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Modelling the joint torques and loadings during squatting at the SmithmachineAndrea Biscarinia; Paolo Benvenutib; Fabio Bottic; Francesco Mastrandread; Silvano Zanusoe

a Department of Surgical, Radiological and Odontostomatologic Sciences, Medical Physics Section,University of Perugia, Perugia, Italy b LAMS Laboratory, University of Perugia, Perugia, Italy c

Department of Internal Medicine, Human Physiology Section, University of Perugia, Perugia, Italy d

Department of Mechanical Engineering, University of Perugia, Perugia, Italy e Department of ExerciseScience, University of Padova, Padova, Italy

First published on: 10 January 2011

To cite this Article Biscarini, Andrea , Benvenuti, Paolo , Botti, Fabio , Mastrandrea, Francesco and Zanuso, Silvano(2011)'Modelling the joint torques and loadings during squatting at the Smith machine', Journal of Sports Sciences, 29: 5, 457 —469, First published on: 10 January 2011 (iFirst)To link to this Article: DOI: 10.1080/02640414.2010.534859URL: http://dx.doi.org/10.1080/02640414.2010.534859

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Modelling the joint torques and loadings during squatting at the Smithmachine

ANDREA BISCARINI1, PAOLO BENVENUTI2, FABIO BOTTI3,

FRANCESCO MASTRANDREA4, & SILVANO ZANUSO5

1Department of Surgical, Radiological and Odontostomatologic Sciences, Medical Physics Section, University of Perugia,

Perugia, Italy, 2LAMS Laboratory, University of Perugia, Perugia, Italy, 3Department of Internal Medicine, Human

Physiology Section, University of Perugia, Perugia, Italy, 4Department of Mechanical Engineering, University of Perugia,

Perugia, Italy, and 5Department of Exercise Science, University of Padova, Padova, Italy

(Accepted 21 October 2010)

AbstractAn analytical biomechanical model was developed to establish the relevant properties of the Smith squat exercise, and themain differences from the free barbell squat. The Smith squat may be largely patterned to modulate the distributions ofmuscle activities and joint loadings. For a given value of the included knee angle (yknee), bending the trunk forward, movingthe feet forward in front of the knees, and displacing the weight distribution towards the forefoot emphasizes hip andlumbosacral torques, while also reducing knee torque and compressive tibiofemoral and patellofemoral forces (and viceversa). The tibiofemoral shear force ft displays more complex trends that strongly depend on yknee. Notably, for1808� yknee� 1308, ft and cruciate ligament strain forces can be suppressed by selecting proper pairs of ankle and hipangles. Loading of the posterior cruciate ligament increases (decreases) in the range 1808� yknee� 1508 (yknee� 1308) withknee extension, bending the trunk forward, and moving the feet forward in front of the knees. In the range15084 yknee4 1308, the behaviour changes depending on the foot weight distribution. The conditions for the developmentof anterior cruciate ligament strain forces are explained. This work enables careful use of the Smith squat in strengtheningand rehabilitation programmes.

Keywords: Squat, torque, joint load, cruciate ligaments, exercise

Introduction

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. There is general

agreement that correctly performed squats are safe

exercises when executed with appropriate load,

adaptation, and supervision (for a review, see

Escamilla, 2001). Injuries attributed to the squat

may result not from the exercise itself, but from

improper technique, pre-existing structural abnorm-

alities, 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.

Squat biomechanics have previously been analysed

with a particular focus on muscle activity (Isear,

Erickson, & Worrell, 1997), safety for knee struc-

tures (ligaments, menisci, and cartilage) (Zheng,

Fleisig, Escamilla, & Barrentine, 1998), and different

squat techniques according to the amount of knee

flexion (semi-, half-, parallel-, and deep-squatting),

stance width (narrow/wide), foot angle position

(adduction/abduction, inversion/eversion) (Escamil-

la, Fleisig, Lowry, Barrentine, & Andrews, 2001a;

Escamilla et al., 2001b), external load type and

positioning (bodyweight squat, dumbbell squat,

front/back barbell squat) (Gullett, Tillman, Gutier-

rez, & Chow, 2008), speed of execution (body-

building/dynamic squat) and external load intensity

(typically expressed as a percentage of body weight)

(Hattin, Pierrynowski, & Ball, 1989). With all these

variations in technique, the possibility of modulating

joint torques, muscle activities, and joint reaction

forces is limited by the moment equilibrium condi-

tion: the centre of mass C of the system constituted

by the user’s body and the weighted barbell should

fall between the forefoot and heel. This limitation is

Correspondence: A. Biscarini, Department of Surgical, Radiological and Odontostomatologic Sciences, Medical Physics Section, University of Perugia, 06100

Perugia, Italy. E-mail: biscarini@fisica.unipg.it

Journal of Sports Sciences, March 1st 2011; 29(5): 457–469

ISSN 0264-0414 print/ISSN 1466-447X online � 2011 Taylor & Francis

DOI: 10.1080/02640414.2010.534859

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overcome when the back is supported by a wall (wall

squat), and by a sliding or lever machine (machine

squat). These methods have been subjected to

biomechanical analysis by Blanpied (1999) and more

recently by Escamilla and co-workers (2009). How-

ever, 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).

In the Smith squat, a barbell is constrained

horizontally to move up and down while 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 op-

posed 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 is unclear, 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. Although previous studies in

which the Smith squat was used focused on testing

issues (Cotterman, Darby, & Skelly, 2005; Harris,

Cronin, & Hopkins, 2007; Paulus, Reiser, & Troxell,

2008; Thomas et al., 2007) and various training

aspects (Harris, Cronin, Hopkins, & Hansen, 2008;

McGuigan, Chiagiarelli, & Tod, 2005; Minahan &

Wood, 2008; Vingren et al., 2008), no study, to our

knowledge, has specifically examined the joint

torques and joint loads (shear and compressive joint

reaction forces) that occur during the execution of

this exercise. Moreover, in the fields of athletic

training, fitness, and rehabilitation, the debate

continues between those who believe 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). Despite this on-going debate, the Smith squat

is used extensively for different purposes: to famil-

iarize beginners with the squat movement, to

periodically change the routine and increase the

lifted load in experienced-user programmes, to

accommodate individuals who may experience pain

in the barbell squat and, finally, as a safer modality of

closed kinetic-chain exercise for knee rehabilitation.

The aims of this paper are to establish the relevant

biomechanical properties of the Smith squat ex-

ercise, and highlight the main differences with the

free barbell squat. To this end, an analytical

biomechanical model was developed for the calcula-

tion of the knee and hip torques, and of the shear and

compressive tibiofemoral joint loads, as a function of

external load, trunk tilt relative to the vertical, and

body configuration for all the combinations of hip,

knee, and ankle joint angles allowed by the Smith

machine. Such calculations also provide important

information on lumbosacral torque and patellofe-

moral force during the different squat techniques

within the Smith machine. The use of the Smith

squat for rehabilitation after cruciate ligament

reconstruction will be addressed in detail.

Methods

Figure 1 illustrates a two-dimensional geometrical

sketch of the Smith squat exercise. The human body

is modelled by 14 linked rigid segments (head, trunk,

upper arms, forearms, hands, thighs, shanks, and

feet), whose weight, dimensions, centre of mass, and

moments of inertia have been deduced from ex-

tensive anthropometric studies (Chandler, Clauser,

McConville, Reynolds, & Young, 1975; de Leva,

Figure 1. Schematic representation of the fundamental elements of

the Smith squat exercise. The barbell, constrained to two

rectilinear vertical tracks, may only move along a vertical line

(y-axis). The external forces acting on the system constituted by

the user and the weighted barbell are reported in the figure: the

weight of the system M~g applied at its centre of mass C ¼ (xC, yC);

the two equal frictionless reaction forces ~RS the tracks exert on the

barbell at their two contact points (0, yW); the shear ~AGR and

normal ~NGR ground reaction forces acting symmetrically on each

foot at a point (xGR, 0) within the contact surface between the foot

and the ground.

458 A. Biscarini et al.

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1996; Zatsiorsky & Seluyanov, 1983; Zatsiorsky,

Seluyanov, & Chugunova, 1990, 1991). The

weighted barbell is placed on the user’s shoulder,

and only moves along a vertical line (y-axis), due to

the mechanical constraint imposed by the rectilinear

tracks.

The external forces acting on the system con-

stituted by the user’s body (B) and the weighted

barbell (W) are: the weight of the system, equivalent

to the vector M~g applied in the centre of mass

C¼ (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 reaction forces the equipment

tracks exert on the barbell, schematized by two equal

frictionless forces ~RS applied at the two contact

points (0, yW) between the barbell and the tracks; the

ground reaction forces acting symmetrically on each

foot, equivalent to two equal vectors ~RGR applied at a

point (xGR, 0) within the contact surface between

each foot and the ground. xGR can be experimentally

determined by a force platform, and depends upon

the user-controlled weight distribution between the

forefoot and the heel. Squat guidelines commonly

suggest this distribution to be uniform. ~RGR may be

usefully decomposed in shear ~AGR and normal ~NGR

vector components. The external forces ~AGR and ~RS

characterize the Smith squat in comparison with the

free barbell squat.

In a quasi-static Smith squat exercise, the equili-

brium condition for the external forces

2~NGR þ 2~AGR þ 2~RS þM~g ¼ 0 ð1Þ

gives the following scalar equations

2NGR �Mg ¼ 0

2ðRSÞx þ 2ðAGRÞx ¼ 0

�(3)

when projected onto the y and x axis, respectively.

NGR and Mg are the magnitude of ~NGR and M~g,

Figure 2. Dependence of the knee and hip torques (tknee and thip) on the trunk inclination (7108� ytrunk�308), for different values of the

knee angle (yknee¼ 1708, 1608, . . . , 908) and ankle angle (yankle¼ 1008, 908, 808, 708, 608), under the condition MW¼MB. Data are

displayed only in the range 708� yhip�1808 (yhip¼908þ yknee – yankle – ytrunk). The symbols . and � represent typical knee and hip torques

respectively for the free barbell squat. The application point of the ground reaction has been located under the medial malleolus, xGR¼ xankle

(Figure 2a), midway between the heel and the tip of the toe, xGR¼ xankleþ0.07m (Figure 2c), and midway between the previous points,

xGR¼ xankleþ 0.035m (Figure 2b).

(2)

Joint torques and loadings in the Smith squat 459

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

of ~AGR and ~RS, respectively. The equilibrium

condition for the external force moments is calcu-

lated with respect to the axis crossing the (xGR, 0)

point and normal to the xy plane:

2yW ðRSÞx � ðxGR � xCÞMg ¼ 0 ð4Þ

Equations (2–4) determine the reaction forces of the

ground and the equipment runners:

NGR ¼Mg

2ð5Þ

ðAGRÞx ¼ �ðxGR � xCÞMg

2yW

ð6Þ

ðRSÞx ¼ðxGR � xCÞMg

2yW

ð7Þ

Knowledge of reaction forces (5–7) allows the

calculation of the torque about a specific joint, i.e.

the torque provided by the muscles crossing that joint

and by the passive joint reaction forces (force due

to ligament tensions and bone-to-bone contacts).

The hip torque thip is derived from the equilibrium

moment equation for the system (WUB) constituted

by the upper body UB (trunk, head, and upper limbs)

and the weighted barbell W:

2thip¼ðyW�yhipÞ2ðRSÞxþðxCWUB�xhipÞðMUBþMWÞg

ð8Þ

Here, MUB is the UB mass and CWUB is the WUB

centre of mass. The knee toque tknee is deduced from

the same equilibrium equation for the lower leg and

foot system (LF),

tknee ¼ �ykneeðAGRÞx þ ðxknee � xGRÞNGR

� ðxknee � xCLFÞmLFg (9)

where mLF is the LF mass, and CLF is the LF centre

of mass. Of course, xjoint, yjoint, and yjoint (joint¼ hip,

knee, ankle, etc.) are the joint coordinates and the

joint angle, respectively.

With the assumption that the knee torque is mainly

provided by the quadriceps, the patellar tendon force

FPT is given by the ratio of tknee to the patellar tendon

moment arm (aPT):

Figure 2. (Continued).

460 A. Biscarini et al.

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FPT ¼1

aPT

��ykneeðAGRÞx þ ðxknee � xGRÞNGR

� ðxknee � xCLFÞmLFg

�(10)

where aPT is a function of yknee. The tibiofemoral

joint load ~f is then obtained from the equilibrium

condition for the external forces acting on the LF

system:

~fþ ~FPT þ ~AGR þ ~NGR þmLF~g ¼ 0 ð11Þ

Projection of this equation on the longitudinal shank

axis, and on a normal to this axis, gives the

compressive (fn) and shear (ft) components of ~f(Biscarini & Cerulli, 2007):

ft ¼�FPTsingPTþNGRcosðyankleÞ�ðAGRÞxsinðyankleÞ�mLFgcosðyankleÞ (12)

fn¼�FPTcosgPT�NGRsinðyankleÞ�ðAGRÞxcosðyankleÞþmLFgsinðyankleÞ ð13Þ

Figure 2. (Continued).

In these equations, gPT is the yknee-dependent

traction angle of ~FPT, which is the angle of the vector~FPT and the longitudinal shank axis. In this study,

the well-known Herzog and Read (1993) polynomial

functions are adopted for aPT(yknee) and gPT(yknee).

The selective evaluation of the components of

the tibiofemoral force ~f allows an estimation of the

loading on specific joint structures. For example, the

anterior (posterior) cruciate ligament provides 86%

(95%) of the total restraining force to anterior

(posterior) drawer (Butler, Noyes, & Grood, 1980).

In the following, we investigate the dependence of

thip, tknee, FPT, ft, fn on the normalized resistance

MW/MB (0�MW/MB� 2, MBg¼ 750 N), and on the

different body configurations allowed by the Smith

equipment and defined by the joint angles yankle

(608� yankle� 1008), yknee (908� yknee� 1808), yhip

(708� yhip� 1808), and ytrunk (7108� ytrunk� 308),under the constraints xW¼ xshoulder¼ 0 (barbell over

the shoulder and constrained on the tracks) and

yGR¼ 0 (feet on the ground). As the application

point of the ground reaction ~RGR in the Smith squat

may be largely controlled by the user, all the results

Joint torques and loadings in the Smith squat 461

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are given for different ~RGR locations: just below the

ankle joint (xGR¼ xankle), midway between the heel

and the tip of the toe (xGR¼ xankleþ 0.07m), and

midway between these previous points (xGR¼xankleþ 0.035m). For comparison, the same quanti-

ties thip, tknee, FPT, ft, fn are also calculated in a

typical free barbell squat exercise (AGR¼RS¼ 0 and

xC¼ xGR).

Results

For any given value of the external load MWg, the

torque on the hip (thip) and knee (tknee) joints may be

strongly modulated by changing the body configura-

tion and positioning within the Smith machine, i.e.

changing one or more of the parameters yankle, yknee,

ytrunk, and xGR (Figure 2). Bending the trunk

forward (increasing ytrunk), moving the foot forward

with respect to the knee (increasing yankle), and

displacing the weight distribution towards the fore-

foot (increasing xGR), while maintaining yknee con-

stant, shifts the torque from the knee to the hip joint.

Both tknee and thip increase when the knee flexion

angle is increased (yknee is decreased) keeping

constant yankle, ytrunk, xGR, and MW. Negative knee

(hip) torques for high (low) values of ytrunk indicate a

flexor knee (hip) torque to be provided by the knee

(hip) flexors. All the quantities thip, tknee, FPT, ft, fn

inherit a linear dependence on Mg from the reaction

forces NGR, (AGR)x, and (RS)x. However, (AGR)x,

(RS)x, and thip implicitly and non-linearly depend,

through the parameters xC and xCWUB, on the ratio

MW/MB that influences the location of the centre of

masses C and CWUB. The results indicate that the

increase of tknee and thip with MW markedly deviates

from linearity (Figure 3), while the ratios of FPT, ft,

fn to Mg are nearly insensitive to MW.

As expected, the intensity jfnj of the compressive

component of the tibiofemoral joint load follows the

same trends displayed by tknee. In fact, jfnj increases

with decreasing yknee, ytrunk, yankle, and xGR, reaching

values as high as 3.4 � Mg for yknee¼ 908, ytrunk¼7108, yankle¼ 608, and xGR¼ xankle (Figure 4).

The cruciate ligament strain forces are mainly

determined by the shear component ft of the

Figure 3. Dependence of the knee and hip torques (tknee and thip) on the trunk inclination (7108� ytrunk� 308), for different values of the

knee angle (yknee¼1508, 1208, 908), ankle angle (yankle¼ 1008, 908, 808, 708, 608), and weighted barbell mass (MW¼0, MB, 2MB), under the

condition xGR¼ xankle. Data are displayed only in the range 708� yhip�1808 (yhip¼908þ yknee – yankle – ytrunk).

462 A. Biscarini et al.

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tibiofemoral joint load (Butler et al., 1980). In this

paper, it is conventionally assumed that a positive

(negative) shear force ft constrains the tibial plateau

posterior (anterior) translation with respect to the

femur, reflecting a load on the posterior (anterior)

cruciate ligament. The anterior cruciate ligament

(ACL) can be stressed appreciably only for xGR¼ xan-

kle in the range 1808� yknee� 1358, with a maximum

typically occurring around yknee¼ 1608 (Figure 5a).

With a progressive decrease of yankle and ytrunk, the

maximum shifts at first towards yknee¼ 1708 and

then towards yknee¼ 1808, but such combinations of

values of yankle and ytrunk (not reported in Figure 5)

would imply hip angles greater than 1808(yhip¼ 908þ yknee – yankle – ytrunk). Within the in-

spected joints range of motion, the jftj values

corresponding to ACL strain force are always smaller

than 0.1 � Mg. For xGR¼ xankleþ 0.035m, a small

residual ACL force (ft �70.03 � Mg) may occur in

the range 1608� yknee� 1508 (Figure 5b). No ACL

force is found for xGR¼ xankleþ 0.07m (Figure 5c).

Within the range 1808� yknee� 1508, the loading

of the posterior cruciate ligament (PCL) decreases

with flexing the knee (decreasing yknee), bending the

trunk backward (decreasing ytrunk), and moving the

foot backward with respect to the knee (decreasing

yankle). Conversely, for yknee� 1308, the PCL loading

increases with decreasing yknee, ytrunk, and yankle. The

transition between these regions with opposite

behaviours occurs in the range 15084 yknee4 1308.ft may reach positive values of about 0.6 � Mg for

yknee¼ 908, yankle¼ 608, and ytrunk¼7108.Figures 2–5 also report the values (represented by

the symbols . and � for knee and hip, respectively)

corresponding to a typical quasi-static free barbell

squat. In contrast to the Smith squat, the torque is

nearly equally shared between the knee and the hip.

The ACL is loaded only with a backward foot weight

distribution (xGR¼ xankle) in the range yknee� 1408.All together, these pictures give an overall view of the

main biomechanical differences between the free

barbell squat and the Smith squat.

Figure 4. Dependence of the axial component of the tibiofemoral joint load fn (normalized to the overall resistance Mg) on the trunk

inclination (7108� ytrunk� 308), for different values of the knee angle (yknee¼ 1708, 1608, . . . , 908) and ankle angle (yankle¼ 1008, 908, 808,708, 608), under the condition MW¼MB. Data are displayed only in the range 708� yhip�1808 (yhip¼908þ yknee – yankle – ytrunk). The

symbol . represents typical fn values for the free barbell squat. The application point of the ground reaction has been located under the

medial malleolus, xGR¼ xankle (Figure 4a), and midway between the heel and the tip of the toe, xGR¼ xankleþ0.07m (Figure 4b).

Joint torques and loadings in the Smith squat 463

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Discussion

In quasi-static free barbell squats, the hip, knee, and

ankle joint angles take ‘‘in-phase’’ values, which,

within small inter-individual variability ranges, are

tightly related to each other. Thus, each phase of the

exercise may be substantially defined by the knee

flexion angle alone, and is characterized by a well-

defined joint torque distribution, i.e. by specific

ratios of the torques at different joints. Conversely, in

the Smith squat, the value of the joint angles may be

changed independently of one another, enabling a

free modulation of the torque distribution among the

joints (Figure 2). For example, the torque may be

intentionally decreased at the knee and increased at

the hip and back, or vice versa, compared with the

free barbell squat. Notably, the hip (knee) torque

may be maintained exquisitely small in the range

1808� yknee� 1008 (1808� yknee� 1208), selecting

suitable ankle and trunk angles. These strategies

may be successfully included in knee, hip, and back

rehabilitation programmes. The back torque has not

been specifically calculated in this paper; however, in

squat exercises, it is definitely proportional to the hip

torque. Indeed, spine extensors act as stabilizers in

maintaining the physiologic spine curves during

the exercise, opposing the spine flexion induced by

the external load. Among the vertebral joints, the

moment of the external load takes a maximum at the

lumbosacral joint, which, in the two-dimensional

simplified adopted human body model, nearly

coincides with the hip joints. Ultimately, the

calculated hip torques can be approximately re-

garded as the maximum spine torque occurring at

the lumbosacral joint.

In contrast to the free squat, the ACL and PCL

load may be suppressed (ft¼ 0) in the range

1808� yknee� 1308 by selecting, for each value of

yknee, one or more specific pairs of ankle and trunk

angles (Figure 5a). This compares favourably with

open kinetic-chain leg extension exercises, where the

condition ft¼ 0 can be obtained only in the range

1808� yknee� 1408, through a complex modification

of leg extension equipment mechanics (Biscarini,

2008, 2010). For yknee5 1308, the condition ft¼ 0

would imply a too high trunk and/or ankle angle.

Thus, a PCL loading (ft4 0) always occurs in this

range. This force can be minimized, together with

Figure 4. (Continued).

464 A. Biscarini et al.

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the compressive tibiofemoral joint load fn and the

overall knee torque tknee, by bending the trunk

forward and moving the feet forward in front of the

knees (Figures 2, 4, and 5). However, this condition

maximizes the hip and back torque (Figure 2).

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 with 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.

Conversely, decreasing the forward trunk inclina-

tion 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 hyperextensions. 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 before undertaking these exercises.

A variety of other joint angle combinations are

allowed by the Smith machine, with intermediate

biomechanical effects, between the two opposite and

Figure 5. Dependence of the shear component of the tibiofemoral joint load ft (normalized to the overall resistance Mg) on the trunk

inclination (7108� ytrunk� 308), for different values of the knee angle (yknee¼ 1708, 1608, . . . , 908) and ankle angle (yankle¼1008, 908, 808,708, 608), under the condition MW¼MB. Data are displayed only in the range 708� yhip�1808 (yhip¼908þ yknee – yankle – ytrunk). The

symbol . represents typical ft values for the free barbell squat. The application point of the ground reaction has been located under the

medial malleolus, xGR¼ xankle (Figure 5a), midway between the heel and the tip of the toe, xGR¼ xankleþ0.07m (Figure 5c), and midway

between the previous points, xGR¼ xankleþ 0.035m (Figure 5b). Positive (negative) shear forces ft correspond to loads on the posterior

(anterior) cruciate ligament.

Joint torques and loadings in the Smith squat 465

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extreme configurations analysed above. Of course,

many of these combinations are spanned in real

quasi-static Smith squat exercises. Nevertheless, all

the corresponding relevant muscle and joint proper-

ties can easily be deduced from Figures 2–5. For

example, in a typical use of the Smith machine, the

trunk and the lower legs are maintained nearly

vertical (ytrunk � 08 and yankle � 908). 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 ~AGR and ~RS, which

characterize the Smith squat exercise. In fact,

compared with the free barbell squat at the same

knee angle, this body configuration entails: (a) nearly

the same levels of knee torque and compressive

tibiofemoral load; (b) a weak increase (decrease) of

ACL-loading (PCL-loading) shear tibiofemoral load;

and (c) an increase of hip and lumbosacral torques,

that becomes remarkable at higher knee flexion angles.

The conditions for the development of ACL strain

force in closed kinetic-chain exercises, and particu-

larly in squat exercises, have been the subject of

much research, often reporting contrasting results

(Escamilla, 2001; Escamilla et al., 1998; Fleming,

Oksendahl, & Beynnon, 2005; Heijne et al., 2004;

Zheng et al., 1998): ACL forces with widely variable

intensities have sometimes been reported in the

range 1808� yknee� 1208. Our results indicate that,

for the Smith and the barbell squats, these differ-

ences can be accounted for in terms of differences in

yankle, yknee, ytrunk, and xGR (Figure 5). Notably, the

ACL loading can be definitely eliminated by squat-

ting with increased forward trunk tilt (in agreement

with Ohkoshi, Yasuda, Kaneda, Wada, & Yamanaka

1991), and by displacing the weight distribution

towards the forefoot (Figures 5b and 5c).

One major limitation of this study concerns the

oversimplified human body model, constituted by

rigid segments linked by hinge joints. Nevertheless,

such models are frequently adopted in biomechanics

when the goal is the calculation of the overall joint

forces and torques in polyarticular exercises (Enoka,

2008).

A more severe limitation affects equations (12)

and (13). The contribution of hamstrings and

gastrocnemius muscles has been neglected in the

calculation of the shear and compressive components

Figure 5. (Continued).

466 A. Biscarini et al.

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of tibiofemoral joint load. The line of action of the

force exerted by the hamstrings on the lower leg is

directed upward and behind the knee. Thus, a

contraction of these muscles enhances the tibiofe-

moral compressive force fn and increases (decreases)

the intensity of the PCL-loading (ACL-loading)

tibiofemoral shear force ft. The enhancement of fn

can be deleterious for the menisci and articular

cartilage, but at the same time increases the joint

stability and protects the cruciate ligaments, oppos-

ing the anterior (posterior) tibial translations induced

by the shear component of the quadriceps force at

small (large) knee flexion angles. On the other hand,

the backward-directed hamstring force component

tends to produce a posterior tibial translation, thus

constituting a supplementary protection for the

ACL, but also a potential stress factor for the PCL.

It is well known that hamstrings activity is appreci-

ably higher in closed kinetic-chain knee extension

exercises than in open kinetic-chain ones. For free

barbell squat, hamstring activity is known to depend

on yknee and increases with the lifting loads, taking

peak values of 12% (Isear et al., 1997), 15% (Ninos,

Irrgang, Burdett, & Weiss, 197), 20% (Stuart,

Meglan, Lutz, Growney, & An, 1996), and 30–

80% (Escamilla et al., 1998, 2001b; Wilk et al.,

1996) of a MVIC (maximum voluntary isometric

contraction force) for MW/MB¼ 0, 0.25, 0.28, and

1.40–1.60, respectively. However, the hamstring

contribution might change significantly from begin-

ners to experienced users, and in the Smith squat is

also believed to depend on yankle, ytrunk, and xGR in

addition to yknee and MW/MB.

For the free barbell squat, Escamilla et al. (1998)

also reported a moderate gastrocnemius activity that

increases progressively as the knee flexes. Due to the

line of action of this bi-articulate muscle, the effects

of its contraction on fn and ft basically enhance the

effects induced by the hamstrings contraction. In the

Smith squat, the contribution of the gastrocnemius is

not realistically predictable, because the user may

freely change the distribution of the weight between

the forefoot and heel due to the support given by the

Smith equipment frame.

For these reasons, hamstring and gastrocnemius

forces have been neglected in this study, and the

calculated values of the tibiofemoral joint load

functions fn and ft only constitute reference lower

limits for the compressive (fn) and PCL-loading

(ft4 0) components, and reference upper limit for

Figure 5. (Continued).

Joint torques and loadings in the Smith squat 467

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the intensity jftj of the ACL-loading component

(ft5 0).

Conclusions

The present paper establishes the relevant biome-

chanical properties of the Smith squat exercise and

the main differences with the free barbell squat,

enabling an optimized use of the Smith squat in

strengthening and rehabilitation programmes. Fig-

ures 2–5 clearly highlight that the muscle activity and

joint load distributions may be widely and usefully

modulated according to the individual’s needs and

demands. The following main findings can be drawn

from these figures:

. FPT, tknee, jfnj and the patellofemoral force

increase with decreasing yknee, ytrunk, yankle, and

xGR;

. thip and the spine torque occurring at the

lumbosacral joint increase with decreasing yknee

and with increasing ytrunk, yankle, and xGR;

. the ACL and PCL load may be suppressed

(ft¼ 0) in the range 1808� yknee� 1308 by

selecting, for each value of yknee, one or more

specific pairs of ankle and trunk angles;

. the ACL loading can be definitely eliminated by

squatting with increased forward trunk tilt and

by displacing the weight distribution towards

the forefoot;

. the PCL loading decreases (increases) in the

range 1808� yknee� 1508 (yknee� 1308) with

decreasing yknee, ytrunk, and yankle. In the range

1508� yknee� 1308, the behaviour changes de-

pending on the value of xGR;

. the increase of tknee and thip with MW markedly

deviates from linearity, while the ratios of ft and

fn to Mg are nearly insensitive to MW.

On the whole, Figures 2–5 constitute a powerful

operative tool for trainers and therapists. Never-

theless, 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 weak-

ness. 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.

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