Swimming motion analysis: 3D joints
kinematics of the upper limb using wearable
inertial and magnetic sensors
Validation through dry-land simulations
, Giovanardi A.
, Di Michele R.
, Cortesi M.
, Gatta G.
, Fantozzi S.
1 Dept. of Electrical, Electronic, and Information Engineering, University of Bologna, Bologna, Italy
2 School of Pharmacy, Biotechnology and Sport Science, University of Bologna, Bologna, Italy
3 Dept. of Biomedical and Neuromotor Sciences, University of Bologna, Bologna, Italy
4 Dept. for Life Quality Studies, University of Bologna, Bologna, Italy
5 Health Sciences and Technologies - Interdepartmental Center for Industrial Research, University of Bologna,
Bologna, Italy, email@example.com
Abstract- The analysis of the joint kinematics during swimming plays a fundamental role both for
sports conditioning and in clinical contexts. A protocol originally designed to perform the 3D kinematic
analysis of the upper limbs during simple motor tasks was modified to be used in a sports setting. The
performance of the modified protocol was evaluated in laboratory during simulated swimming trials
performed by nine swimmers. A stereophotogrammetric system was used as gold standard.
Considering both front crawl and breaststroke swimming styles and all joint degrees of freedom
modeled (shoulder, elbow and wrist), the protocol implemented showed an accuracy adequate for the
purposes of the research (median values of RMSE, CMC and R were 7°, 0.95 and 0.95, respectively).
Keywords-swimming; inertial and magnetic sensors;upper limb;3D joint kinematics
The analysis of 3D joint kinematics during swimming plays a major role for both the sports conditioning and
clinical contexts. In the first case, the identification of key biomechanical factors that lead to the best propulsive
efficiency is the basis for performance enhancement as well as to get valuable information for didactical
purposes. In the second case, a kinematic assessment of the swimming technique would be an important tool to
detect altered movement patterns that can lead to an injury or that are related to previous injuries.
To acquire swimming kinematics of the upper limbs, underwater cameras are typically used. Traditionally,
markers are drawn on the skin of the swimmer and tracked [1,2]. Alternatively, a markerless approach was
recently exploited . However in both cases, only the 3D position of the anatomical landmarks and 2D angles
were analyzed. To the knowledge of the present authors, only one study using video analysis focused on 3D
joint kinematics of the shoulder and elbow during front-crawl swimming . Nevertheless, all studies based on
video analysis have a number of drawbacks, including the analysis being limited to underwater phases and to a
single stroke due to the limited field of view (strictly associated with the number of cameras). In addition, long
installation and calibration procedures, and long elaboration time are required even when an automatic tracking
procedure is used . Finally, quantitative video analysis can only be performed off-line, and thus it cannot be
used by coaches during training sessions to make direct feedbacks about the swimming technique.
To overcome the limits of video analysis, in the last ten years, wearable inertial-magnetic measurements units
(IMMUs) were exploited for the kinematic analysis of swimming. These devices, being directly fixed on the
swimmer, allow a continuous data acquisition during the whole swim. Furthermore, they require a simple
measurement set-up and have the potentiality to provide coaches with online performance parameters during
training sessions. In literature, swimming phases, stroke frequency, time parameters, velocity profile were
measured using IMMUs and validated against appropriate measurement systems . More recently, sets of
sensors were applied to the swimmer, on wrists, lower back, arms or legs, in order to better estimate kinematic
variables referred to various body segments [7-9]. However, to the knowledge of the present authors, none of
the previous studies investigated the 3D kinematics of upper limbs joints during swimming, and there are no
protocols specifically designed for this kind of sports setting.
The protocols previously proposed for upper limb kinematics using inertial sensors were validated in
ambulatory settings, for simple and slow movements [10-12], and thus must be extended to the sports context
in order to be used for kinematic analysis of swimming. Among the different solutions available, the protocol
proposed by Cutti et al.  was chosen for the main following reasons: (1) It was specifically designed for
being implemented with IMMUs; (2) It is suitable and accurate as a stereophotogrammetric system for the
estimation of the 3D joint angles kinematics of the upper limb (shoulder, scapula, elbow) in a clinical context;
(3) It can be adapted to use different IMMU systems capable to compute the orientation of the IMMUs with
respect to a fixed, global system of reference; (4) It can be adapted for the use in sports contexts; (5) It has a
simple and quick set-up in the acquisition phase as it requires only three calibration trials.
Therefore, the aim of the present study was to adapt the protocol proposed by Cutti et al.  to the swimming
context, extending the kinematics analysis also to the wrist joint, and to validate the protocol in dry-land
conditions using the stereo-photogrammetry as gold standard.
From a biomechanical point of view, each side was modeled as an open kinematic chain constituted by thorax,
upper-arm, forearm and hand with 7 degrees of freedom. Similarly to the representation described by Cutti et
al. , the shoulder was considered as the ball-and-socket joint between thorax and arm, while the elbow was
considered as the double-hinge joint (with non-intersecting axes) between arm and forearm. The newly
introduced wrist joint was modeled as the double-hinge joint formed by forearm and hand.
For each segment that formed 2 joints, both a proximal and a distal embedded anatomical reference systems
(ARSs) were defined. ARSs definitions introduced by Cutti et al.  was adopted apart from the facts that: (1)
the static calibration acquired for the definition of the thorax ARS was performed with the subject lying still,
because the orientation estimation of the IMMUs was demonstrated to be more accurate in such a position; (2)
the proximal forearm ARS was rotated of -90°along the Y-axis because the elbow joint during swimming is
almost completely pronated in many phases of a stroke; (3) the ARS of the hand was assumed to be aligned
with the distal forearm ARS during the static calibration trial. The positioning of IMMUs on body segments is
shown in fig. 1 (left). The sensor on the thorax was fixed by aligning the X-axis to the longitudinal axis of the
flat portion of the sternum, since the orientation of the X-axis of the IMMU is directly used for the computation
of the thorax ASOR. The sensor on the humerus was fixed laterally, in order both to allow the swimmer a
natural swim style, and to maximally reduce the soft tissue artifacts, thus over the central third of the humerus,
slightly posterior to it . The sensor on the forearm was fixed over the distal flat surface of radius and ulna,
with the IMMU Z-axis pointing away from the wrist. The sensor on the hand was fixed over its dorsum, with
the IMMU Z-axis pointing away from the hand.
Figure 1. Left: inertial and IMMUs positioning on body segments detailing the anatomical system of reference
axes. Right: lateral and anterior views during front crawl simulation.
The protocol required three types of calibration tasks. A static trial in which the subject lied on a table keeping
his arms alongside the body, and at the same time holding the dorsum of the hands aligned to the upper side of
the forearms. The second and third calibration tasks were dynamic trials in which the subject was standing, and
had to perform: (1) a flexion-extension of the elbow, from about 10° to 130° of flexion, keeping a constant
pronation-supination (2) a full-range pronation-supination of the elbow, keeping a constant flexion-extension.
In both the cases, the number of arm-stroke cycles to collect for each task was conventionally set equal to 5, 3
tasks should have been acquired, and very fast or very slow movement were not advisable.
All the axes of rotation of the elbow were modeled as mean helical axes, and computed using the algorithm
defined by Woltring et al. . At the end of this process, each ARS is known with respect to the
corresponding IMMU technical system of reference, and can be computed frame by frame for each dynamic
task. The joint angles were processed then by decomposing the relative orientation of adjacent segments. The
shoulder flexion-extension, intra-extra rotation and abduction-adduction were calculated using the XY’Z’’
Euler sequence; the elbow flexion-extension and pronation-supination were calculated using the XZ’Y’’ Euler
sequence; the wrists flexion-extension and ulnar-radial deviation were calculated using the XY’Z’’ Euler
sequence. The Euler sequence used for the shoulders was different from the one proposed by Cutti et al. .
The XY’Z’’ sequence was chosen because it better represents the kinematics of the shoulder when it performs
wide movements, and when these movements are not performed mainly around just one axis of rotation (i.e.
pure flexion-extension), as usually happens in a clinical context. The carrying angle of the elbow (rotation
around Z’ axis) and the hypothetic internal-external rotation angle of the wrist (rotation around Y’ axis) were
not considered, according to the joint model adopted.
This test aimed to evaluate the 3D joint kinematic analysis of the upper limbs during swimming simulations
using an IMMU system (Opal, APDM, Portland, Oregon, USA, 7 nodes, 128Hz). To this aim, a
stereophotogrammetric system (SMART-DX 7000, BTS Bioengineering, Italy, 7 cameras, 250Hz) was used as
the gold standard system. In order to be able to compare kinematic data estimated from both the IMMU and the
stereophotogrammetric system, seven clusters were built and firmly fixed onto the swimmer’s body. Each
cluster was made of a rigid light-weighted wooden plate (width 8cm x length 15cm x depth 1cm) containing
one IMMU and four retro-reflective passive markers (10 mm diameters)
Nine male swimmers (Age: 27.1±0.6 years; Height 180.4±5.2 cm; Weight 76.4±6.2 Kg; Training 10.7±3.6
years) agreed to participate and freely signed the informed consent. The inclusion criteria were the following:
(1) a swimming experience at least in regional competitions; (2) no recent musculoskeletal injuries; and (3) no
pain feel before or during the tests. Regarding the swimming style, 56% of the participants were specialized in
the front crawl, 33% in the breaststroke and 11% in the butterfly. Concerning the swimming level, 78% of the
participants were either current or former professionals, while 22% were amateurs. The swimmers were asked
to swim in the same way they would have done in a swimming pool (fig.1 Right). For each trial, 10 arm-strokes
cycles were requested but the participants could stop the test if they felt pain or tiredness. The main number of
arm-strokes cycles was 7, so about 40 complete arm-strokes cycles were available for each swim style (front
crawl and breast stroke) and for each athlete.
For the computation of the orientation of each unit with respect to the global system of reference and thus of
the ARSs, three Kalman-based algorithms were examined: (1) one from the Motion Studio software provided
by the APDM (KBE), (2) one presented by Madgwick et al.  with a value of gain fixed (KMA) in all the
trials, and (3) one presented by Madgwick et al.  with different values of gain (KMB) optimized for three
different examined trials: calibration, front crawl and breaststroke. Descriptive statistics was used to summarize
the characteristics of the participants. The performance of the IMMU and the SPS during simulated swimming
in laboratory were compared for each joint and degree of freedom by means of root mean square error (RMSE),
Pearson product-moment correlation coefficient (R), coefficient of multiple correlation (CMC) . The
analyses were performed using the R statistical software (version 3.0.1).
For the front crawl, the CMC was 0.94 (0.07) for KMA, 0.96 (0.06) for KMB and 0.87 (0.43) for KBE; for the
breaststroke, the CMC was 0.98 (0.04), 0.98 (0.06) and 0.93 (0.25) for KMA, KMB and KBE, respectively. In
both front crawl and breaststroke, as expected, the KMB showed slightly higher CMC values than the KMA,
and definitely higher CMC values than the KBE. Therefore, the KMB optimized algorithm was used. Overall,
there were no significant differences between the left and right sides in both front crawl and breaststroke for
both the examined indices.
Analyzing the front crawl, the results showed: 1) the median value of RMSE was equal to 7.42 degrees,
ranging from 3.25 degrees for the wrist ulnar-radial deviation to 14.65 degrees for the elbow flexion-extension;
2) the median value of CMC was equal to 0.95, ranging from 0.88 for the wrist ulnar-radial deviation to 0.99
for the shoulder flexion-extension, and for the internal and external rotation; 3) the median value of R was
equal to 0.95, ranging from 0.90 for the wrist ulnar-radial deviation to 0.99 for the shoulder flexion-extension.
Concerning the breaststroke style, the following results were found: 1) the median value of RMSE was equal to
5.39 degrees, ranging from 3.41 degrees for the shoulder internal-external rotation to 8.55 degrees for the
elbow flexion-extension; 2) the median value of CMC was equal to 0.99, ranging from 0.92 for the wrist ulnar-
radial deviation to 0.99 for the shoulder flexion-extension, for the abduction-adduction, for the internal and
external rotation, and for the elbow flexion-extension; 3) the median value of R was equal to 0.99, ranging
from 0.94 for the wrist ulnar-radial deviation to 1.00 for the shoulder flexion-extension and for the abduction-
adduction. An example of the shoulder joint angles are shown in fig.2.
Figure 2. Shouder joint angles estimated using IMMUs (black line) and stereophotogrammetric system (green
line) for front crawl (top) and breaststroke (bottom).
In laboratory, simulated swimming trials were carried out in dry-land conditions, recorded by an inertial and
magnetic measurement units system and simultaneously by a stereophotogrammetric system. The use of
simulated arm-strokes in laboratory was chosen because: (1) it allows a better control of all procedures, (2) the
gold standard is more accurate than conventional underwater video-camera systems, and (3) the complete
swimming stroke cycle can be recorded, including the aerial or recovery phase. An effective movement of the
trunk and upper limbs during the aerial phase is essential to place correctly the hand to use it as a rudder during
the propulsive phases. Considering both the front crawl and breaststroke swimming styles and all the joint
degrees of freedom modeled, the comparison between the gold standard and the inertial sensor system showed
median values of RMSE (about 7°), low enough for the purposes of research, high median values of CMC
(0.95), and high median values of R (0.95). Thus, the protocol implemented correctly estimated the 3D
orientation of the shoulder, elbow and wrist joints during swimming with accuracy adequate for the purposes.
McCabe, C.B., Psycharakis, S., Sanders, R.,2011. Kinematic differences between front crawl sprint and
distance swimmers at sprint pace. J Sports Sci 29, 115-123.
P. Figueiredo, P., Sanders, R., Gorski, T., Vilas-Boas, J.P., Fernandes, R.J., 2013. Kinematic and
electromyographic changes ruring 200m front crawl at race pace. Int J Sports Med, 34, 49-55.
Ceseracciu, E., Sawacha, Z., Fantozzi, S., Cortesi, M., Gatta, G., Corazza, S., Cobelli, C., 2011.
Markerless analysis of front crawl swimming. J Biomech 44, 2236-2242.
Ceccon, S., Ceseracciu, E., Sawacha, Z., Gatta, G., Cortesi, M., Cobelli, C., Fantozzi, S., 2013. Motion
analysis of front crawl swimming applying CAST technique by means of automatic tracking. J Sports Sci
Magalhaes, F.A., Sawacha, Z, Di Michele, R., Cortesi, M., Gatta, G., Fantozzi, S., 2013. Effectiveness of
an automatic tracking software in underwater motion analysis. J Sports Sci Med. 12, 660-667.
Ohgi, Y., Ichikawa, H., Miyaji, C., 2002. Microcomputer-based acceleration sensor device for swimming
stroke monitoring. JSME Int J Series C Mech Syst, Mach Elem & Manufac, 45, 960-966.
Bächlin, M., Tröster, G., 2012. Swimming performance and technique evaluation with wearable
acceleration sensors. Perv Mobile Comput, 1574-1192.
Dadashi, F., Crettenand, F., Millet, G.P. et al., 2013. Automatic front-crawl temporal phase detection
using adaptive filtering of inertial signals. J Sports Sci 31, 1251-60.
Hagem, R.M., Thiel, D.V., O'Keefe, S. et al., 2013. Real-time swimmers' feedback based on smart
infrared (SSIR) optical wireless sensor. Electr Lett 49, 340-341.
Luinge, H., Veltink P., Baten C., 2007. Ambulatory measurement of arm orientation. J Biomech 40, 78-
Cutti, A.G., Giovanardi, A., Rocchi L., Davalli, A., Sacchetti R., 2008. Ambulatory measurement of
shoulder and elbow kinematics through inertial and magnetic sensors. Med Biol Eng Comp 46, 169-178.
Picerno, P., Cereatti A., Cappozzo, A., 2008. Joint kinematics estimate using wearable inertial and
magnetic sensing modules. Gait & Post 28, 588-595.
Woltring, H.J., Long, K., Osterbauer, P.J., Fuhr, A.W., 1994. Instantaneous helical axis estimation from
3-D video data in neck kinematics for whiplash diagnostics. J Biomech 27, 1415-1432.
Madgwick, S.O.H., Harrison, A.J.L., Vaidyanathan, R., 2011. Estimation of IMU and MARG orientation
using a gradient descent algorithm, IEEE International Conference on Rehabilitation Robotics. IEEE,
Zurich, Switzerland, pp. 1-7.
Ferrari, A., Cutti, A.G., Cappello, A., 2010. A new formulation of the coefficient of multiple correlation
to assess the similarity of waveforms measured synchronously by different motion analysis protocols.
Gait & Post 31, 540-542.