An Extended Kinematic Model
for Arm Rehabilitation Training and Assessment
Kui Wang, Siyi Li, Chang Xu, Ningbo Yu*
Abstract— In the rehabilitation training and assessment of
upper limbs, the conventional kinematic model treats the arm
as a serial manipulator and maps the rotations in the joint space
to movements in the Cartesian space. While this model brings
simplicity and convenience, and thus has been overwhelming
used, its accuracy is limited, especially for the distal parts
of the upper limb that execute dexterous movements. In this
paper, a novel kinematic model of the arm has been proposed,
which has been inspired by the biomechanical analysis of
the forearm and wrist anatomy. One additional parameter is
introduced into the conventional arm model, and then both the
forward and inverse kinematic models of five parameters are
derived for the motion of upper arm medial/lateral rotation,
elbow flexion/extension, forearm pronation/supination, wrist
flexion/extension and ulnar/radial deviation. Then, experiments
with an advanced haptic interface have been designed and
performed to examine the presented arm kinematic model.
Data analysis revealed that accuracy and robustness can be
significantly improved with the new model. This extended
arm kinematic model will help device development, movement
training and assessment of upper limb rehabilitation.
I. INTRODUCTION
Hand and arm function play an important role in our
daily life activities, thus people suffering from functional
deficits of the upper limbs are often severely impaired in
the execution of simple tasks [1]. Recovery of hand and arm
function can strongly improve the life quality of the stroke
patients.
Assessment is an essential part of the entire rehabilitation
process. In clinical practice, there are some assessment
tests for the arm and hand function, such as functional
independence measure[3], modified Ashworth spasm rating
scale[4] and the Fugl-Meyer Motor Assessment Scale[5], et
al. However, these assessment tests have some limitations,
such as time-consuming, lack of quantitative measures and
low precision. Thus, a more objective, reliable and simple
assessment is need for the recovery of arm and hand function.
Many researches have been performed by using movement
related parameters for assessment of rehabilitation induced
This work is supported by the National Natural Science Foundation
of China (61403215), the Natural Science Foundation of Tianjin
(13JCYBJC36600) and the Fundamental Research Funds for the Central
Universities.
Corresponding author Assoc. Prof. Dr. Ningbo Yu is with the Institute
of Robotics and Automatic Information Systems, Nankai University, and
Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Haihe
Education Park, Tianjin 300353, China. Phone: +86 (0)22 2350 3960 ext.
801, Email: nyu@nankai.edu.cn.
Mr. Kui Wang, Ms. Siyi Li, and Mr. Chang Xu are with the Institute
of Robotics and Automatic Information Systems, Nankai University, and
Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Haihe
Education Park, Tianjin 300353, China.
recovery [1], [2]. Besides the parameters in the Cartesian
space, parameters in the joint space are also of special
interest for the fact that they are in accordance with the
human biomechanical principles. As for the upper limb
movement, the wrist motion is dexterous.
In robot-assisted rehabilitation of the upper limbs, both
development of robotic training devices or exploration of
assessment methods need a reliable kinematic model [6]. The
conventional arm kinematics model has been much simplified
for the convenience of forward and inverse kinematic
analysis, but they may not be sufficiently accurate to indicate
important biomechanical aspects of arm movements. In the
biological or biomechanical fields, there are studies on the
arm joint movements by investigating the motion of each
individual bone as well as the relative motion between the
bones, and imaging techniques such as CT have been used
[7], [8]. Nevertheless, these models are too complicated for
use in rehabilitation training and assessment.
Therefore, in this work we propose a novel extended
kinematic model of the arm. By introducing one more
parameter into the conventional arm kinematic model,
accuracy and robustness can be significantly improved.
This extended arm kinematic model will help device
development, movement training and assessment of upper
limb rehabilitation.
The rest of the paper is organized as follows. The
next section introduces the conventional arm kinematic
model and demonstrates its limitations with experimental
data. Section III describes the extended kinematic model
with experimental results for validation. Finally, section IV
concludes the paper.
II. T
HE CONVENTIONAL ARM KINEMATIC MODEL AND
LIMITATIONS
A. Arm Movements for Haptic Interaction with Elbow Fixed
The human upper limb has been generally modeled in
the biomechanical literature as three rigid components,
connected by revolute joints. The upper limb of human
is usually considered as a serial model with a total of
7 DoFs[6]. The three rigid components are the the hand,
the upper arm and the forearm. The shoulder joint is
considered as a 3-DoFs ball and socket joint. The 3
rotational DoFs attached to the joint are extension/flexion,
adduction/abduction and lateral/medial rotation[9]. The
elbow joint is responsible for elbow flexion/extension
articulation, and the forearm for pronation/supination.
117
2016 International Conference on Advanced Robotics an
Mechatronics (ICARM)
978-1-5090-3364-5/16/$31.00 ©2016 IEEE