85

Journal of Applied Biomechanics, 2013, 29, 85-97 © 2013 Human Kinetics, Inc.

Andrea Biscarini (Corresponding Author) is with the Department of Surgical, Radiological and Odontostomatologic Sciences, Medical Physics Section, University of Perugia, and with the LAMS Laboratory, University of Perugia, Perugia, Italy. Fabio M. Botti is with the LAMS Laboratory, University of Perugia, and with the Department of Internal Medicine, Human Physi-ology Section, University of Perugia, Perugia, Italy. Vito E. Pettorossi is with the Department of Internal Medicine, Human Physiology Section, University of Perugia, Perugia, Italy.

Joint Torques and Joint Reaction Forces During Squatting With a Forward or Backward Inclined Smith Machine

Andrea Biscarini, Fabio M. Botti, and Vito E. PettorossiUniversity of Perugia

We developed a biomechanical model to determine the joint torques and loadings during squatting with a backward/forward-inclined Smith machine. The Smith squat allows a large variety of body positioning (trunk tilt, foot placement, combinations of joint angles) and easy control of weight distribution between forefoot and heel. These distinctive aspects of the exercise can be managed concurrently with the equipment inclina-tion selected to unload specific joint structures while activating specific muscle groups. A backward (forward) equipment inclination decreases (increases) knee torque, and compressive tibiofemoral and patellofemoral forces, while enhances (depresses) hip and lumbosacral torques. For small knee flexion angles, the strain-force on the posterior cruciate ligament increases (decreases) with a backward (forward) equipment inclination, whereas for large knee flexion angles, this behavior is reversed. In the 0 to 60 degree range of knee flexion angles, loads on both cruciate ligaments may be simultaneously suppressed by a 30 degree backward equip-ment inclination and selecting, for each value of the knee angle, specific pairs of ankle and hip angles. The anterior cruciate ligament is safely maintained unloaded by squatting with backward equipment inclination and uniform/forward foot weight distribution. The conditions for the development of anterior cruciate liga-ment strain forces are clearly explained.

Keywords: Smith squat, joint load, cruciate ligaments, line of gravity

Squatting, a fundamental strengthening exercise, is an integral part of many training programs in sports and fitness, and is commonly prescribed in rehabilitative inter-ventions. Squat biomechanics have been the subject of extensive research studies with particular focus on muscle activity and safety for knee structures.1–12 A variety of different squat techniques and equipment has been devel-oped over the years to comply with the postural, joint, and muscular needs and demands of individual people and special populations. These squat variants are primarily characterized by different modalities of administration of the resistance load, which is represented by body weight, and by the gravitational overload directly provided by weighted barbells, dumbbells, and belts, or transmitted to the body by lever and/or cable/pulley systems. The resistance load system, together with the instantaneous values of the kinematical parameters, determines muscle

forces, and the joint reaction forces resulting from bony contact forces and ligament tensions. Knowledge and control of muscular and joint forces occurring during exercises is of fundamental importance in the design of suitable rehabilitation and conditioning programs, as well as for injury prevention.13,14

Different equipment imposes specific degrees of mechanical constraint to the squat exercise. For example, in the free barbell squat, the center of mass (C) of the system consisting of the user’s body and the weighted barbell should fall between forefoot and heel, and conse-quently hip, knee, and ankle joint angles take “in-phase” values which, within small inter-subject variability ranges, are tightly related to each other. Thus, each phase of the exercise is characterized by a well-defined joint torque distribution, i.e., by specific ratios of the torques at different joints.

The Smith machine (Technogym, Cesena, Italy) is a popular piece of equipment used in weight training and particularly in squat exercises (Smith squat). It consists of a barbell constrained to move up and down sliding along rectilinear steel tracks (Figure 1). In the Smith squat, the tracks’ reaction forces (

RS in Figure 1) acting on the

barbell compensate forward or backward imbalances of C determined by backward or forward foot displacements or trunk tilts. Therefore, the value of the joint angles may be changed independently of the other, enabling a wider range of exercise positions and, concurrently, a wider

An Official Journal of ISBwww.JAB-Journal.comORIGINAL RESEARCH

86 Biscarini, Botti, and Pettorossi

range of possibilities for modulating the distributions of muscle activity and joint loads.

In contrast to the free barbell squat, little attention has been devoted in the literature to understand the spe-cific biomechanical properties of the Smith squat, despite its great popularity and its extensive use for different purposes. For long time the safety and effectiveness of the Smith squat has only been the subject of a continuous and heated debate in the fields of athletic training, fitness, and rehabilitation.15 Only in very recent times, Biscarini et al16 developed a specific biomechanical model for this exercise and derived the knee, hip, and lumbosacral joint torques, the shear and compressive components of the tibiofemoral joint loads, and the patellofemoral force, as a function of external load, foot positioning, trunk tilt, and body configuration, for all the combinations of hip, knee, and ankle joint angles allowed by the Smith machine. It was clearly highlighted that, compared to the free barbell squat, the Smith squat may be largely patterned to modu-late the distribution of muscle activities and minimize the mechanical load on specific joint structures.

Muscle activity and joint load distribution may be further modulated as the equipment’s tracks are inclined by an angle α with respect to the vertical, by an equal α rigid rotation of the Smith machine and its ground platform (Figure 1). This is equivalent to a reverse α rotation of the line of gravity with respect to the machine. The different body positioning (backward/forward trunk tilt, foot placement, and ankle, knee, and kip angles) and equipment inclinations can be managed concurrently to get specific biomechanical outcomes.

Joint torques and forces in Smith squat have previ-ously been assessed only for a vertical orientation (α = 0) of equipment tracks.16 The aim of this paper is to gain full understanding of the equipment potential by extending the calculations to squat exercises performed in a back-ward or forward inclined Smith machine (with different degrees of inclination α). The final goal is to define the most favorable combinations of equipment inclination and body positioning to unload specific joint structures while focusing the activation on selected muscle groups. The possible applications in training and rehabilitation are discussed with particular focus on the control of the strain-forces on cruciate ligaments and lumbosacral joint. Finally, we will address the postural implications associ-ated with the forward/backward equipment inclination.

Methods

The human body is modeled by 14 linked rigid segments (head, trunk, upper arms, forearms, hands, thighs, shanks and feet), whose relevant biomechanical parameters (weight, dimensions, center of mass, and moments of inertia) have been deduced from extensive anthropometric studies.17–20 The weighted barbell, placed on the user’s shoulder, may only slide along the rectilinear tracks of the Smith machine (Figure 1). The direction of the tracks (y-axis) may be inclined by an angle α with respect to the vertical, by an equal α rigid rotation of the Smith machine and its ground platform (x-axis), that is assumed to be integral with the machine (Figure 2). The joint angles θankle, θknee, and θhip, take a value of 0° when, due to an ideal full flexion, the corresponding bony segments overlap each other. The angle θtrunk defines the trunk tilt with respect to the tracks.

The external forces acting on the system (WB) con-stituted by the user’s body (B) and the weighted barbell (W) are equivalent to the following vectors (Figure 1):

• TheweightMg of the system, applied in the center

of mass C = (xC, yC) of the system (M is the sum of the mass MW of the weighted barbell and the mass MB of the user’s body).

• The two equal and frictionless (x-axis oriented) reaction forces

RS exerted by equipment’s tracks on

the barbell, and applied at the two contact points (0, yW) between the barbell and the tracks.

• The shear (parallel to the ground platform) andnormal (to the ground platform) ground reaction

Figure 1 – Sketch of the fundamental elements of the Smith squat exercise: the barbell, constrained to two rectilinear tracks, may only move along a line (y-axis). The external forces acting on the system constituted by the user and the weighted barbell are reported in the figure.

Backward/Forward Inclined Smith Squat 87

forces AGR and

NGR , acting symmetrically on each foot, and applied at a point (xGR, 0) within the contact surface

between each foot and the ground.

The location of the application point of the ground reaction forces depends upon the user-controlled weight distri-bution between forefoot and heel, and can be instantly determined during the exercise with the use of a force platform.

In a quasi-static Smith squat exercise, the external forces are subjected to the equilibrium condition

2NGR + 2

AGR + 2

RS +M

g = 0 (1)

Projection of this equation onto the y and x axes gives

2NGR −Mgcosa = 0

2(RS )x + 2(AGR)x −Mgsina = 0⎧⎨⎩

(2)

(3)

where NGR and Mg are the magnitudes of NGR and M

g, while (AGR)x and (RS)x are the scalar x-components of

AGR and

RS, respectively. The equilibrium condition for the axial moments of the external forces takes a simple form when the moments are calculated in respect to the axis crossing the (xGR, 0) point and normal to the xy plane:

2yW (RS )x − yCMgsina − (xGR − xC )Mgcosa = 0 (4)

Equations (2–4) determine the reaction forces of the ground and the equipment tracks:

NGR =Mgcosa

2 (5)

(RS )x =yCMgsina + (xGR − xC )Mgcosa

2yW (6)

(AGR)x =Mgsina

2− yCMgsina + (xGR − xC )Mgcosa

2yW (7)

With the knowledge of such reaction forces, one can calculate a specific joint torque (the torque provided by the muscles crossing the joint and by the passive joint reaction forces due to ligament tensions and bone-to-bone contacts) from the moment equilibrium equation applied to an appropriately selected mechanical subsystem delimited by that

Figure 2 – The barbell rectilinear trajectory (y-axis) may be inclined by an angle α with respect to the vertical, by an equal α rigid rotation of the Smith machine and its ground platform (x-axis), that is assumed to be integral with the machine. Positive (negative) values of θtrunk correspond to a forward (backward) trunk tilt compared to the equipment tracks (y-axis); positive (negative) values of α correspond to a backward (forward) equipment inclination.

88 Biscarini, Botti, and Pettorossi

joint. For example, the hip torque τhip is derived from the equilibrium moment equation for the system (WUB) consti-tuted by the upper body UB (trunk, head, and upper limbs) and the weighted barbell W:

2t hip = (yW − yhip)2(RS )x + (xCWUB − xhip)(MUB +MW )gcosa − (yCWUB − yhip)(MUB +MW )gsina (8)

Here, MUB is the UB mass, and CWUB is the WUB center of mass. The torque τLS on the lumbosacral joint is directly obtained by the right-hand-side of Equation (8), by simply replacing the whole trunk with the portion of the trunk above the lumbosacral joint, and the hip coordinates with the lumbosacral joint coordinates. As these joints are very close to each other, it is approximately τLS ≈ 2τhip. The knee torque τknee is deduced from the same equilibrium equation for the lower leg and foot system (LF)

t knee = −yknee (AGR)x + (xknee − xGR)NGR − (xknee − xCLF )mLFgcosa + (yknee − yCLF )mLFgsina (9)

where mLF is the LF mass, and CLF is the LF center of mass.The determination of a joint reaction force (the force due to ligament tensions and bone-to-bone contacts) requires

the selective knowledge of the force for each muscle crossing that joint. Unfortunately, in general, this information cannot be deduced from the knowledge of the joint torque, without the use of arbitrary optimization procedures.21 However, if the torque of the knee flexor muscles is negligible compared to the knee extensor torque provided by the quadriceps, then the patellar tendon force FPT can be given as the ratio of τknee to the patellar tendon moment arm aPT:

FPT ≅t knee

aPT (10)

With this approximation, the tibiofemoral joint reaction force

f is obtained analytically from the equilibrium condition for the external forces acting on the LF system

f +FPT +

AGR +

NGR +mLF

g = 0 (11)

Projection of this equation on the longitudinal shank axis, and on a normal to this axis, gives the compressive (ϕn) and shear (ϕt) components of

f, respectively:22,23

ft = −FPT singPT + NGR cos(uankle )− (AGR)x sin(uankle )−mLFgcos(a +uankle ) (12)

fn = −FPT cosgPT − NGR sin(uankle )− (AGR)x cos(uankle )+mLFgsin(a +uankle ) (13)

In Equations (12) and (13), γPT is the patellar-tendon traction angle, that is the θknee-dependent angle of the vector

FPT and the longitudinal shank axis. In this study,

the well-known Herzog and Read24 polynomial functions are adopted for aPT(θknee) and γPT(θknee).

It is commonly known that the patello-femoral compressive force ϕPF increases with patellar-tendon force and degree of knee flexion.25 Thus, within the approximation of Equation (10), for any given value of θknee (that sets the value of aPT), ϕPF is only determined by the knee torque τknee, and comes to be a monotonic increasing function of τknee.

In the following, we will direct our attention to the dependence of τhip, τLS, τknee, ϕt, ϕn, and ϕPF on the inclination angle α of the Smith machine, for all the different body configurations corresponding to the fol - lowing ranges of joint angles: 60° ≤ θankle ≤ 100°, 90° ≤ θknee ≤ 180°, – 10° ≤ θtrunk ≤ 30°, and 70° ≤ θhip ≤ 180° (θhip = 90° + θknee – θankle – θtrunk); and for different locations of the application point of the ground reaction force: just below the ankle joint (xGR = xankle), and midway between the heel and the toe tip (xGR = xankle + 0.07m). For comparison, the same joint torques and forces are also reported for a typical free barbell squat exercise (α = 0, AGR = RS = 0 and xC = xGR). Maple software

package (Maplesoft, Waterloo, Canada) was used for the calculation.

ResultsThe joint torques τknee and τhip (and τLS) and the joint reaction forces ϕt and ϕn can be accurately controlled by selecting an appropriate overload resistance MW, and by changing both the equipment inclination α, and the parameters θankle, θknee, θtrunk, and xGR that define the body configuration within the Smith machine (Figures 3 to 8). The ratios of the quantities τknee, τhip, FPT, ϕt, and ϕn, to the total resistance Mg, turn out to be nearly insensitive to the overload resistance MWg. For this reason, only the condition MW = MB has been considered (Figures 3 to 8), and the forces ϕt and ϕn have been normalized to Mg (Figures 4 to 8). In fact, a change in the ratio MW/MB slightly influences the location of the centers of mass C and CWUB, and, consequently, slightly changes the lever arms, about the joint axes, of the weight forces acting on WB and WUB systems.

For a given value of knee angle θknee, |ϕn| decreases and torque shifts from the knee to the hip joint, by increas-ing the backward equipment inclination or by reducing its forward inclination (increasing α), bending the trunk

Backward/Forward Inclined Smith Squat 89

forward (increasing θtrunk), moving the foot forward with respect to the knee (increasing θankle), and displacing the weight distribution towards the forefoot (increasing xGR), and vice versa (Figures 3, 4, 7, and 8). The torques τknee and τhip, and the intensity |ϕn| of the compressive tibio-femoral force, increase almost linearly when the knee flexion angle is increased (θknee is decreased) keeping constant the other parameters (Figures 3 and 4). Negative knee (hip) torques occurring for high (low) values θtrunk

Figure 3 – Dependence of the knee and hip torques (τknee and τhip) on the trunk inclination (–10° ≤ θtrunk ≤ 30°), for different values of knee angle (θknee = 150, 120, 90°), ankle angle (θankle = 100, 90, 80, 70, 60°), and equipment inclination (α = –30° and 30°) under the conditions MW = MB and xGR = xankle (application point of the ground reaction located under the medial malleolus). Data are displayed only in the range 70° ≤ θhip ≤ 180° (θhip = 90° + θknee – θankle – θtrunk), and the circle points represent typical knee and hip torques for the free barbell squat.

indicate a knee (hip) flexor torque to be provided by the knee (hip) flexors. Notably, with changing the equipment inclination α from –30° to 30°, the peak values of τknee and |ϕn|/Mg (obtained for θknee = 90°, θankle = 60°, θtrunk = –10°, xGR = xankle) reduce from 200 N·m to 150 N·m (Figure 3) and from 3.3 to 2.65 (Figure 4) respectively, whereas the peak value of τhip (obtained for θknee = 120°, θankle = 100°, θtrunk = 30°, xGR = xankle + 0.07m) rises from 175 N·m to 225 N·m (Figure 7).

90 Biscarini, Botti, and Pettorossi

The shear component ϕt of the tibiofemoral joint reaction force displays a non-monotonic dependence on θknee (Figures 5 and 6) and can be largely patterned by changing the equipment inclination α. ϕt determines to a great extent the strain-forces on cruciate ligaments. For example, Butler et al26 highlighted that the anterior cruciate ligament, ACL, (posterior cruciate ligament, PCL) provides 86% (95%) of the total restraining force

to anterior (posterior) drawer in non-weight-bearing cadaveric knees. We conventionally assume that a positive (negative) shear force ϕt opposes the posterior (anterior) translation of the tibial plateau with respect to the femur, reflecting a load on the PCL (ACL). Both ACL and PCL can be stressed appreciably in the range 180° ≥ θknee ≥ 130°, whereas only PCL stress occurs for θknee < 130°. Nevertheless, the ACL stress is completely suppressed

Figure 4 – Dependence of the axial component ϕn of tibiofemoral joint reaction force (normalized to the overall resistance Mg) on the trunk inclination (–10° ≤ θtrunk ≤ 30°), for different values of knee angle (θknee = 150, 120, 90°), ankle angle (θankle = 100, 90, 80, 70, 60°), and equipment inclination (α = –30° and 30°), under the conditions MW = MB and xGR = xankle (application point of the ground reaction located under the medial malleolus). Data are displayed only in the range 70° ≤ θhip ≤ 180° (θhip = 90° + θknee – θankle – θtrunk), and the circle points represent typical ϕn values for the free barbell squat.

91

Fig

ure

5 –

Dep

ende

nce

of th

e sh

ear

com

pone

nt ϕ

t of

tibio

fem

oral

join

t rea

ctio

n fo

rce

(nor

mal

ized

to th

e ov

eral

l res

ista

nce

Mg)

on

the

trun

k in

clin

atio

n (–

10° ≤ θ t

runk

≤ 3

0°),

for

di

ffer

ent v

alue

s of

kne

e an

gle

(θkn

ee =

170

, 160

, . .

. , 9

0°),

and

ank

le a

ngle

(θ a

nkle =

100

, 90,

80,

70,

60°

), a

nd f

or a

bac

kwar

d eq

uipm

ent i

nclin

atio

n (α

= 3

0°),

und

er th

e co

nditi

ons

MW

= M

B a

nd

x GR =

xan

kle

(app

licat

ion

poin

t of

the

gro

und

reac

tion

loca

ted

unde

r th

e m

edia

l m

alle

olus

). P

ositi

ve (

nega

tive)

she

ar f

orce

s ϕ t

cor

resp

ond

to l

oads

on

the

post

erio

r (a

nter

ior)

cru

ciat

e lig

amen

t, an

d th

e ci

rcle

poi

nts

repr

esen

t typ

ical

ϕt v

alue

s fo

r th

e fr

ee b

arbe

ll sq

uat.

92

Fig

ure

6 –

Dep

ende

nce

of th

e sh

ear

com

pone

nt ϕ

t of

tibio

fem

oral

join

t rea

ctio

n fo

rce

(nor

mal

ized

to th

e ov

eral

l res

ista

nce

Mg)

on

the

trun

k in

clin

atio

n (–

10° ≤ θ t

runk

≤ 3

0°),

for

dif

-fe

rent

val

ues

of k

nee

angl

e (θ

knee

= 1

70, 1

60, .

. . ,

90°

) an

d an

kle

angl

e (θ

ankl

e = 1

00, 9

0, 8

0, 7

0, 6

0°),

and

for

a f

orw

ard

equi

pmen

t inc

linat

ion

(α =

–30

°),

unde

r th

e co

nditi

ons

MW

=

MB a

nd x

GR =

xan

kle (

appl

icat

ion

poin

t of

the

grou

nd r

eact

ion

loca

ted

unde

r th

e m

edia

l mal

leol

us).

Pos

itive

(ne

gativ

e) s

hear

for

ces ϕ t

cor

resp

ond

to lo

ads

on th

e po

ster

ior

(ant

erio

r)

cruc

iate

liga

men

t, an

d th

e ci

rcle

poi

nts

repr

esen

t typ

ical

ϕt v

alue

s fo

r th

e fr

ee b

arbe

ll sq

uat.

Backward/Forward Inclined Smith Squat 93

on the whole knee ROM, independently of the values of θankle and θtrunk, by squatting with 30° backward equip-ment inclination, and displacing the center of foot weight distribution in forward direction (Figure 7), at least up to midway between the heel and the toe tip (xGR = xankle + 0.07m). This last condition is obtained with a uniform weight distribution between forefoot and heel, as com-monly suggested in free barbell squat guidelines. The strain-force on ACL is maximum for α = –30°, θknee = 160°, and xGR = xankle, where ϕt takes its minimum value given by –0.12·Mg (Figure 6), and equivalent to –176 N assuming MW = MB = 75 kg. The magnitude of this value is considerably smaller than the ultimate tensile load 1725–2160 N of young human ACLs.27,28 The strain-force on PCL always increases with decreasing xGR and α. For θknee ≤ 130° it is also a decreasing function of θknee, θtrunk, and θankle, whereas for 180° ≥ θknee ≥ 150°, it reverses this behavior and becomes an increasing function of these three parameters. The transition between these regions with opposite behaviors occurs in the range 150° > θknee > 130°.

Ultimately, the peak values of both ACL and PCL strain-forces are minimized (maximized) with backward (forward) inclined equipment (Figures 5, 6, 7, and 8). A backward equipment inclination (α = 30°), combined with a forward foot weight distribution (xGR = xankle + 0.07m), not only suppresses the ACL force, but also minimizes the peak PCL force (Figure 7). On the other hand, combining a backward equipment inclination (α = 30°) with a backward foot weight distribution (xGR = xankle), and selecting appropriate values of θankle and θtrunk, one can maintain ϕt exquisitely small for θknee ≥ 120°, thus obtaining, at the same time, negligible ACL and PCL strain-forces in this range (Figure 5).

DiscussionIn quasi-static free barbell squat, the knee, hip, and ankle angles are closely related one another, and the torque is nearly equally shared between the knee and the hip (symbols • and � in Figure 3). Conversely, in the Smith squat, each joint angle may be changed independently of the other, enabling a free modulation of the torque distri-bution among the joints: the torque may be intentionally lowered at the knee and enhanced at the hip and back, or vice versa, in comparison with the free barbell squat.16 A forward or backward inclination of the Smith machine greatly extends the range of possibilities for modulating the torque distribution among the joints. For example, with a forward (backward) equipment inclination and a backward (forward) foot weight distribution, the hip (knee) torque may be maintained exquisitely small in the whole range 180° ≥ θknee ≥ 90°, selecting suitable values of the ankle and trunk angles. Furthermore, a change in equipment inclination α from –30° to 30° (from 30° to –30°) gives a 33% increment (25% decrease) in hip peak torque and a 25% decrease (33% increment) in knee peak torque, when xGR = xankle and θankle, θknee, and θtrunk span the selected ranges (Figure 3).

The equipment inclination can also be effectively managed to minimize the force on specific joint struc-tures. For example, with a 30° backward equipment inclination, the shear component ϕt of the tibiofemoral joint reaction force may be suppressed in the range 180° ≥ θknee ≥ 120° by selecting, for each value of θknee, one or more specific pairs of ankle and trunk angles (Figure 5). This compares favorably with the standard vertical Smith squat, where the corresponding range is 180° ≥ θknee ≥ 130°,16 and also with open kinetic-chain leg extension exercises, where the condition ϕt = 0 can be achieved only for 180° ≥ θknee ≥ 140° by a controlled displacement of the application point of the resistance along the shank during the exercise.29

The conditions for the development of ACL strain-force in squat exercises is a subject of paramount impor-tance in sport rehabilitation. A great amount of data has been collected over the years, with the use of different techniques, spanning from theoretical modeling to the surgical implants of strain gauges on the ACL. However, on the whole, these research activities give contrasting results, and a clear understanding of the problem is still lacking. In fact, negligible ACL forces were reported in several studies,1,5,7,9,10,30,31 whereas forces with widely variable intensities were reported in the range 180° ≥ θknee ≥ 120° in a comparable number of studies.2,3,13,32–36 We recently highlighted that, for the Smith squat exercise, these differences can be accounted for in terms of differ-ences in θankle, θtrunk, and xGR, and, most importantly, that the ACL loading can be nearly completely eliminated by squatting with increased forward trunk tilt and by dis-placing the weight distribution toward the forefoot.16 The present results indicate that a backward equipment incli-nation (α = 30°) further protects the ACL, and definitely eliminates the ACL strain-force, when associated with a forward foot weight distribution (xGR = xankle + 0.07m), independently of trunk tilt and foot positioning (Figure 7).

It was previously recognized that some extreme body configurations allowed by the Smith machine may be dangerous for lower back and knees.16 The equipment inclination may even worsen these critical situations. For example, one might strengthen hip and back extensors with knee safety by squatting with backward inclined equipment, bending the trunk forward and moving the feet forward in front of the knees. However, this body configuration entails considerably high hip flexion angles, and the backward inclination of the equipment, due to the action of gravity, tends to further enhance the hip flexion. In this condition, the lumbar spine may dangerously compensate by flexing more than usual under loading, especially in the presence of inflexibility of hamstrings (when knees are nearly straight), gluteus maximus and adductor magnus (when knees are bent). Likewise, squat-ting with a forward inclined equipment, backward trunk tilt, and feet backward behind the knees, preserves the back joints and maximizes both the quadriceps involve-ment and the peak force on the knee joint structures. However, this body positioning induces a full hip exten-sion, and the forward equipment inclination, due to the

94

Fig

ure

7 –

Dep

ende

nce

of k

nee

and

hip

torq

ues

(τkn

ee a

nd τ

hip)

, and

of a

xial

and

she

ar (ϕ

n and

ϕt)

com

pone

nts

of ti

biof

emor

al jo

int r

eact

ion

forc

e (n

orm

aliz

ed to

the

over

all r

esis

tanc

e M

g), o

n th

e tr

unk

incl

inat

ion

(–10

° ≤ θ t

runk

≤ 3

0°),

for

dif

fere

nt v

alue

s of

kne

e an

gle

(θkn

ee =

150

, 120

, 90°

) an

d an

kle

angl

e (θ

ankl

e = 1

00, 9

0, 8

0, 7

0, 6

0°),

and

for

a b

ackw

ard

equi

p-m

ent i

nclin

atio

n (α

= 3

0°),

und

er th

e co

nditi

ons

MW

= M

B a

nd x

GR =

xan

kle +

0.0

7m (

appl

icat

ion

poin

t of

the

grou

nd r

eact

ion

loca

ted

mid

way

bet

wee

n th

e he

el a

nd th

e to

e tip

). D

ata

are

disp

laye

d on

ly in

the

rang

e 70

° ≤ θ h

ip ≤

180

° (θ

hip

= 9

0° +

θkn

ee –

θan

kle –

θtr

unk)

and

the

circ

le p

oint

s re

pres

ent t

ypic

al v

alue

s fo

r th

e fr

ee b

arbe

ll sq

uat.

95

Fig

ure

8 –

Dep

ende

nce

of k

nee

and

hip

torq

ues

(τkn

ee a

nd τ

hip)

, and

of a

xial

and

she

ar (ϕ

n and

ϕt)

com

pone

nts

of ti

biof

emor

al jo

int r

eact

ion

forc

e (n

orm

aliz

ed to

the

over

all r

esis

tanc

e M

g), o

n th

e tr

unk

incl

inat

ion

(–10

° ≤ θ t

runk

≤ 3

0°),

for d

iffe

rent

val

ues

of k

nee

angl

e (θ

knee

= 1

50, 1

20, 9

0°) a

nd a

nkle

ang

le (θ

ankl

e = 1

00, 9

0, 8

0, 7

0, 6

0°),

and

for a

forw

ard

equi

pmen

t in

clin

atio

n (α

= –

30°)

, und

er th

e co

nditi

ons

MW

= M

B a

nd x

GR =

xan

kle

+ 0

.07m

(ap

plic

atio

n po

int o

f th

e gr

ound

rea

ctio

n lo

cate

d m

idw

ay b

etw

een

the

heel

and

the

toe

tip).

Dat

a ar

e di

spla

yed

only

in th

e ra

nge

70° ≤ θ h

ip ≤

180

° (θ

hip

= 9

0° +

θkn

ee –

θan

kle –

θtr

unk)

, and

the

circ

le p

oint

s re

pres

ent t

ypic

al v

alue

s fo

r th

e fr

ee b

arbe

ll sq

uat.

96 Biscarini, Botti, and Pettorossi

action of gravity, further enhances this condition. The lower back may dangerously hyperextend under loading, especially in the presence of hip flexor inflexibility and/or abdominal weakness.

One major limitation affects the present study. The specific contribution of hamstrings and gastrocnemius muscles has been neglected in Equations (12) and (13), that is, in the calculation of the shear and compressive components of tibiofemoral joint load (ϕt and ϕn). How-ever, in the Smith squat, these contributions are not real-istically predictable, because the user may freely change the weight distribution between the forefoot and heel, due to the support given by the Smith machine, especially if the equipment is inclined. The qualitative effects of such muscle activations on ϕt and ϕn have been addressed in great detail in a previous work:16 the calculated values of the tibiofemoral reaction forces ϕn and ϕt only consti-tute reference lower limits for the compressive (ϕn) and PCL-loading (ϕt > 0) components, and reference upper limit for the intensity |ϕt| of the ACL-loading component (ϕt < 0). Actually, the current biomechanical study repre-sents the necessary framework for further experimental investigations in which motion analysis, EMG, and force platform data will be simultaneously recorded. This will entail a huge experimental activity due to the number of parameters that can be changed independently of the other (MW, α, θankle, θknee, θtrunk, and xGR) in the inclined Smith squat exercise.

Further limitations stem from the simplified biome-chanical joint model adopted in this study. For example, a model which includes the soft tissue structures of the knee and the complex geometry of the articular surfaces would be necessary to know how the net tibiofemoral loads ϕn and ϕt are distributed across the different structures of the knee. Such information is needed to achieve a quantitative assessment of the strain-force on the cruciate ligaments.

The present model refers to a quasi-static Smith squat exercise. In dynamic squat, high joint accelerations and inertial effects associated with the overload may appreciably affect the values of joint torques and joint reaction forces. Typically, the joint torques and loadings are increased (decreased) at the beginning (end) of the concentric phase and at the end (beginning) of the eccen-tric phase of the exercise.37,38 However, these effects can be quantified only on a case-by-case basis, and do not affect the general trends set by the equipment inclination (Figures 3–8), which are the subject of this article.

In conclusion, a controlled change of inclination of the Smith squat equipment can be effectively used to unload specific joint structures while focusing the activation on selected muscle groups. The information on the equipment inclination can be integrated with those concerning body positioning and foot weight distribution to get a complete set of indications for a full and careful use of the Smith squat in strengthening and rehabilitation programs. These indications are summarized in the following.

Patellar tendon force (FPT), knee torque (τknee), patel-lofemoral (ϕPF) and tibiofemoral (|ϕn|) compression forces increase with decreasing θknee, θtrunk, θankle, xGR, and α

(inclining the equipment forward). The hip torque (τhip) and the spine torque occurring at the lumbosacral joint (τLS) increase with decreasing θknee and with increasing θtrunk, θankle, xGR, and α, (inclining the equipment backward).

The ACL and PCL strain-force may be simultane-ously suppressed (ϕt = 0) in the range 180° ≥ θknee ≥ 120° by a backward equipment inclination (α = 30°) and selecting, for each value of θknee, one or more specific pairs of ankle and trunk angles. The ACL loading can be definitely eliminated by squatting with a backward equipment inclination (α = 30°) and a uniform or forward foot weight distribution.

For small (large) knee flexion angle, in the range 180° ≥ θknee ≥ 150° (θknee < 130°), the PCL strain-force decreases (increases) with decreasing θknee, θtrunk, θankle, and α, that is, inclining the equipment forward. In the range 150° > θknee ≥ 130°, the PCL strain-force still decreases by decreasing α (inclining the equipment forward). The peak value of both ACL and PCL loading, occurring in the range 180° ≥ θknee ≥ 90°, is minimized by a backward equipment inclination.

For any given value of the equipment inclination α, the ratios to the total resistance Mg of the calculated torques (τknee, τhip) and joint reaction forces (ϕt and ϕn) are nearly insensitive to the value of overload resistance MWg, at least for MW ≤ 2MB. Thus, Figures 3 through 8 actually give the trends of τknee, τhip, ϕt, and ϕn for any real value of overload resistance.

References 1. Dahlkvist NJ, Mayo P, Seedhom BB. Forces during

squatting and rising from a deep squat. Eng Med. 1982;11(2):69–76. PubMed doi:10.1243/EMED_JOUR_1982_011_019_02

2. Nisell R, Ekholm J. Joint load during the parallel squat in powerlifting and force analysis of in vivo bilateral quadri-ceps tendon rupture. Scandinavian Journal of Sports Sci-ences. 1986;8(2):63–70.

3. Hattin HC, Pierrynowski MR, Ball KA. Effect of load, cadence, and fatigue on tibiofemoral joint force during a half squat. Med Sci Sports Exerc. 1989;21(5):613–618. PubMed

4. Wretenberg P, Feng Y, Lindberg F, Arborelius UP. Joint moments of force and quadriceps activity during squatting exercise. Scand J Med Sci Sports. 1993;3(4):244–250. doi:10.1111/j.1600-0838.1993.tb00389.x

5. Wilk KE, Escamilla RF, Flesing GS, Barrentine SW, Andrews JR, Boyd ML. A comparison of tib-iofemoral joint forces and electromyographic activ-ity during open and closed kinetic chain exercises. Am J Sports Med. 1996;24(4):518–527. PubMed doi:10.1177/036354659602400418

6. Isear JA, Erickson JC, Worrell TW. EMG analysis of lower extremity muscle recruitment patterns during an unloaded squat. Med Sci Sports Exerc. 1997;29(4):532–539. PubMed doi:10.1097/00005768-199704000-00016

7. Zheng N, Fleisig GS, Escamilla RF, Barrentine SW. An analytical model of the knee for estimation of internal forces during exercise. J Biomech. 1998;31(10):963–967. PubMed doi:10.1016/S0021-9290(98)00056-6

Backward/Forward Inclined Smith Squat 97

8. Escamilla RF. Knee biomechanics of the dynamic squat exercise. Med Sci Sports Exerc. 2001;33(1):127–141. PubMed

9. Escamilla RF, Flesing GS, Zheng N, Barrentine SW, Wilk KE, Andrews JR. Biomechanics of the knee during closed kinetic chain and open kinetic chain exercises. Med Sci Sports Exerc. 1998;30(4):556–569. PubMed doi:10.1097/00005768-199804000-00014

10. Escamilla RF, Fleisig GS, Zheng N, et al. Effects of tech-nique variations on knee biomechanics during the squat and leg press. Med Sci Sports Exerc. 2001;33(9):1552–1566. PubMed doi:10.1097/00005768-200109000-00020

11. Escamilla RF, Fleisig GS, Lowry TM, Barrentine SW, Andrews JR. A three-dimensional biomechani-cal analysis of the squat during varying stance widths. Med Sci Sports Exerc. 2001;33(6):984–998. PubMed doi:10.1097/00005768-200106000-00019

12. Escamilla RF, Zheng N, Imamura R, et al. Cruciate liga-ment force during the wall squat and the one-leg squat. Med Sci Sports Exerc. 2009;41(2):408–417. PubMed doi:10.1249/MSS.0b013e3181882c6d

13. Shelburne KB, Pandy MG. Determinants of cruciate-ligament loading during rehabilitation exercise. Clin Biomech (Bristol, Avon). 1998;13(6):403–413. PubMed doi:10.1016/S0268-0033(98)00094-1

14. Fleming BC, Oksendahl H, Beynnon BD. Open- or closed-kinetic chain exercises after anterior cruciate ligament reconstruction? Exerc Sport Sci Rev. 2005;33(3):134–140. PubMed doi:10.1097/00003677-200507000-00006

15. Griffing J. (2010). Smith squat (accessed at http://www.exrx.net/Kinesiology/SmithSquat1.html).

16. Biscarini A, Benvenuti P, Botti FM, Mastrandrea F, Zanuso S. Modelling the joint torques and loadings during squat-ting at the Smith machine. J Sports Sci. 2011;29(5):457–469. PubMed doi:10.1080/02640414.2010.534859

17. Zatsiorsky V, Seluyanov V. The mass and inertia character-istics of the main segments of the human body. In: Matsui H, Kobayashi K, eds. Biomechanics VIII-B. Champaign, IL: Human Kinetics; 1983:1152–1159.

18. Zatsiorsky V, Seluyanov V, Chugunova L. In vivo body segment inertial parameters determination using a gamma-scanner method. In: Berme N, Cappozzo A, eds. Biomechanics of Human Movement: Applications in Rehabilitation, Sports and Ergonomics. Worthington, OH: Bertec Corp.; 1990:186–202.

19. Zatsiorsky V, Seluyanov V, Chugunova L. Methods of determining mass-inertial characteristics of human body segments. In: Chernyi GG, Regirer SA, eds. Contemporary Problems of Biomechanics. Boston, Massachusetts: CRC Press; 1991:272–291.

20. de Leva P. Adjustments to Zatsiorsky-Seluyanov’s segment inertia parameters. J Biomech. 1996;29(9):1223–1230. PubMed doi:10.1016/0021-9290(95)00178-6

21. Tsirakos D, Baltzopoulos V, Bartlett R. Inverse optimiza-tion: functional and physiological considerations related to the force-sharing problem. Crit Rev Biomed Eng. 1997;25:371–407. PubMed doi:10.1615/CritRevBiomed-Eng.v25.i4-5.20

22. Biscarini A, Cerulli G. Modeling of the knee joint load in rehabilitative knee extension exercises under water. J Biomech. 2007;40(2):345–355. PubMed doi:10.1016/j.jbiomech.2005.12.018

23. Biscarini A. Biomechanics of off-center monoarticular exercises with lever selectorized equipment. J Appl Bio-mech. 2010;26(1):73–86. PubMed

24. Herzog W, Read LJ. Lines of action and moment arms of the major force-carrying structures crossing the human knee joint. J Anat. 1993;182:213–230. PubMed

25. Reilly DT, Martens M. Experimental analysis of the quad-riceps muscle force and patello-femoral joint reaction force for various activities. Acta Orthop Scand. 1972;43:126–137. PubMed doi:10.3109/17453677208991251

26. Butler DL, Noyes FR, Grood ES. Ligamentous restraints to anterior-posterior drawer in the human knee: a biome-chanical study. J Bone Joint Surg Am. 1980;62(2):259–270. PubMed

27. Noyes FR, Butler DL, Grood ES, Zernicke RF, Hefzy MS. Biomechanical analysis of human ligament grafts used in knee-ligament repairs and reconstructions. J Bone Joint Surg Am. 1984;66(3):344–352. PubMed

28. Woo SL, Hollis JM, Adams DJ, Lyon RM, Takai S. Ten-sile Properties of the Human Femur-Anterior Cruciate Ligament-Tibia Complex: The Effects of Specimen Age and Orientation. Am J Sports Med. 1991;19(3):217–225. PubMed doi:10.1177/036354659101900303

29. Biscarini A. Minimization of the knee shear joint load in leg-extension equipment. Med Eng Phys. 2008;30(8):1032–1041. PubMed doi:10.1016/j.medeng-phy.2007.12.012

30. Lutz GE, Palmitier RA, An KN, Chao EY. Comparison of tibiofemoral joint forces during open kinetic-chain and closed kinetic-chain exercises. J Bone Joint Surg Am. 1993;75(5):732–739. PubMed

31. Stuart MJ, Meglan DA, Lutz GE, Growney ES, An KN. Comparison of intersegmental tibiofemoral joint forcesand muscle activity during various closed kinetic chain exer-cises. Am J Sports Med. 1996;24(6):792–799. PubMed doi:10.1177/036354659602400615

32. Beynnon BD, Johnson RJ, Fleming BC, Stankewich CJ, Renstrom PA, Nichols CE. The strain behavior of the ante-rior cruciate ligament during squatting and active flexion-extension: a comparison of an open and a closed kinetic chain exercise. Am J Sports Med. 1997;25(6):823–829. PubMed doi:10.1177/036354659702500616

33. Singerman R, Berilla J, Archdeacon M, Peyser A. In vitro forces in the normal and cruciate-deficient knee during simulated squatting motion. J Biomech Eng. 1999;121(2):234–242. PubMed doi:10.1115/1. 2835109

34. Toutoungi DE, Lu TW, Leardini A, Catani F, O’Connor JJ. Cruciate ligament forces in the human knee during rehabilitation exercises. Clin Biomech (Bristol, Avon). 2000;15(3):176–187. PubMed doi:10.1016/S0268-0033(99)00063-7

35. Kvist J, Gillquist J. Sagittal plane knee translation and electromyographic activity during closed and open kinetic chain exercises in anterior cruciate ligament- deficient patients and control subjects. Am J Sports Med. 2001;29(1):72–82. PubMed

36. Heijne A, Fleming BC, Renstrom PA, Peura GD, Beynnon BD, Werner S. Strain on the anterior cruciate ligament during closed kinetic chain exercises. Med Sci Sports Exerc. 2004;36(6):935–941. PubMed doi:10.1249/01.MSS.0000128185.55587.A3

37. Paulus DC, Reiser RF, Troxell WO. Peak lifting velocities of men and women for the reduced inertia squat exercise using force control. Eur J Appl Physiol. 2008;102(3):299–305. PubMed doi:10.1007/s00421-007-0585-6

38. Biscarini A. Measurement of power in selectorized strength training equipment. J Appl Biomech. 2012;28:229–241.