or lower back experience greater forces and
torques than those to which they are accustomed.
Rules
1.
Place feet shoulder width apart
2.
Knees should point same direction as feet throughout movement
3.
Keep back straight
4.
Keep head facing forward
5.
Keep feet flat on floor (do not allow heels to raise off of platform);
6.
Keep equal distribution of weight through fore foot and heel (pushing with both heel and forefoot)
7.
Hip and ankle flexibility is important for both execution and safety in this movement.
Free barbell squat
Squat biomechanics have previously been analysed with particular focus on
•
•
•
muscle activity (Isear et al., 1997),
safety for knee structures (ligaments, menisci and cartilage) (Zheng et al., 1998),
different squat techniques (Escamilla et al., 2001a and 2001b; Gullet et al., 2008; Hattin et al., 1989)
according to the:
–
–
–
–
–
–
degree of knee flexion (semi-, half-, parallel-, and deep-squatting)
stance width (narrow/wide)
foot angle position (adduction/abduction, inversion/eversion)
external load type and positioning (bodyweight squat, dumbbell squat front/back barbell squat)
speed of execution (bodybuilding/dynamic squat)
external load intensity (typically expressed in % bodyweight)
In all these technique variations, the
possibility of modulating joint
torques, muscle activities and joint
reaction forces is limited by the
moment equilibrium condition: the
center of mass C of the system
constituted by the user’s body and
the weighted barbell should fall
between the forefoot and heel.
Wall squat and machine squat
This limitation is overcome when the back is supported by a wall (wall squat), and by a sliding or lever
machine (machine squat). These methods have been biomechanically analyzed by Blanpied (1999)
and, recently, by Escamilla and co-workers (2009). However, the trunk is constrained so that its
inclination during the exercise is fixed (wall squat and sliding-machine squat) or changes only
according to equipment mechanical design (lever-machine squat).
Smith squat
In the Smith squat, a barbell is constrained horizontally to move up and
down sliding along vertical steel tracks. The tracks’ reaction forces
compensate forward or backward imbalances of C determined, for example,
by backward or forward foot displacements, respectively. Moreover, as
opposed to the wall and machine squats, the trunk inclination can change
freely at each phase of the exercise.
Therefore, the Smith squat offers a wider range of exercise positions and,
concurrently, a wider range of possibilities for modulating the distributions
of muscle activity and joint loads.
If the latter is an opportunity or a limitation was not investigated, since
different elements interacting with each other should be taken into
account: external load, foot positions, degree of forward/backward trunk
tilt relative to the vertical, hip and knee angles.
In fact, even though a number of papers where the Smith squat was
utilized were previously published in relation to testing issues (Paulus et al.,
2008; Harris et al., 2007; Thomas et al., 2007; Cottermann et al., 2005) and
to analyze various training aspects (Harris et al., 2008; Minahan & Wood,
2008; Vingren et al., 2008; McGuigan et al., 2005 ), there are not, to our
knowledge, studies specifically designed to analyze joint torques and joint
loads (shear and compressive joint reaction forces) occurring during the
execution of this exercise.
Smith squat debate
In the fields of athletic training, fitness, and rehabilitation, a constant debate exists among those
arguing that the Smith machine exercise could be dangerous because the path is unnatural and the
machine prevents the body from determining its natural movement, and those who consider this
exercise even safer and more effective than the standard barbell squat (Griffing, 2010).
from: www.exrx.net
"First, there is no clinical evidence or research data whether published or not, of which I am aware
(which of course may simply mean I haven't come across it yet) that would lead one to conclude
(according to the accepted statistical methods for the treatment of data to establish a correlation or
causal relationship) that squats performed on a Smith-machine apparatus pose any inherent danger to
either the knees or the spine when performed correctly. If anyone can offer such evidence I would
greatly (and sincerely) appreciate him or her sharing it, or letting me know where I can acquire it.
Alternatively I would also be interested in discussing any Biomechanical models that he or she may have
used to arrive at this conclusion. Anecdotal accounts, opinion, and conjecture, regardless of the source
or the forum, do not constitute evidence.”
Despite this on-going debate, the Smith squat is extensively used for different purposes:
•
to familiarize beginners with the squat movement,
•
to periodically change the routine and increase the lifted load in experienced-user programmes,
•
to accommodate individuals that may feel pain on the barbell squat,
•
and, finally, as a safer modality of closed kinetic-chain exercise for knee rehabilitation.
The biomechanical model
Barbell -multipower force
( RS ) x 
( xGR  xC ) Mg
2 yW
Hip and knee torques
 hip  ( yW  yhip )2( RS ) x  ( xCWUB  xhip )(M UB  M W ) g
 knee   yknee ( AGR ) x  ( xknee  xGR ) N GR  ( xknee  xCLF )mLF g
Patellar tendon force (quadriceps force)
FPT 

1
 yknee ( AGR ) x  ( xknee  xGR ) N GR  ( xknee  xCLF )mLF g
a PT

Shear and compressive tibiofemoral force
t  FPT sin  PT  NGR cos(qankle )  ( AGR ) x sin(qankle )  mLF g cos(qankle )
n  FPT cos  PT  NGR sin(qankle )  ( AGR ) x cos(qankle )  mLF g sin(qankle )
N GR 
Mg
2
( AGR ) x  
( xGR  xC ) Mg
2 yW
Ground reaction force
Conclusions
Conclusion 1:
•
•
•
•
knee torque,
patellar tendon force,
the axial tibiofemoral compression,
and the patello-femoral force
increase with decreasing
•
•
•
•
the knee angle,
the trunk ankle,
the ankle angle,
and displacing the weight distribution
towards the heel.
Conclusion 2:
•
•
Hip torque
and the spine torque occurring
at the lumbosacral joint
increase with decreasing
•
the knee angle
and with increasing
•
•
•
the trunk ankle,
the ankle angle,
and displacing the weight
distribution towards the heel.
Conclusion 3:
•
the ACL and PCL load may be suppressed
in the range of knee angkes between 180° and 130°
by selecting, for each value of the knee angle,
one or more specific pairs of ankle and trunk angles;
Conclusion 4:
•
the ACL loading can be definitely eliminated
by squatting with increased forward trunk tilt
and by displacing the weight distribution towards the forefoot;
Conclusion 5:
•
•
•
the PCL loading decreases in the range 180 ≥ qknee ≥ 150° with decreasing the knee
angle, the trunk ankle, the ankle angle.
the PCL loading decreases in the range qknee < 130° with increasing the knee angle, the
trunk ankle, the ankle angle.
In the range 150 ≥ qknee ≥ 130° , the behavior changes depending on the weight
distribution
180 ≥ qknee ≥ 150°
qknee < 130°
Conclusion 6:
•
•
the increase of knee torque and hip torque with the resistance Mw markedly deviates
from linearity,
while the ratios of axial and shear component of the tibiofemoral force to Mg are
nearly insensitive to Mw.
Conclusion 7:
in a typical use of the Smith machine, the trunk and the lower-legs are maintained nearly vertical.
Intuitively, a spine in line with gravity and knees in vertical with feet is commonly believed to minimize
the knee and back loadings. However, this estimation neglects the effects of the external forces which
characterize the Smith squat exercise.
In fact, compared to the free barbell squat at
the same knee angle, this body configuration
entails:
•
nearly the same levels of knee torque
and compressive tibiofemoral load;
•
a weak increase of ACL-loading shear
tibiofemoral load;
•
a weak decrease of PCL-loading shear
tibiofemoral load;
•
an increase of hip and lumbosacral
torques, that become remarkable at
higher knee flexion angles.
Understanding the Smith squat
Safe issue #1
The shear tibiofemoral force can be minimized, together
with the compressive tibiofemoral joint load and the
overall knee torque, by bending the trunk forward and
moving the feet forward in front of the knees.
However, this condition maximizes the hip and back
torque. Although this can be useful for strengthening hip
and back extensors with knee safety, it also results in
enhanced vertebral joint loads.
Moreover, when exasperated, this configuration entails
considerably high hip flexion angles, compared to the free
squat at equal knee angles. In that case, the lumbar spine
may dangerously compensate by flexing more than usual
under loading, especially in the presence of hamstring
inflexibility when knees are nearly straight, and in the
presence of gluteus maximus or adductor magnus
inflexibility when knees are bent.
Therefore, suitable flexibility assessments of hip extensors
must be executed before this specific kind of Smith squat is
performed.
Safe issue #2
Conversely, decreasing the forward trunk inclination and
moving the feet backward behind the knee shifts the joint
torque from the hip to the knee muscles preserving the
back joints, but strongly increases the compressive
tibiofemoral joint load, and the patellofemoral joint load
as well. Indeed, the patellofemoral force is known to
increase with quadriceps force and knee flexion angle.
Moreover, when exasperated, this configuration involves a
full hip extension and even the possibility of involuntary
hip hyper-extensions. Thus, in the presence of hip flexor
inflexibility and/or abdominal weakness the lower back
may dangerously hyperextend more than usual under
loading.
Suitable preventive assessments of abdominal strength
and hip flexors flexibility are necessary prior to
undertaking these exercises.
Summary
•
In the Smith squat, the value of the joint angles may be changed independently of the other,
and the weight distribution may bee freely displaced between the forefoot and the hell.
•
The muscle activity and joint load distributions may be widely and usefully modulated according
to the individual’s needs and demands.
•
Some extreme body configurations allowed by the Smith machine may be dangerous for lower
back and knees, especially in the presence of hip flexor/extensor inflexibilities and abdominal
weakness.
•
In the absence of previous flexibility and strength assessments, only reasonably small changes
from the regular barbell squat patterns are advisable in order to attain the intended goal with
the Smith squat exercise.
Reviewers’ comments
Reviewer: 1
Comments to the Author
This is an interesting and well written manuscript. Standard biomechanical analysis equations have been used to
characterize joint loadings in a spectrum of body configurations only possible with the Smith machine. The
impact has now been quantified and will be useful as a reference for future research. This is excellent work that
deserves to be published.
Reviewer: 1
Comments to the Author
This is a very interesting and useful study that used a biomechanical analysis of the joint moments and forces to
determine the differences between the Smith machine squat and the free barbell squat and the loading of the
structures in the knee. Overall this is an excellent and high quality study that advances knowledge and makes an
important contribution in the area.
Conclusioni Generali
I modelli biomeccanici consentono
•
di valutare in modo non invasivo i momenti articolari, le forze di reazione articolari di compressione e di
taglio, durante esercizi statici o dinamici in presenza di carichi esterni.
•
di progettare nuove attrezzature per il potenziamento muscolare o la riabilitazione che simultaneamente
ottimizzano la forza muscolare e minimizzano i carichi articolari.
7.3 Cardiovascular equipments
Studi su
• Ergonomia
• Attivazioni muscolari
• Controllo e riduzione dei carichi articolari
Cardio wave presentation