Secondary Logo

Journal Logo

Original Research

Kinematics of the Trunk and the Lower Extremities During Restricted and Unrestricted Squats

List, Renate; Gülay, Turgut; Stoop, Mirjam; Lorenzetti, Silvio

Author Information
Journal of Strength and Conditioning Research: June 2013 - Volume 27 - Issue 6 - p 1529-1538
doi: 10.1519/JSC.0b013e3182736034
  • Free



The squat exercise is a basic movement used in fitness training, strength training, and rehabilitation. In the bfu report 39 (23), the squat exercise was found to be one of the most predominant exercises in terms of risk of injury and risk of complaint. The report, assessing the injuries and discomforts that arose during a period of 12 months within a group of 6,680 gym members, found that leg presses and free weight squat exercises lead to back injuries and back discomfort 23. The proper form of execution of the squat exercise is essential to minimize its injury risk (3).

The squat can be performed in a restricted (r) or an unrestricted (unr) manner. In the r-type squat, the shanks are only allowed to move until the most anterior part of the knees reach a vertical line extending upward from the toes. The r-type squat is frequently used in fitness centers (3). A 1970s study (1) stated that greater shearing forces impinge upon the knee in unr-type squats and as a result of this finding, most fitness center instructors do not allow unr-type squats.

Fry et al. (8) suggested that the r-type squat could produce excessive forces at the hips and low back. Recently in a study of hip moments, Lorenzetti et al. (17–19) showed that r-type squats result in larger hip moments compared with the unr type, whereas hip angles did not differ between the 2 squatting techniques. However, it is unclear what effect the restriction of displacement in the lower limbs has on the kinematics of the trunk. It can be assumed that compensatory motion of the trunk takes place when shank motion is restricted. Thus, it is necessary to investigate whole-body motion and especially trunk motion during squatting exercises. Thus, there is a need for objective assessment tools.

Most of the trunk models based on skin marker assessments that are currently in use either consider the trunk as a single segment (6,12,24,27) or describe spinal motion (5,7,26). Crosbie et al. (4) divided the trunk into 3 segments—the lumbar, lower trunk, and upper trunk—each defined by 3 skin markers, allowing for the description of 3-dimensional segmental kinematics. Locomotion and daily exercises were studied using a multi-segment trunk model (13). The authors used 14 markers for the pelvis and the trunk. Compared with the extensive range of different marker sets used to assess the kinematics of the lower extremities, very little work has been performed concerning the trunk.

The kinematic investigation of different types of squatting exercise is important for developing strategies for appropriate strength training (18). The aim of this study was to compare lower extremity and trunk motion (dependent variables) between r and unr squats for the load conditions of 0% body weight (BW), 25% BW, and 50% BW loading (independent variables). This included the development of a suitable trunk marker set and a kinematic procedure to assess the kinematics of the trunk during squats based on skin markers.


Experimental Approach to the Problem

First, the subjects performed a standing trial in an anatomically upright position. To determine the ankle, knee, and hip joint centers (HJC)/axes of the skin marker model using functional approaches, 4 basic motion tasks (BMT) were performed (Table 1). After these tasks, the subjects performed r and unr squats with zero, 25% BW and 50% BW loading using a barbell. Each of the 6 conditions was performed for 8 repetitions. In the r squat, the position of the most anterior part of the knee was not allowed to move beyond that of the toes. This restriction was visually self-controlled by the subject with the use of a live projection of the side view of knee and toes and a pile marking the front edge of the toes on a screen in front of the subject (17). With the latter set up, no external force was applied to restrict the motion of the shank and mimics a common training situation with guidelines of a coach and visual control in a mirror. The unr squat was performed with no restriction on the motion of the shank. The dependent variables were the joint angles and curvature of the spine, and the independent variables were the execution type and the extra load.

Table 1:
Basic motion tasks (BMT) performed for the functional estimation of the ankle and hip joint centers and the knee joint axis (uk).


Thirty subjects, all movement science students experienced in weightlifting, with no history of back problems, participated in this study. The subjects had no specific sports activity background. The subjects were instructed to wear their normal sports shoes and to have a reasonable nutrition and hydration level. On average, the 30 subjects weighed 67 ± 11 kg, had heights of 174 ± 8 cm, and were 25 ± 4 years. The study was approved by the Eidgenössische Technische Hochschule Zurich ethics committee. All subjects gave informed consent by signing the corresponding permission form.


The 3D motion analysis system used was a 12-camera VICON MX system (Oxford Metrics Group, Oxford, UK). The camera resolution was 2,352 × 1,728 pixels, the capture frequency used was 50 Hz, and the capture volume was 300 × 500 × 200 cm. The instrumental error marker position detection is ≤1 mm.

The marker set for the kinematic assessment (IfB Marker Set) consisted of 40 skin markers on the lower extremities, 7 markers on the pelvis, and 24 markers on the trunk (Figure 1). The markers used had diameters of 9 and 14 mm. The allocation used of markers to segments is shown in Figure 1. Each segment is defined by a redundant marker cluster based on the following principles:

  • (a) Marker visibility: all markers should be visible by at least 2 cameras during the entire gait cycle.
  • (b) Marker cluster distribution: the distance between markers and their offset from the lines joining the other markers should be as large as possible, thereby maximizing the mean cluster radius (25).
  • (c) Number of markers: each segment cluster consists of a redundant number of markers, as an increase from 3 to 4 or 5 markers improves the estimation of orientation accuracy (2).
  • (d) Markers are located at positions on the body that show minimal skin movement artifacts.
Figure 1:
The IfB Marker Set and joint coordinate systems used, including functionally estimated joint centers (yellow markers). The entire marker set consisted of 71 markers (because of a shortage of space, foot markers are only shown on the left leg of the skeleton). Red markers are used for segment tracking and to define the marker-based joint coordinate system; grey markers are only used for segment tracking. The hip joint center is used as a virtual marker for the thigh segment.

The lower extremity marker set was used previously for the assessment of a level gait (15,27), running (16,27), and stair walking (10).

A segmental approach was applied to data from the whole body, and the kinematics of the trunk was also assessed using a curvature approach. The data analysis was performed in Matlab R2010 (Mathworks, Natick, MA, USA).

Segmental Approach

The position and orientation of each segment was determined relative to the reference segments defined by the standing trial using a least-squares fit of the corresponding marker point clouds (9). It follows that the neutral position (0° rotation) was defined by the standing trial. Joint rotations were described from the distal relative to the proximal segment for the lower extremities (foot motion: forefoot relative to rearfoot; ankle motion: rearfoot relative to shank; knee motion: shank relative to thigh; hip motion: thigh relative to pelvis) and from the lower segment relative to the upper segment for the trunk (pelvic relative to lumbar, lumbar relative to thoracic segments). A helical axis approach was used (28). To define clinically interpretable rotational components, the attitude vector was decomposed along the axes of the marker-based joint coordinate systems (28).

The ankle joint center, knee joint axis (uk), and HJC were estimated via functional approaches. A functional approach was chosen to decrease the influence of anatomical landmark displacement and to allow higher accuracies than those obtained with prediction approaches (14). The ankle and hip joints were modeled for these purposes as ball-and-socket joints, and the knee joint was modeled as a hinge joint. With the use of the corresponding BMT, as described in Table 1, the joint centers, respectively, and axes were determined by minimizing the sum of the differences between the modeled and the measured locations of the marker points.

The marker-based joint coordinate systems are orthogonal right-handed coordinate systems built using the functionally estimated joint centers, respectively, and axes.

The definitions for these coordinate systems are as follows and are illustrated in Figure 1.

  • (a) Foot-joint coordinate system: The posteroanterior axis eff connects HL and TO and is the leading axis. The direction of the mediolateral axis efs is perpendicular to eff and parallel to the ground. The vertical axis eft is perpendicular to the latter 2 axes.
  • (b) Ankle-joint coordinate system: the vertical axis eat, the connecting line between ankle joint center and KJC, is the leading axis. The direction of the mediolateral axis eas is perpendicular to eat and lies in the plane spanned by the malleoli and the KJC. The posteroanterior axis eaf is perpendicular to the latter 2 axes.
  • (c) Knee-joint coordinate system: the mediolateral axis eks is defined by the functional estimated knee joint axis uk. The direction of the vertical axis ekt is perpendicular to eks and lies in the plane spanned by eks and the HJC. The posteroanterior axis ekf is perpendicular to the latter 2 axes.
  • (d) Hip-joint coordinate system: the mediolateral axis ehs is parallel to the line connecting the 2 anterior superior iliac spine markers. The direction of the vertical axis eht is perpendicular to ehs and lies in the plane spanned by KJC and ehs. The anteroposterior axis ehf is perpendicular to the latter 2 axes.
  • (e) Pelvic-joint coordinate system: the mediolateral axis eps is parallel to the line connecting the 2 anterior superior iliac spine markers. The direction of the vertical axis ept is perpendicular to eps and the plane spanned by the right and left anterior superior iliac spine and sacrum markers.
  • (f) Trunk-joint coordinate system: the vertical axis ett, the connecting line between the spine markers L5 and C7, is the leading axis, and it points cranially. The transverse axis, ets, is perpendicular to ett and lies in the plane spanned by ett and the connecting line between the right and left lateral back on height L4 markers markers, pointing from left to right. The posteroanterior axis etf is perpendicular to the latter 2 axes and points to the front.

Hence, clinical rotations are described as provided in Table 2.

Table 2:
Description of clinical rotations based on the joint coordinate systems shown in Figure 1.*

Curvature Approach for Trunk Kinematics

To assess the sagittal plane curvature of the lumbar and the thoracic spine, corresponding marker positions were projected onto the sagittal trunk plane, defined as the plane spanned by ett and etf. The curvature was estimated by the reciprocal of the radius of a circle that was fitted by a least-squares approach into the 5 corresponding markers (Figure 2).

Figure 2:
Curvature approach—the curvature is defined as the reciprocal of the radius R of a circle that was fitted into 5 corresponding markers (L1–L5).

Cycle Definition

A squat cycle was defined as starting in a more or less upright position, moving down to the lowest position achieved during the squat and returning upward again. The start and end points of the cycle were defined by the vertical velocity of the barbell (vbarb > 0.02 min·s−1) tracked by 2 markers attached to the ends of the barbell. For each condition, the mean and SD were calculated over 8 repeated cycles.

Range of Motion

The range of motion (ROM) was defined as the range between the minimal and maximal rotation values obtained.

Statistical Analyses

The influence of the squat technique used (r vs. unr) and the presence of an extra load on the joint angles and ROMs were analyzed using a multiple repeated-measures analysis of variance. Eight valid executions were averaged for the statistical calculations of each technique. The significance was determined at p < 0.05. Statistical calculations were performed using IBM SPSS software version 19 (SPSS AG, Zurich, Switzerland).


Segmental Trunk Motion

For all weight conditions and squat types, segmental trunk rotation was predominant in the sagittal plane, and rotation in the frontal and transverse planes was small (Figure 3). Comparing the unr technique to the r squat, the pelvis relative to lumbar segment flexion/extension, showed a small but not statistically significant increase in ROM in r over unr squats (Table 3). The ROM for flexion/extension between the lumbar and the thoracic segments was significantly larger for r squats compared with unr squats (Table 3).

Figure 3:
Trunk kinematics—segmental approach. Mean and SD of all 30 subjects are reported. Condition: restricted squat with 25% bodyweight loading.
Table 3:
ROM of the segmental sagittal-plane rotations. Mean and SD of 30 subjects are reported.*

The ROM between the pelvis and the lumbar segments decreases significantly under the condition of a 50% BW load compared with 0% BW and 25% BW load conditions (Figure 4). The ROM between the lumbar and the thoracic segments increases significantly from 0% BW to 25% BW loads and significantly decreases from 25% BW to 50% BW loads. Thus, the largest ROM for the lumbar segment relative to the thoracic segment was observed for a 25% BW load (Figure 4).

Figure 4:
Load dependency—mean and SD of all 30 subjects and both squat types (r and unr) are reported. *Significant difference between the loading conditions (p < 0.05).

Curvature of the Trunk

The curvature of the lumbar and the thoracic spine decreases during the first half of the squat cycle, from upright standing to the lowest position of the cycle, and increases again during the second half of the cycle, during rising until the upright start position (Figure 5).

Figure 5:
Trunk kinematics—curvature approach. Mean and SD of all 30 subjects are reported. Condition: restricted squat with 25% bodyweight loading.

When comparing the 2 squat techniques, the subjects show a significant increase in thoracic curvature ROM in the r squat condition compared with the unr condition. Equivalent behavior, but no significant difference, is observed in the lumbar curvature under the 2 conditions (Table 4).

Table 4:
ROM of the sagittal-plane curvature of the lumbar and the thoracic spine. Mean and SD of 27 subjects are presented.*

The curvature of the spine shows a clear load dependency. There is a significant decrease in the lumbar curvature ROM with increasing loads (Figure 4). The thoracic curvature shows a significant decrease in ROM from 25% BW to 50% BW. However, from 0% BW to 25% BW, the thoracic curvature ROM slightly increases but not significantly (Figure 4).

Segmental Rotations of the Lower Extremities

Sagittal-plane rotations of the lower extremities were predominant, as observed in the trunk, and the transverse- and frontal-plane rotations were small (Figure 5). The observed motion between the forefoot and the rearfoot was also marginal in the sagittal plane (Figure 6).

Figure 6:
Lower leg kinematics—segmental approach. The mean and SD of all 30 subjects are reported. Condition: restricted squat with 25% bodyweight loading.

The ROM of the knee and the ankle is significantly larger in unr-type squats compared with r-type squats (Table 3). The ROM of the foot and hip did not differ between the 2 techniques (r and unr; Table 3). Under different loading conditions, the ROM of the ankle and the knee significantly increased, from 0% BW to 25% BW and 50% BW (Figure 4), respectively, whereas the ROM of the hip significantly decreased with an increase in load (Figure 4).

Cycle Repeatability

The repeatability of waveforms within a test day is described by the coefficient of multiple correlation (CMC) (11). The average CMC of the vertical barbell motion (Figure 7) over all subjects and all 6 conditions was 0.99 (Table 5).

Figure 7:
Vertical bar motion. Mean and SD of all 30 subjects are reported. Condition: restricted squat with 25% bodyweight loading.
Table 5:
Coefficients of multiple correlation describing the repeatability of waveforms within a test day. The mean and SD of all subjects and all conditions are reported.*

Generally, sagittal-plane rotations exhibited larger CMCs than frontal- and transverse-plane rotations (Table 5). The CMC for sagittal-plane trunk rotation was larger for rotations between the pelvis and the lumbar segment than for rotations between the lumbar and the thoracic segments (Table 5).


A marker set and a corresponding data processing protocol have been developed to assess the kinematics of the lower extremities and the trunk. The kinematics of the trunk were assessed using a 3D segmental approach using 3 trunk segments and 1 pelvic segment and by using a sagittal-plane spine curvature analysis. Both approaches are suitable for assessing the movement of the trunk during squatting.

Cycle repeatability was high for the barbell motion during squatting. Segmental rotations exhibited higher cycle repeatability for the sagittal plane than for the transverse and frontal planes. In the sagittal plane, the kinematics of the ankle, knee, hip, and pelvis relative to the lumbar segment were highly repeatable between cycles, whereas the repeatability of the kinematics of the foot and lumbar relative to the thoracic segments and spine curvature was lower. It is unclear whether the cycle repeatability is primarily influenced by variance in execution by the subject or whether skin movement artifacts are also relevant influences. The cycle repeatability of joint rotations is lower than it is during level gait (11), as expected, because squatting is performed much less frequently than walking.

The smaller sagittal plane ROM occurring in the ankle joint in the r squat in comparison with the unr is given by the restriction demanded in the r technique and confirms that the squat has been executed correctly. The restriction in the motion of the shanks in the r-type squat results in an increased ROM in the trunk, especially between the lumbar and the thoracic segments, but no increase in ROM in the hip occurs. The increased thoracic curvature in the r-type squat represents increased flexion within the thoracic spine. Thus, a restriction of the shank results in an increase in trunk motion.

To prevent a backward fall, the restriction in shank motion needs to be compensated for by increased motion of the hips or the trunk to maintain stability with the center of mass vertically aligned above the base. The present data have revealed that this compensatory motion occurs in the trunk. Based on an assumption of a simple mechanical model, we can assume that a restriction in shank motion, resulting in increased trunk flexion, leads to higher stresses in the lower back. Extensive loading of the spine during r-type squats has already been suggested by Fry et al. (8).

An increase in the extra load leads to an increase in the ROM of the ankle and knee and a decrease in the ROM of the hip and between the pelvis and the lumbar segment. It follows that with an additional load, the same range of movement of the barbell is reached using the distal joints rather than the proximal joints.

An increase in the extra load leads to a smaller curvature of the lumbar spine, representing a straightening of the lumbar spine. This load-dependent straightening of the spine is in agreement with the work of Meakin et al. (21). The load conditions of this study (0% BW, 25% BW, and 50% BW) is a refinement of the loading range used in the study of McKean et al. (20). However, it has to be kept in mind that in a hypertrophy training, the load may exceed this range.

Although the present marker set included redundant marker point clouds to improve orientation accuracy (2), the work of Mörl and Blickhan (22) showed a close relationship between a skin marker and its correspondent anatomical landmark on the vertebrae and that there is no impact during squatting, kinematic assessment is still limited by skin movement artifacts. The trunk coordinate system is based on markers and not functional approaches. Therefore, the influence of anatomical landmark displacement artifacts is present, and testers should be well trained in attaching markers. The last and potentially largest limitation of this method in the assessment of trunk kinematics is that the segmental approach breaks the trunk into only 3 rigid segments. Future studies should compare skin marker trunk assessment methodologies with imaging methodologies that allow the direct assessment of the kinematics of the vertebrae by magnetic resonance imaging or videofluoroscopy.

Practical Applications

In this study, whole-body kinematics was compared between 2 types of squatting over 3 loading conditions. For the trunk, the 3D segmental trunk motion was based on a 3-segment trunk model, and the sagittal-plane spine curvature was determined. Generally, it was found that the lumbar spine exhibits load-dependent straightening. Not surprisingly, the ROM of trunk flexion during squatting increases with a restriction in shank motion. Therefore, we predict that there is less stress on the lower back during an unrestricted squat than during a restricted squat. Practitioners should not be overly strict with athletes/clients in coaching against anterior knee displacement during performance of the squat. A certain amount of anterior displacement at the knee during unrestricted squatting may prevent undue stress on the lumbar spine and potential for back discomfort. Thus, when training leg muscles, the unrestricted squat may be the best choice.


The authors have no conflict of interest. This study was not funded. Alex Stacoff was an investigator on this project. We miss him.


1. Ariel BG. Biomechanical analysis of the knee joint during deep knee bends with heavy load. Biomech Model Mechanobiol IV: 44–52, 1974.
2. Challis JH. A procedure for determining rigid body transformation parameters. J Biomech 28: 733–737, 1995.
3. Chandler T, Stone M. The squat exercise in athletic conditioning: A review of the literature. NSCA J 13: 51–58, 1991.
4. Crosbie J, Vachalathiti R, Smith R. Patterns of spinal motion during walking. Gait Posture 5: 6–12, 1997.
5. D'Amico M, Grillet C, Mariotti S, Roncoletta P. Functional evaluation of the spine through the analysis of lateral bending test kinematics by mean of non-ionising technique. In: Three Dimensional Analysis of Spinal Deformities, D'Amico M, Merolli A, Santambrogio GC, eds. Oxford, UK: I Press, 1995. pp. 197–202.
6. Ferrarin M, Rizzone M, Bergamasco B, Lanotte M, Recalcati M, Pedotti A, Lopiano L. Effects of bilateral subthalamic stimulation on gait kinematics and kinetics in Parkinson's disease. Exp Brain Res 160: 517–527, 2005.
7. Frigo C, Carabalona R, Dalla Mura M, Negrini S. The upper body segmental movements during walking by young females. Clin Biomech (Bristol, Avon) 18: 419–425, 2003.
8. Fry AC, Smith JC, Schilling BK. Effect of knee position on hip and knee torques during the barbell squat. J Strength Cond Res 17: 629–633, 2003.
9. Gander W, Hrebicek J. Least squares fit of point clouds. In: Solving Problems in Scientific Computing Using Maple and Matlab. Berlin, Germany: Springer, 1997. pp. 339–349.
10. Husa-Russell J, Ukelo T, List R, Lorenzetti S, Wolf P. Day-to-day consistency of lower extremity kinematics during stair ambulation in 24-45 years old athletes. Gait Posture 33: 635–639, 2011.
11. Kadaba MP, Ramakrishnan HK, Wootten ME, Gainey J, Gorton G, Cochran GV. Repeatability of kinematic, kinetic, and electromyographic data in normal adult gait. J Orthop Res 7: 849–860, 1989.
12. Kramers-de Quervain IA, Muller R, Stacoff A, Grob D, Stussi E. Gait analysis in patients with idiopathic scoliosis. Eur Spine J 13: 449–456, 2004.
13. Leardini A, Biagi F, Merlo A, Belvedere C, Benedetti MG. Multi-segment trunk kinematics during locomotion and elementary exercises. Clin Biomech (Bristol, Avon) 26: 562–571, 2011.
14. Leardini A, Cappozzo A, Catani F, Toksvig-Larsen S, Petitto A, Sforza V, Cassanelli G, Giannini S. Validation of a functional method for the estimation of hip joint centre location. J Biomech 32: 99–103, 1999.
15. List R. Joint kinematics of unconstrained ankle arthroplasties. In: Proceedings of D-MAVT. Zurich, ETH Zurich, 2009.
16. List R, Unternaehrer S, Stacoff A, Ukelo T, Stuessi E. Two-segment foot kinematics during running. J Biomech 39: S550, 2006.
17. Lorenzetti S, Gülay T, Stoop M, List R, Gerber H, Stüssi E. Comparison of the angles and corresponding moments in the knee and hip during restricted and unrestricted squats. J Strength Cond Res 26: 2829–2836, 2012.
18. Lorenzetti S, Stoop M, Ukelo T, Gerber H, Stüssi E. Comparison of angles and the corresponding moments in knee and hip during restricted and unrestricted squats. In: Presented at ISBS 2009, Limerick, 2009.
19. Lorenzetti S, Stoop M, Ukelo T, Gerber H, Stüssi E, Müller R. Angles and moments during unrestricted and restricted squats. In: Proceedings of ISB 2009, Cape Town, 2009.
20. McKean MR, Dunn PK, Burkett BJ. Quantifying the movement and the influence of load in the back squat exercise. J Strength Cond Res 24: 1671–1679, 2010.
21. Meakin JR, Smith FW, Gilbert FJ, Aspden RM. The effect of axial load on the sagittal plane curvature of the upright human spine in vivo. J Biomech 41: 2850–2854, 2008.
22. Morl F, Blickhan R. Three-dimensional relation of skin markers to lumbar vertebrae of healthy subjects in different postures measured by open MRI. Eur Spine J 15: 742–751, 2006.
23. Müller R. Fitness centers: injury and discomfort in training. bfu report, Bern Switzerland Federal Institute for Injury Prevention. Bern, Switzerland: BFU, 1999.
24. Nguyen TC, Baker R. Two methods of calculating thorax kinematics in children with myelomeningocele. Clin Biomech (Bristol, Avon) 19: 1060–1065, 2004.
25. Soderkvist I, Wedin PA. Determining the movements of the skeleton using well-configured markers. J Biomech 26: 1473–1477, 1993.
26. Whittle M, Levine D. Measurement of lumbar lordosis as a component of clinical gait analysis. Gait Posture 5: 101–107, 1997.
27. Wolf P, List R, Ukelo T, Maiwald C, Stacoff A. Day-to-day consistency of lower extremity kinematics during walking and running. J Appl Biomech 25: 369–376, 2009.
28. Woltring HJ. 3-D attitude representation of human joints: A standardization proposal. J Biomech 27: 1399–1414, 1994.

trunk kinematics; curvature of the spine

Copyright © 2013 by the National Strength & Conditioning Association.