PAMM · Proc. Appl. Math. Mech. 17, 215 – 216 (2017) / DOI 10.1002/pamm.201710077
Investigating human thumb models via their range of motion volumes
, Michael Roller
, Staffan Björkenstam
, and Sigrid Leyendecker
Chair of Applied Dynamics, University of Erlangen-Nuremberg, 1 Immerwahrstrasse, D-91058 Erlangen, Germany.
Fraunhofer ITWM, Fraunhofer Platz 1,67663 Kaiserslautern, Germany.
Fraunhofer-Chalmers Centre, Chalmers Science Park, SE-412 88 Göteborg, Sweden.
The human thumb possesses joint axes with intricate descriptions, which enable the thumb to perform complex motions like
opposition. To validate a thumb multibody model kinematically, we ﬁrstly study the difference in the volumes of the thumb tip
workspace for the maximum range of motion (RoM) and the grasp RoM. We compare the volume difference for ﬁve models
(with same joint designs but different axes locations and orientations) with data from literature. Secondly, we compute the
rotation of the thumb along the longitudinal axis (internal rotation) for one joint for different postures. We compare the
rotations for the ﬁve models with measured data from literature. In both checks, the results obtained from simulation are in
close agreement with literature data and consequently the thumb model’s kinematics is validated.
2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
1 Thumb anatomy and model
Fig. 1: The thumb anatomy with bone and joint
nomenclature as introduced in Section 1 is shown
on the left, reproduced from . The thumb
model with joint axes is shown on the right.
Anatomically, the thumb is made of three bodies, connected by three joints, as
shown in Figure 1 (left). The bones from base to tip are the ﬁrst metacarpal (I
MC), the proximal phalanx (PP) and the distal phalanx (DP), connected in se-
ries with the trapezium bone in the wrist through the carpometacarpal (CMC),
the metacarpophalengeal (MCP) and the interphalangeal (IP) joints, each hav-
ing two, two and one degrees of freedom (DoF), respectively. The three joints
exhibit the ﬂexion-extension (ﬂex-ext) motion, while the CMC and the MCP
also show the adduction-abduction (add-abd) motion. The CMC and the MCP,
though at times approximated as universal joints, see , actually have non-
intersecting and non-orthogonal (nino) rotation axes, which allows these bod-
ies to show rotation along the bones’ longitudinal axes, named as pronation-
supination (pro-sup). To study the thumb kinematics, a multibody model is
created with three bodies and three joints, namely nino joints for the CMC and
the MCP and revolute joint for the IP, as shown in Figure 1 (right). The axes
locations and orientations and the bones dimensions are taken from cadaver
studies from [2, 5]. This model is created in terms of the director formulation,
see . After applying the internal (six for each body) and external constraints
(four each for the CMC and the MCP joints, ﬁve for the IP joint), the number of independent coordinates reduces to ﬁve. The
kinematic update to move the thumb conﬁguration from one time-step to next is performed using the nodal reparameterisation
function as described for an arm model in . The cadaver studies for axes data provide the results from measurements of
seven thumbs in the form of mean ± standard deviation with high anatomical variance, see [2,5]. The model created using the
mean values of the cadaver studies is named as the base model. Monte-Carlo simulations were performed to understand the
anatomic variance variation and it led to four biomechanically distinct thumb models, see , presented in Denavit-Hartenberg
(DH) notation and named as types I, II, III and IV. The anatomically variable (AV) models are converted from the DH notation
to director formulation.
2 Validation Techniques
In the ﬁrst method, the thumb is moved by giving inputs to all DoFs to create a set of the thumb tips in different positions. A
point cloud is generated with such a points set and its volume is calculated using α-shapes with an α-shape radius of 0.5. This
volume is calculated for the base model and the AV models for maximum and grasp RoMs and the reduction of grasp with
respect to the maximum volume is calculated. These values are compared with each other and with results from . In the
second method, the measure of the thumb internal rotation is evaluated. This is majorly contributed by the CMC to rotate the I
MC, and its value was ﬁrst measured by Cooney, see , for different postures, namely resting, ﬂexion, extension, abduction,
tip pinch and grasp
. The measurement was done using T-shaped surface markers and results were presented in the mean ±
Corresponding author: e-mail email@example.com, phone +49 9131 85 61018, fax +49 9131 85 61011
the ﬂexion, extension and abduction postures are named by Cooney and do not imply pure rotations around CMC ﬂex-ext and add-abd axes.
2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim