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1. Local Hand Control for Tezpur University Bionic Hand
Grasping
Nayan M. Kakoty and Shyamanta M. Hazarika
Biomimetic and Cognitive Robotics Lab
School of Engineering
Tezpur University, INDIA
{nkakoty,smh}@tezu.ernet.in
ABSTRACT
Tezpur University (TU) Bionic Hand is a biomimetic ex-treme
upper limb prosthesis. The Hand is intended to emu-late
grasping operations involved during 70% of daily living
activities and have been developed using a biomimetic ap-proach.
This paper focus on the development of a local hand
control for grasping by TU Bionic Hand. Grasp primitives:
finger joint angular positions and joint torques are derived
through kinematic and dynamic analysis. TU Bionic Hand
emulates the grasp types following the dynamic constraints
of human hand. The joint angle trajectories and velocity
profiles of the Hand finger are in close approximation to
those of the human finger.
1. INTRODUCTION
A prosthetic hand needs to mimic the human hand both in
functionality and geometry. Higher functionality and con-trollability
leads to stable grasping and therefore expected
to be readily accepted by amputees. But instead of a great
stride for prosthetic hands with optimal performance char-acteristics
i.e. characteristics close to the human hand, there
still is a gap between state of the art prosthesis and human
hand grasping. The need for improving the functionality and
controllability of the prosthesis arises from the desire to use
prostheses as if it is a natural part of the body during Daily
Living Activities (DLA). To have such a prosthesis control,
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the control schema should satisfy the dynamic constraints
of human hand [18].
In previous research intending towards a human-like control
for prosthesis, Electromyogram (EMG) signals have been
widely used as an interface tool for prosthetic hands [1, 5].
Successful results on EMG recognition would bring a su-perior
control and replicates the neural control of human
hand. However, most of these are followed by only with
on/off control for prosthetic arms depending on the results
of EMG recognition [8, 13]. Current control schemes are
non-intuitive in the sense that the user is required to learn
to associate muscle remnants actions to unrelated postures
of the prosthesis [4]. Further control is still rudimentary be-ing
limited to a few hand postures or a simple proportional
estimate of force. In order to bridge the gap towards hu-man
like control, a Local Hand Control (LHC) replicating
the muskuloskeletal control of human hand is needed. This
can be implemented through a kinematic and dynamic anal-ysis
of the prosthesis satisfying the dynamic constraints of
human hand.
To overcome the limitation of previous kinematic model ig-noring
the state-space for multifingered robotic hand, Mon-tana
[16] has provided a configuration-space description of
the kinematics of the fingers plus-object system. A kine-matic
model is developed for a dexterous end-effector to
predict tendon tensions and tip forces during grasping and
shows similar joint motion behavior to that of the human
hand [21]. Derivation of kinematic and dynamic equations
for biomechanical analysis of human hand has been reported
in [19]. Robotic finger control technique using inverse kine-matics
to find the joint angular position have been reported
in [22]. Inspite of all these great stride, none of the control
based on above analysis are anywhere close to the natural
hand.
We concentrated on the development of a LHC for Tezpur
University (TU) Bionic Hand. Grasp primitives: finger joint
angular positions and joint torques are derived through kine-matic
and dynamic analysis. The analysis explores the dy-namic
constraints of human hand finger. The simulation
results shows that the joint angle trajectories and velocity
profiles of the prosthetic hand finger are in close approxima-tion
to those of the human finger.
The rest of the paper is structured as follows: TU Bionic
Hand and the proposed control architecture are described
Permission to make digital or hard copies of all or part of this work for
personal or classroom use is granted without fee provided that copies are
not made or distributed for profit or commercial advantage and that
copies bear this notice and the full citation on the first page. Copyrights
for components of this work owned by others than ACM must be
honored. Abstracting with credit is permitted. To copy otherwise, or
republish, to post on servers or to redistribute to lists, requires prior
specific permission and/or a fee.
Request permissions from Permissions@acm.org.
AIR '13, July 04 - 06 2013, Pune, India
Copyright 2013 ACM 978-1-4503-2347-5/13/070133;$15.00
http://dx.doi.org/10.1145/2506095.2506122

2. in section 2. Section 3 describes the LHC following the
kinematic and dynamic analysis of the Hand. The results
obtained for TU Bionic Hand finger joint trajectories and
velocity are discussed in section 4. The paper concludes
with final comments are in section 5.
2. TU BIONIC HAND
TU Bionic Hand shown in Figure 1 has been developed in-spired
by human hand anatomy. For details on design and
development of TU Bionic Hand, please refer to [11]. For
completeness of the paper, we are presenting a brief descrip-tion
of TU Bionic Hand.
Figure 1: Ventral view of the
TU Bionic Hand
TU Bionic Hand consists of five digits: four fingers and one
thumb. Each finger consists of three links replicating the
distal, middle and proximal phalanx. The links are con-nected
through revolute joints corresponding to distal in-terphalangeal
(DIP) joint, proximal interphalangeal (PIP)
joint and metacarpophalangeal (MCP) joint of human hand.
Thumb consist of two links. The palm is two piece and can
move inward and outward to form grasps. The prototype
joint range motion and dimensions closely resembles the hu-man
hand as tabulated in [11].
Table 1: Specification of the Actuating Motors
Parameter Value
Gear Ratio 0.03
No load Speed 250 Revolutions per minute
No Load Torque 0.0764 Nm
Diameter 160 mm
Length 300 mm
Diameter of motor pulley 10 mm
Abduction and adduction is not implemented in TU Bionic
Hand. N + 1 tendon system is used as media to transmit
forces from actuators to the joints. For N + 1 tendon system,
see [17, chapter 5: p 299]. Extensor and flexor tendons
are placed on the dorsal and ventral side of each finger and
connected to individual actuation unit (a DC geared motor)
embedded in the palm. The motors for flexion are placed on
the ventral side and for extension are placed on the dorsal
side of the palm. Tendons are connected to the pulley of
the motors, passing through a series of hollow guides. The
developed prototype possess a total of (3 × 3 of fingers +
2 of thumb + 1 of the palm + 3 of wrist) = 15 Degrees of
Freedom (DoF). Each finger tip is equipped with film like
force sensors to measure the fingertip force applied on the
object to be grasped.
2.1 Control Archtiecture
Figure 2 shows the “LHC” within the control architecture
for TU Bionic Hand. The control is two layered: Superior
Hand Control (SHC) and LHC.
Grasp Type
Transformation of the Grasp Type into
the fingers to be actuated
Prosthetic Hand equipped with Force
Sensor
Fingertip force sensor feedback
Superior Hand Control
Grasp Planning
Evoked Action Potentials or Electromyogram
Grasp Recognition Architecture
Machine
Learning
Visual Feedback
Local Hand Control
Grasp Primitives
PID Control
Kinematic
Analysis
Dynamic
Analysis
Actuation of Motors corresponding to
the Grasp Recognized
Figure 2: Schematic of Two Layered Control Archi-tecture.
The dotted region highlights the LHC
In an earlier paper [12], we presented details of the SHC and
have shown an average recognition rate of 97.5% for the six
grasp types: power, palm-up, oblique, hook, pinch and pre-cision.
SHC provides the information about the grasp type
attempted by the user based on the forearm EMG signals.
On recognition of the grasp type, classification architecture
commands the LHC to actuate the corresponding motors on
the prototype to replicate the identified grasp.
The LHC is the interface between the SHC and the pros-thetic
hand. LHC identifies the fingers to be actuated for
performing recognized grasp. The finger actuation is con-trolled
through a proportional-integral-derivative controller
(PID) customized with fingertip force sensor. Based on the
kinematic and dynamic analysis of the finger, grasp primi-tives
i.e. finger joint angular positions and joint torques are
determined. The Hand perform the six grasp types following
the dynamic constraints of human hand.

3. 3. LOCAL HAND CONTROL
The LHC is responsible for controlling the finger joint angu-lar
positions and velocities following the dynamic constraints
of human hand [14]. The detailed LHC is shown in Fig-ure
3 wherein K, J, F and Td are motor constant, inertia
of finger links, frictional constant of the motor and external
disturbance torque. The kinematic and dynamic analysis
are computed in 40 msec., the PID controller settles the fin-gertip
force at desired value in a period of 200 msec. and
the actuator outputs the desired force at the fingertip in a
period of 8 msec.
Actuator
(1, 2, 3)
Td(s)
+ + Fa
_
Kinematic
Analysis
(as detailed in
section 5.1)
Dynamic
Analysis
(as detailed in
section 5.2)
Fd
(1,
2,
3)
™
PID
Controller
(Kp + sKd + Ki/s)
™ K/s(Js+F) Force
Sensor
1/K
20 msec
20 msec
200 msec
8 msec
Figure 3: Detailed schematic diagram of LHC with
proportional gain Kp = 200, differential gain KD =
10 and integral gain KI = 100
The LHC maps the identified grasp type into the actuation
of the corresponding motors [13]. Kinematic and Dynamic
analysis leads to evaluation of grasp primitives - finger joint
angular position and joint torques. The finger joint angu-lar
positions are obtained as detailed in 3.1. The desired
joint torques = {1, 2, 3} calculated in accordance to the
finger model as detailed in section 3.2 are applied to the
MCP, PIP and DIP. Using equation 17, the desired force
at the fingertips are calculated. The controller sends the
actuating signal to the motors at time t = T0. On estab-lishing
contact between the fingertip and the object being
grasped, the force sensor sends a signal to the controller at
time t = T1 and the controller stops the actuating signal.
The time duration of actuation of the motor is calculated
as t = T1 − T0. On establishing contact by fingertip with
the object to be grasped, the extensor motor is stalled. The
flexor motor torque is controlled to prevent the fingertip
force from exceeding the desired force. From the force sen-sor,
the actual force is measured. The difference between the
measured force and desired force is the error to minimize. A
typical PID controller is used to reduce the error. The LHC
prevents the fingertip force from exceeding a critical value
with the joints at a pose for the grasp attempted. Following
the neuromuscular time constraint [9], LHC commands the
prosthesis to form the attempted grasp in an approximate
period of 250 msec.
3.1 Kinematic Analysis
To discuss the kinematics and dynamics of a finger, we con-sider
a planner schematic structure of the index finger; as
shown in Figure 4; wherein each link Li(i = 1, 2, 3) corre-sponds
to the proximal, middle and distal phalanges. MCP,
PIP and DIP joint angles are 1, 2 and 3 respectively. The
initial forward kinematics based on Denavit-Hartenberg (D-H)
parameters of the schematic representation in Figure 4
is presented in Appendix-I.
Yo
Y1
Y2
3 23
L3 DIP 2
L2
PIP 22
Z2 X1
L1 1
MCP 21
Xo
Zo
Z1
X2
Figure 4: A planner schematic structure of the index
finger
Direct kinematic equations are used to obtain the fingertip
position and orientation according to the joint angles. With
three revolute joints, the finger has three rotational DoF (¯
= {1, 2, 3}T ) leading to the finger end effector having pose
(¯x = {x, y, }T ). For kinematic analysis, the first step is to
establish the mapping from joint angles (the vector of three
generalized rotational coordinates ¯ ={1, 2, 3}T ) to link
end point position and orientation of the finger for a given
set of link lengths ¯L
= {L1, L2, L3}. From the Denavit-
Hertenberg parameters of the finger as stated in Table 2, the
fingertip pose ¯x with respect to the base frame (Xo, Yo,Zo)
can be computed as:
¯x = G(¯) =
2
4
Gx (¯)
Gy (¯)
G(¯)
3
5 (1)
2
4
x
y
3
5 =
2
4
L1C1 + L2C12 + L3C123
L1 S1 + L2 S12 + L3S123
1 + 2 + 3
3
5 (2)
where G(¯) is the geometric model defined by the trigono-metric
equations for the end point position {x, y}T and ori-entation
{} of the last link as a function of ¯ and link
lengths of the finger ¯L. C1 ,C12 and C123 denotes cos(1 ),
cos(1 + 2 ) and cos(1 + 2 + 3 ) and S1 , S12 and S123 de-notes
sin(1 ), sin(1 + 2 ) and sin(1 + 2 + 3 ) respectively.
Since flexion and extension is performed by pulling and re-leasing
the flexor and extensor tendons, the joint angles de-pends
on the tendon length pulled (lm) and released (lm′ )
by the motors [10]. Tendon length while the finger is max-imally
extended is lo = L1 + L2 + L3 . When the finger is

4. flexed, the flexor tendon is pulled by the motor. Let lx be
the resulting flexor tendon length and 1 , 2, 3 be the joint
angles respectively. Change in flexor tendon length lm is the
difference of lo and lx.
lm = lo − lx
= (L1 + L2 + L3 ) −
(L1C1 + L2C12 + L3C123 ) (3)
In order to replicate the motion feature of human finger
into the prototype, we considered the dynamic constraints
of human fingers. Following the anatomical and empirical
studies on linear relationship between finger joints presented
in [14], following constraints which relates one joint angle to
another are used:
1 = 0.52 (4)
2 = 1.53 (5)
Substituting the above constraints i.e, equations (4) and (5)
into equation (3), we have the following relation between 1
and lm.
lm = (L1 + L2 + L3 ) − (L1 cos(1 )
+L2 cos(2.1 ) + L3 cos(4.1 /3 )) (6)
In a similar way, the length of the extensor tendon released
by the motor is given as:
lm′ = (L1 + L2 + L3 ) + (L1 cos(1 )
+L2 cos(2.1 ) + L3 cos(4.1 /3)) (7)
Since, lm is the length of the tendon pulled by the motor;
lm can be computed using equation 7 given diameter of the
pulley connected to the motor, d; time of rotation of the
motor, t and revolution per minute of the motor, N.
lm = dNt (8)
The values of d and N are known a priori as tabulated in
Table 1. t is computed from force sensory feedback. The
start time is achieved from initiation of the actuating sig-nal
to the motor and the time of contact is on receiving a
feedback signal from fingertip sensor.
3.2 Dynamic Analysis
For dynamic analysis, we refer to the schematic represen-tation
of the finger in Figure 5. Tendon routing the finger
joints d1, d2 and d3 are the distance of the center of mass of
the phalanges from the respective joints MCP, PIP and DIP
(E1,E2 and E3) respectively. I1, I2 and I3 are the moment of
inertias of the three phalanges about an axis passing through
their center of masses. m1,m2 and m3 are the masses of the
proximal, middle and distal phalanges respectively. a and b
are half the finger width and distance of the tendon guides
form the finger joints. Lagrangian method was used to de-rive
the mathematical model of the finger [17]. The tendons
were assumed to be inextensible and inertial effects of the
pulley and all frictional effects are neglected. The dynamic
equation can be written starting from the Lagrangian for-mulation
as:
[M()]¨ + [C(, ˙
)] + G() = (9)
where [M()] is 3 x 3 mass matrix of the finger; C[, ˙] is
3 x 1 vector and includes the coriolis terms and centrifugal
terms, G() is 3 x 1 vector of the gravity terms and is 3
d3Extensor Tendon (h2)
3
R3 E3 d2
2
Yo
L3
R2 E2
L2
Z o
a 1 d1
Flexor Tendon (h1) L1
R1 E1 X o
Flexor Motor (m)
pulley
Extensor Motor (m)
pulley
b
b
Figure 5: Schematic of the finger representing ten-don
routing, center of mass and moment of inertias
of the phalanges in the finger
x 1 generalized torque input vector on phalanges (produced
by tendons).
The chain like nature of a manipulator leads us to consider
how forces and moments propagate from one link to the
next originating at the actuator. Typically the finger applies
some force on the object to be grasped with the free end.
We wish to solve for the joint torques which must be acting
to keep the system in static equilibrium. In considering the
static forces in a manipulator, we first lock all the joints so
that the manipulator becomes a structure at the point the
finger touches the object to be grasped. We then consider
each link in this structure and write a force moment balance
relationship in terms of the link frames. Finally, we compute
what static force must be acting about the joint axis for the
manipulator to be in static equilibrium.
The joint torques exactly balances the finger tip force in
the static equilibrium situations. The Jacobian transpose
maps finger tip forces into equivalent joint torques [17]. The
rotational kinetic input to the end effector is the net of
three torques ( = {1, 2, 3}T ) at MCP, PIP and DIP
joints respectively to produce the output wrench vector ( ¯W
= {fx, fy, z}T ). The transformation from joint torques
which balances the wrench vector ¯W
is given by,
¯ = J(¯)T ( ¯W
)
=
−L1S1−L2S12−L3S123 −L2S12−L3S123 −L3S123
L1C1+L2C12+L3C123 L2C12+L3C123 L3C123
1 1 1
#T
.
fx
fy
z
#
where J(¯) is the Jacobian matrix relating the joint space to
the finger tip space. It is partial derivatives of the geometric

5. model of the link chain given by equation 2 with respect to
¯. Next, we wish to describe how forces applied at the end of
the tendons are related to the torque applied at the joints.
Following [17], the extension function 1 for the flexor and
extensor tendons are given as:
h1 ()=lm+2
p
a2 +b2 cos(tan−1(a/b)+1/2)−2b−R2 2−R3 3
(10)
h2 () = lm′ + R1 1 + R2 2 + R3 3 (11)
The coupling function relating the tendon force and the joint
torques is computed as:
Hc =
2
4
dh1 /d1 dh2 /d1
dh1 /d2 dh2 /d2
dh1 /d3 dh2 /d3
3
5 (12)
Now the joint torque in terms of tendon force is given as:
¯ = Hc.F (13)
=
2
4−pa2 + b2sin(tan−1(a/b) + 1/2) R1
−R2 R2
−R3 R3
3
5
»
F1
F2
.
–
(14)
where F1 and F2 are the forces on the flexor and extensor
tendons respectively.
Considering the motor torque for flexion of the finger as T1
and r as the radius of the pulley connected to the motor, we
have
F1 = T1 /r (15)
For a serial manipulator with pivoted joints z = 0. Fol-lowing
the work reported in [7], we measured the force in
the direction of the object to be grasped i.e. fx using the
sensors placed at the fingertip and fy = 0 assumed. Consid-ering
these, equation 10 becomes
¯ = J(¯)T ( ¯W
)
=
#T
−L1S1 − L2S12 − L3S123 −L2S12 − L3S123 −L3S123
L1C1 + L2C12 + L3C123 L2C12 + L3C123 L3C123
1 1 1
fx
.
00 #
(16)
From equation 14 and 16, we have fx, desired fingertip force
as follows:
1Extension function measures the displacement of the end
of the tendon as a function of the joint angles of the finger
fx = −
p
(a2 + b2 )(sin(tan−1((a/b) + 1/2)F1 + R1F2
−L1 S1 − L2 S12 − L3 S123
(17)
4. RESULTS AND DISCUSSIONS
The LHC emulates the grasps type in the Hand following
the dynamic constraints of human hand finger through a
PID controller. We have used RoboAnalyzer V.4 [20] for
kinematic and dynamic analysis of the prosthetic hand. We
report analysis for the hand performing a pinch grasp. The
pinch grasp is used for grasping small object like pen, pencil
etc. Preshaping of the grasp is performed by flexing the
index finger and thumb in opposition. For our experiment,
the index finger and the thumb moves towards each other
from a tip to tip angular distance of 175◦. The object to
be grasped is hold between the index finger and the thumb.
The other fingers remain fully extended during execution of
the grasp. Figure 6 shows the index and thumb end position
during pinch grasp.
120
100
80
60
40
20
−20
−40
−60
−80
0 10 20 30 40 50 60 70 80 90 100
0
Angular Position in Degree
Time in msec
Figure 6: End Position of the Index Fin-ger
and Thumb during Pinch Grasp
On establishing contact with the object to be grasped at
around 80-100 msec, finger end positions are retained. Fig-ure
7(A), (B) and (C) shows the MCP, PIP and DIP joint
trajectories of the index finger for TU Bionic Hand. These
has been derived following inverse and forward kinematic
simulations as stated in [20]. It has been found that the PIP
joint moves at a rate of 2.06 (i.e. y/x in Figure 7) times to
that of the MCP joint and 1.61 (i.e. y/z in Figure 7) times to
that of the DIP joint; which follows the dynamic constraints
of the human hand closely as stated in equation 4 and 5.
The finger joint trajectories of human hand as reported in
[15] is shown in Figure 7(D). As can be seen, the finger joint
trajectories of the Hand are in close approximation to the
human finger joint trajectories.
Figure 8(a) shows the velocity profiles of prosthetic hand
index finger joints. Velocity profile of human hand fingers
as reported in [3] is shown in Figure 8(b). The velocity pro-files
of TU Bionic Hand are in line with the velocity profile
of human fingers. This also satisfies the statement that the
“velocity profiles of the finger joints are bell shaped” as re-ported
in [2].

6. A
B
C
x
y
z
D
Figure 7: Joint Trajectories of Prosthetic Hand In-dex
Fingers: (A) MCP Joint (B) PIP Joint (C) DIP
Joint. (D) Human Hand Index Finger (Figure ’c’
adapted from [15]).
Figure 8: Velocity profiles of (a) Prosthetic Hand
Index Finger Joints (b) Human Hand Finger MCP
(solid line) and PIP (dotted line) joints (Figure ’b’
adapted from [3]).
5. FINAL COMMENTS
Development of a LHC for TU Bionic following the dynamic
constraints of human hand is reported. The grasp primi-tives:
finger joint angular positions and joint torques are
derived through kinematics and dynamics. The simulation
results depicts that TU Bionic Hand follows the human hand
dynamic constraints closely. The joint angle trajectories and
velocity profiles of the prosthetic hand finger are in close ap-proximation
to those of human finger. Embedment of the
control architecture for the developed TU Bionic hand is
part of ongoing research.
Acknowledgment
The authors gratefully acknowledge Prof. S. K. Saha from
the Indian Institute of Technology, Delhi, INDIA for his
helpful suggestions and comments in carrying forward the
research reported here. Financial support received from De-partment
of Electronics and Information Technology, Gov-ernment
of India through its project Design and Develop-ment
of Cost-effective Bio-signals Controlled Prosthetic Hand;
1(9)/2008-ME TMD is gratefully acknowledged.
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Appendix-I
The Denavit-Hartenberg parameters [6] describing the finger
kinematics are illustrated in Table 2; where i is the joint
angle from the Xi−1 axis to the Xi axis about the Zi−1 axis,
d1 is the distance from the origin of the (i−1)th coordinate
frame to the intersection of the Zi−1 axis with the Xi−1
axis along the Zi−1 axis, ai is the offset distance from the
intersection of the Zi−1 axis with the Xi axis and i is the
offset angle from the Zi−1 axis to the Zi axis about the Xi
axis with i = 1, 2, 3.
Table 2: Denavit-Hartenberg Parameters of the Fin-ger
Link i−1 ai−1 di i
1 0 0 0 1
2 0 L1 = 30 mm 0 2
3 0 L2 = 25 mm 0 3