Kinga Stasik
Lodz University of Technology,
Department of Mechanics of Textile Machines
ul. Żeromskiego 116, 90-924 Łódź, Poland
E-mail: kinga.stasik@p.lodz.pl
Method of Separating Fabric from a Stack –
Part 2
Abstract
A mathematical model of the gripper mechanism with an electric drive, characterised by an
increased work surface is presented in the paper. Equations describing the kinematic and
dynamic characteristics have been formulated for this model. The resulting equations have
been solved numerically. The calculation results illustrating the rheological reaction of the
material to the operation of the gripper have been shown in diagrams.
Key words: gripper for textiles, computer control, mathematical model, garment production, robotisation.
Introduction. Mathematical
models of grippers for textiles
Existing grippers very often use springs
for compression [1 – 3]. Textiles are exposed to destruction because come into
contact with the jaws in a very small area
and they do not have the ability to control the compression force. Papers [4, 5]
proposed an improvement associated
with it, where the spring is replaced with
a motor which is intended to prevent the
crossing of the permissible pressures for
the fabric so that there is no destruction.
n Equations of motion
Employing the principle of virtual works
for moving parts of the gripper described
in [6] in Figure 1 (see page 80), supplemented with moments of inertia of the
guide rollers of the belt I2c, I3c, I4c, which
move with velocity ϕ2r2c, the frictional
forces between the belt and separating
fabric layer T1 and T2 and the weight of
the separating fabric mh and mv, we can
write a dynamic equation of motion in
the following form:
d2 ϕ 3
d2 ϕ1
d2 ϕ 2
d
dϕ1 − I2c
dϕ 2 +
− I3c
d ϕ 3 − I4 c
2
2
d
tdt
d
tdt
d
t 2
d
t
Despite the use of the motor dinstead
of d2 ϕ
2
2
2
2
d
ϕ
ϕ1
ϕ
ϕ
d
d
3
2
4
Mm dϕ1 −toI1ccontrol
dϕ1the
− I2c
dϕ2 − I3c
d ϕ 3 − I4 c
dϕ 4 −+m tk (1)22 dϕ2r22c +
the spring and the ability
d
t 2
d
t 2
d
tdt2
d
tdt2
d
t
size
of the pressure
on thedmaterial,
forc2
ϕ3
d2 ϕ1
d2 ϕ 2
d2 ϕ 4
d2 ϕ 2
− I3textiles
Mm dϕ1 − I1c es acting
dϕ1 − pointwise
I2c
dϕ2on
d ϕ 3 − I4 c
dϕ 4 − mtktk
dϕ2r22c +− (T1 + T2 )dϕ 2 r2c = 0
c
d
t 2
d
t 2
d
t 2 may still
d
t 2
d
tdt2
be too large.
Reducing pressures necessary to maintain the fabric is possible by increasing
the contact surface of the jaws. Therefore
the solution to this problem proposed
is agripper for textiles with parallel fingers [5]. The fingers are in contact with
the separating fabric over a much larger
area than grippers gripping the fabric in
a “pinch” [4].
Mm dϕ1 − I1c
The forces of friction between the belt
and separation fabric layer equal, respectively, to:
T1 = µp(Nv+mhg), T2 = µpNh
(2)
Equation 1, taking account of the friction
forces T1 and T2 (2) and masses mh and
mv (4a, 4b), as described in [6], after the
transformation can be written as:
I1c
d2 ϕ3 r1cr2c
d2ϕ1
d2ϕ2 r1c
d2ϕ 4 r1c r2c
+ I2c
+ I3c
+ I4c
+ (m
2
2
22
d
t
d
t
Rc
d
t
R cr3c
d
t 2 R c r4c
dt
dt
dt
d2 ϕas
d2ϕ1
d2ϕ2 r1c serve
d2ϕ 4 r1c r2c
d2 ϕ r r 2
The grippersI discussed
3 r1c r2 c
+ I2c could
+ I3c
+ I4c
+ (m v + mh ) 22 1c 2c + (3)
1c
2
2
2
2
d
t
d
t
R
d
t
R
r
d
t
R
r
d
t
Rc
dt
dt
such for textiles, but they need
to have c 3c
c 4c
c
r
r
the fabric between their fingers. Effective
+ µ p (N v + Nh + m h g) 1c 2c − Mm = 0
Rc
separation of the fabric requires a mechanism introducing the fabric between its Using the formulas defining the derivafingers. This paper describes a mecha- tive of a composite function:
nism for introducing the fabric between
2
d2 ϕ 2 d2 ϕ1 dϕ 2  dϕ1  d2 ϕ 2
fingers using frictional forces, which can
=
+


d
t  dϕ12
d
tdt2
d
tdt2 dϕ1  dt
be realized by using an endless belt, pull2
2
2
ing the fabric by force of friction in the
d ϕ 3 d ϕ1 d ϕ 3  d ϕ1  d 2 ϕ 3
=
+


(4)
direction of the blockage place, where is
tdt  dϕ12
d
tdt2
d
t 22 dϕ1  d
dt
a fold formed entering between the belt
2
d2 ϕ4 d2 ϕ1 dϕ4  dϕ1  d2 ϕ4
= 22
+

and foot. The further movement of the
22
d
t
d
t
dϕ1  d
t  dϕ12
dt
dt
dt
belt will unfold the fabric between the elements involved in separating the fabric and substituting to expression (3) we oblayer [6].
tain a second order differential equation:
Stasik K. Method of Separating Fabric from a Stack – Part 2.
FIBRES & TEXTILES in Eastern Europe 2014, Vol. 22, No. 2(104): 79-83.
79
ϕ2r2c = ϕ3r3c, ϕ1
ϕ3
r r
dϕ 3
r r
= 1c 2c
= 1c 2c ,
dϕ1 R c r3c
ϕ1 R c r4c
,
(7)
r r
ϕ2r2c = ϕ4r4c, ϕ1 1c 2c = ϕ 4 r4c
Rc
r r
r r
ϕ4
dϕ 4
= 1c 2c
= 1c 2c ,
ϕ1 R c r4c
dϕ1 R c r4c
After substituting Equations 6 and 7 into
Equation 5, we then obtain a system of
Equation 8 of the first order.
Figure 1. Distribution and directions of moments in the gripper’s movable part system described in [6] in Figure 1; I1c, I2c, I3c, I4c, - moments of inertia of guide rollers of the belt,
ϕ1,…,4 - angles of rotation of guide rollers of the belt, r1c, r2c, r3c, r4c, Rc - radii of rolls
of the gripper, Mm – drive torque of the motor of rolls, T1 i T2 - boundary frictional forces
between the belt and separating layers of the fabric, mh – mass of the fabric lying on the
table (not picked up yet), mv – mass of the fabric between the foot and belt.
For the purpose of numerical calculation
of a simplified system of Equations 8,
assuming that the guide roller belts are
identical, and their moments of inertia
I2c, I3c, I4c, radii r2c, r3c, r4c and angles
of rotation ϕ2, ϕ3, ϕ4 are created equal.
Using relationships (6) and (7) between
the angles of rotation and radii of wheels,
we can write that:
dϕ 2 dϕ 3 dϕ 4 r1c
=
=
=
and
dϕ1 dϕ1 dϕ1 R c
d2 ϕ2 d2 ϕ3 d2 ϕ 4
=
=
=0
dϕ12
dϕ12
dϕ12
(9)
After substituting Equation 9 into the
system of Equations 8, the following is
obtained:
dϕ A
= ϕB
dt
d
t
Figure 2. Step of pressing the textile package to the table (A) and a compression of separated layer between the foot and moving part of the gripper (C) described in [6], msv, msh
- weight of the respective elements of the gripper.
2
Between

dϕ3 r1c r2c
dϕ2 r1c
dϕ4 r1c r2c
dϕ r r 2  dthe
ϕ angles
+ I3c
+ I4c
+ (m v + mh ) 2 1c 2c  21 +
I1c + I2c
dϕ1 R c
dϕ1 R c r3c
dϕ1 R c r4c
dϕ1 R c  d
t

+ I3c
c
r1c r2c
= ϕ 3 r3c
Rc
of rotation ϕ1,…,4
and the radii of circles r1c, r2c, r3c, r4c, Rc
dϕ3 r1c r2c
dϕ4 r1c r2c
d ϕ r r 2  d2 ϕ
+ I4c
+ (m v + mh ) 2 1c 2c  21 +
dϕ1 R c r3c
dϕ1 R c r4c
dϕ1 R c  d
tdt
can be formulated thus:
2
 d2ϕ2 r1c
d2ϕ3 r1c r2c
d2ϕ4 r1c r2c
d2ϕ2 r1c r22c  dϕ1 
+ I2c
+ I3c
+ I4c
+ (m
 +
(5)
v + mh )

2
dϕ12 R c r3c
dϕ12 R c r4c
dϕ12 R c  d
t 
 dϕ1 R c
ϕ2Rc = ϕ1r1c,
2
d ϕ3 r1c r2c
d ϕ4 r1c r2c
d ϕ r r  dϕ1 
+ I4c
+ (m v + mh ) 22
 +

dϕ12 R c r3c
dϕ12 R c r4c
dϕ1 R c  dt
d
t 
2
2
2
2
1c 2 c
+ µp (Nv + Nh + mh g)
r1c r2c
− Mm = 0
Rc
r
ϕ2
= 1c
ϕ1 R c
,
dϕ 2 r1c
=
dϕ1 R c
ϕ2r2c = ϕ3r3c = ϕ4r4c ϕ 2 = ϕ1
(6)
r1c
Rc
dϕ A
= ϕB
dt
d
t
Mm − µp (Nv + Nh + mhg)
+ (m v + mh )
r1c r2c  d2 ϕ2 r1c
d2 ϕ3 r1c r2c
d2 ϕ4 r1c r2c
− I2c
+I3c
+ I4c
+
2
2
Rc
dϕ A R c r3c
dϕ2A R c r4c
 dϕ A R c
d2ϕ2 r1c r22c  dϕ A 


dt
dϕ2A R c  d
t 
2
dϕ BA
= ϕB
d
t
dt
2
2
2
2
r r 
r 
r r 
r r 
I1c + I2c  1c  + I3c  1c 2c  + I4c  1c 2c  + (m v + mh ) 1c 2c 
 R c r4c 
 Rc 
 Rc 
 R c r3c 
Equation 8.
80
(8)
dϕB
=
dt
d
t
Mm − µp (Nv + Nh + mhg)
r
I1c + 3I2c  1c
 Rc
2
r1c r2c
Rc
(10)

r r
 + (m v + mh ) 1c 2c

 Rc



2
While manipulating a package of fabrics,
the gripper presses the fabric lying on the
table in a stack (Figure 2.A) and a layer
is separated from the stack between the
foot and gripper’s movable part (Figure 2.C).
The motion of the gripper along the vertical direction is initiated by an electric
motor 9 with a driving torque Mmv and
an angle of rotation of the main shaft φv
by means of a screw 7 with a pitch hsv,
which transforms the rotary motion of the
motor into a vertical translatory one [6].
Analogously the motion of the gripper
along the horizontal direction is performed by means of an electric motor 18
with a moment Mmh and angle of rotation
of the main shaft φh and a screw 16 of
pitch hsh [6].
FIBRES & TEXTILES in Eastern Europe 2014, Vol. 22, No. 2(104)
Figures 3 and 4 present the distribution
of accelerations and forces acting on the
mass of the gripper msh along the horizontal and msv vertical direction.
The mass msh consists of gripper elements, i.e. a plate 13 with three belt guide
rollers 3, an electric motor 4 and a rubber
belt 2 (Figure 2.C and 1 [6]), while the
mass msv consists of a mass msh, a spring
15 and guides 19 for stabilisation of the
gripper motion along the horizontal direction, an electric motor 18, and casing
14 (Figure 2.A and 1 [6]).
a)
b)
Figure 3. Distribution of acceleration and forces acting on the mass of the gripper moving
along the horizontal (a) and vertical (b) direction, driven by an electric motor 19 (a) and
9 (b)[6].
The dynamic equations of motion for
the systems shown in Figure 3 can be
presented using the principle of virtual
works:
Mmmh
h − Nh
d
x
d 2 x h dx
d
x h
dx h
− msh
=0
sh
dϕ h
d
tdt2 dϕ h
Mmmv
v − Nv
d
xdx v
d2 x v d
x v
dx
− msv
=0
sv
2
dϕ v
d
ϕv
d
tdt
(11)
ϕv
ϕh
hsh
hsv
sv
sh , x v =
2π
2π
(12)
where hsh and hsv mean the movement of
the movable part of the gripper attributable to one rotation of the motor shaft.
From the above equations, the following
can be obtained:
d
x h h sh
dx
= sh
dϕ h
2π
2
d xh
b)
Figure 4. Scheme of compression of the fabric layer with a force Nh (a) and Nv (b).
The linear coordinates xh and xv and angular coordinates φh and φv define the
position of the systems with masses msh
and msv. Motion functions xh = xh(φh)
and xv = xv(φv), which define geometrical relationships between the rotary motion of motors 9 and 18 and the horizontal and vertical motion of the gripper, are
determined as:
xh =
a)
Equations 15 are then written in the form
of first-order equations for computer solution of the method of numerical integration:
while the package of fabrics lying on the
table (Figure 4.b) has been assumed in
the following form:
k v1
k v2
d
u
3
Nv =
uv +
u v + c tv
hsh
sh
L
L
Mmh
m
h − Nh
gt nilv + gt t
gt nilv + gt t
dj
d
ϕhB
dj
dϕhB
hA
2π
hB
LLtthh
L th
=j
ϕhB
=
h
B
2
dt
d
t
dt
d
t
 hsh
sh 
k v1
k v2
d
u v
msh
du

3
sh 
u +
u + ctvtv
2πv =
N
dt
Lt v
Lt v
d
t
(16)
g n + gt
gt nilv + gt
h sv
sv t ilv
L
L
L
M
−
N
th
t
h
t
h
mv
m
v
v
dϕhA
dj
dj
dϕhA
vA
2π
vB
=j
ϕhA
=
vB
2
dt
dt
d
t
d
t
for uv > 0 and Lh > 0.001
(18)
 hsv
sv 

msvsv 
 2π 
k
k
d
u
du v
3
Nv = v1 u v + v 2 u v + c tvtv
In paper [7] a model of fabric in the form
gt nilv
gt nilv
d
tdt
of serially connected elements - springs
and silencers has been described. For the
purposes of this study nonlinear deformation (third degree) of the compression
material has been selected. Assumed values of the elasticity constants of the fabric kh1, kh2, kv1 and kv2 describing e the
deformation of the third degree for the
sample selected, were determined on the
basis of the results given in [8]. The relationships between compressive forces Nh
and deformations uh in the fabric layer
between the foot and gripper’s movable
part (Figure 4.a) have been assumed in
the following form:
for uv > 0 and Lh ≤ 0.001
Nv = 0 for uv ≤ 0
where Nh denotes the force that compresses the fabric between the foot and
(13)
the gripper’s movable part, Nv the force
d2 x v
dx
d
x v hsvsv
=
, dϕ 2 = 0
that compresses the package of fabrics
dϕ v
2π
v
lying on the table, (kh1, kh2, kv1, kv2) elasticity constants, cth, ctv damping coeffiEmploying the formula that defines a decients, uh, uv compression, gt thickness
rivative of the complex function:
of one layer of fabric, nilh = 0, 1 or 2 [6]
2
dx
d2 x v d2 ϕ v d
x v  dϕ v  d 2 x v
the number of layers of the compressing
=
+

(14)
d
t  dϕ 2v
d
tdt2
d
tdt2 dϕ v  dt
fabric between the foot and gripper belt,
n
ilv the number of layers in the stack, Lt
which after taking into account relations
the
total length
of the fabric lying on the
k h1
k h2
d
u h
(13) and after substituting to equations
3
uh + cLthth the
Nh =
uh +
table,
length
of fabric lying on the
L
L
(11), we obtain the second order differd
t
gtnilh + gt t
gt nilh + gt t table calculated by the formula (5a [6]),
ential equations:
Ltvtv
L tv
Ltv length of the compression fabric lok
k
d
u
du
3
h
1
h
2
h
2
2
N
uh +
uh + c th
=
cated between the foot and belt (5b [6]).
h sh
h
 h sh
sh
sh  d ϕ h
Lt
L
d
t
dt
= Mmh
msh
m
h − Nh
sh 
 2π  d
gtnilh + gt t
2
2π gtnilh + gt L
(17)
 tdt

LLtvtv
uh = nilhgt - rdh,
tv
(15)
2
2
hsv
 h ssv
uv = uv1 + uv2 + ... + uvn (19)
for uh > 0
sv
v  d ϕv
= Mmv
− Nv

msvsv 
m
v
Nh = 0 for uh ≤ 0
uv = nilvgt - rdv
2π
tdt2
 2π  d
,
dϕ h2
=0
FIBRES & TEXTILES in Eastern Europe 2014, Vol. 22, No. 2(104)
81
In the sample the normal forces Nh and
Nv compress for rdh < gt, rdv < gt, where
gt stands for the thickness of one layer of
the fabric. If rdh ≥ gt and rdv ≥ gt then the
forces Nh = 0 and Nv = 0. In Figure 6
uv1 = uv2 = ... = uvn denotes compressions
of subsequent fabric layers, whose thicknesses are equal to gt1 = gt2 = ... =gtn;
rdh is the distance between the foot and
the gripper’s movable part, calculated
with relationship (20); rdv is the distance
of the gripper from the table, calculated
with relationship (20), where x0h and x0v
mean distances rdh and rdv at the initial
time instants.
The logic feedbacks controlling the gripper’s operation and stating that if the
compressive forces are lower than the
assigned forces Nh < Nset and Nv < Nset,
then the values of the supply voltage increases by Δeh (eh := eh + Δeh) and Δev
(ev := ev + Δev), have been introduced
into the computer program. On the other hand, if Nh > Nset and Nv > Nset, then
eh := eh - Δeh and ev := ev - Δev. Nset denotes the force with which the gripper
should act on the fabric. Simultaneously
the current intensity cannot exceed the
admissible value.
The increment values of the electromotive forces Δeh and Δev in the following
steps are expressed as products of current electromotive forces eh and ev, increases in forces ΔNh and ΔNv relative to
the setpoint force (ΔNh = Nh - Nset and
ΔNv = Nv - Nset), integration step Δt and
numbers εh and εv, agreed in order to
reach a converging solution:
Δev=ev·ΔNv·Δt·εv
Δeh=eh·ΔNh·Δt·εh
-2
x10
(24)
where Tm denotes the motor time constant, cm - motor rigidity, Ωm - motor
angular velocity at which the moment is
equal to zero, im - current intensity, Lm inductance, Rm - resistance, em - supply
voltage, Kbm, Ktm - motor constants, and
φ1 - angle of rotation of the motor.
Assumptions for
the calculation and results
The computer program simulates the
work of the gripper, extended by equation
(4 - 8), as described in [6] and (1 - 24).
Appropriate parameters for the gripper,
motors and textiles have been selected as
follows:
ndimensions: r1c = 0.0062 m,
r2c = 0.0138 m, Rc = 0.0116 m,
x0v = 0.008 m, x0h = 0.008 m,
n mass moment of inertia of the guide
roller belt: I2c = 55·10-7 kgm²,
n masses of relevant parts of the gripper: msh = 0.18 kg, msv = 0.25 kg,
n pitch of the screw h = 0.002 m,
n gear ratio j = 4,
n weight of one layer of the fabric
mtk = 0.02 kg, length of one layer of
the fabric Lt = 0.4 m, coefficient of
friction of the belt to the fabric
μp = 0.3, the number of layers of fabric in the stack nilv = 4, thickness of
compression fabric: gt = 0.002 m,
n elasticity constants of textile:
kv1 = kh1 := 1·105 N/m;
kv2 = kh2 := 1·1011 N/m3,
n damping coefficients
cv = ch = 0.01 Ns/m;
nnumber εv = εh = 18.48, integration
step Δt = 4.51·10-5.
7.22
MMmm,[Nm]
Nm
(21)
Tm =
5.42

d
M m
1  
dϕ 
dM
=
c m  Ωm − 1  − Mm  (23)
d
t
Tm  
d
t 
dt
dt

0.09
t [s]
t, s
The motor has been assumed as follows:
n An electric motor for driving the rollers which lead the belt (item 4, Figure 1 in [6]) characterised by:
constant voltage Kb = 0.038 V/(rad·s),
constant torque Kt = 13.2 Nm/A,
resistance R = 343 Ω, inductance
L = 53·10-3 H, supply voltage e = 25 V
and mass moment of inertia of the rotor I1c = 5·10-8 kgm².
n The electric motor initiating the vertical
movement of the gripper (item 9, Figure
1 in [6]) is characterised by:
constant voltage Kbv = 0.038 V/(rad·s),
constant torque Ktv = 0.33 Nm/A,
resistance Rv = 343 Ω, inductance
Lv = 53·10-3 H, supply voltage
ev = 10 V.
n The electric motor initiating the horizontal movement of the gripper (item
18, Figure 1 in [6]) is characterised
by:
constant voltage Kbh = 0.038 V/(rad·s),
constant torque Kth = 0.33 Nm/A,
resistance Rh = 343 Ω, inductance
x10
1.22
1.18
0.86
1.10
0.98
0.86
0.54
0.22
0.05
Figure 5. Time history of the motor torque
Mm [Nm] used for driving the rollers leading the belt.
1.50
The equations of moments of the motors:
driving the rollers which lead belt 4, initiate the vertical motion of gripper 9, and
initiate the horizontal motion of the gripper 18, as shown in Figure 1 in [6], are
expressed by the formulas:
0.01
-3
-3
x10
(22)
6.62
6.02
Mmv, [Nm]
Nm
d
rdrdh hsh dϕ h
du h
du
= − dh = sh
,
d
t
d
t
2π dt
d
t
dt
dt
d
rdr
h dϕ v
du v
du
= − dvdv = svsv
d
t
d
t
2π dt
d
t
dt
dt
82
Kbmbm
K tm
Lm
tm ·⋅ K
, cm = R
,
Rm
m
M
e
Ωm = m , im = m
K
Kbm
tm
tm
b
m
ϕh
ϕv
hsvsv (20)
hsh
v = x0v −
sh , rddv
2π
2π
MMmh
, Nm
mh[Nm]
rdh
dh = x 0h −
0.01
0.05
t [s]
t, s
0.09
0.74
0.59
1.49
t [s]
t, s
-2
x10
Figure 6. Time history of the motor torque Mmh and Mmv in Nm used for initiating the horizontal and vertical movement of the gripper.
FIBRES & TEXTILES in Eastern Europe 2014, Vol. 22, No. 2(104)
-4
x10
1.80
uuvv,[m]
m
u huh[m]
,m
3.01
2.01
1.20
0.60
1.01
0.01
Reducing pressures necessary to maintain the fabric is achieved by increasing
the contact surface of the respective elements of the gripper.
-6
x10
4.01
0.01
0.05
t [s]
t, s
0
0.09
0.59
1.49
t [s]
t, s
x10
-2
Figure 7. Time history of the compression of the material uh and uv in m.
Computer programs describing the work
of grippers for textiles allow analysis of
the behavior of the system, which shortens the design process of the device.
Modelling studies showed that there is a
possibility to choose relevant parameters
of these mechanisms.
20.68
N
Nhh, m
[m]
Nvv, m[m]
N
17.47
14.68
11.47
8.68
2.68
The model of the gripper developed,
which is characterized by an increased
working surface, was granted a patent as
an invention on 31.01.2008 [9].
5.47
0.01
0.05
t [s]
t, s
0.09
0.47
0.59
1.49
t t,[s]s
-2
x10
Figure 8. Time history of the compressing force on the fabric layer located between the
gripper and foot Nh in N and of the stack of the fabric Nv in N.
Lh = 53·10-3 H, supply voltage
eh = 10 V.
Simulation calculations were carried out
for various parameters and the results
obtained are shown in the graphs (Figures 5 - 8).
Graphs (Figure 8) show that compressive forces Nh & Nv achieve a maximum
value, then decrease and stabilise with
time until reaching a constant setpoint
value Nset.
It has been observed that the stabilisation
of parameters up to the value of the force
assigned Nset takes place sooner for the
vertical direction than for the horizontal
one, whereas the values of the compressive forces Nv and Nh that cause the deflection of the fabric are close.
These plots illustrate the rhelogical reaction of the fabric to the gripper operation.
Under the influence of the forces the fabric is compressed in the stack uv between
the gripper and foot uh (Figure 7), the
values of which, as for forces Nh & Nv
stabilise in time and cause compression
in the range of 0.05%.
FIBRES & TEXTILES in Eastern Europe 2014, Vol. 22, No. 2(104)
Entering the edge of the fabric between
the respective elements of the gripper
was realised by using the endless belt and
then pulling the fabric by the force of
friction in the direction of the blockage
place where the fold entering between
the belt and foot is formed.
nConclusions
A mathematical model of the gripper
separating fabric from a stack has been
developed and the phenomena of separation actions of the layer examined. The
assumptions made have been confirmed.
Thanks to the motors, whose torques are
controlled as a function of the size of the
pressure, the gripper exerts a sufficient
force on the separating fabric to prevent
the slipping out of fabric while not exceeding the limit values which may cause
damage to the fabric.
A force value Nzad was established that
the gripper would exert on the separating fabric to prevent it from slipping
out while not exceeding the limit force.
This is achieved by replacing the clamping spring in appropriate elements of
the gripper and having an electric motor
whose torque is controlled as a function
of the size of the pressure.
The feedback adjusts the value of electromotive forces eh and ev, and consequently the values of the current intensity
ih and iv and driving torques motors Mmh
and Mmv are obtained.
References
1. Fort J. Darnieulles, France: Gripper for
Textile Cloth or The Like; Patent Number: 4,526,363; Date of Patent: Jul. 2,
1985.
2. Keeton JH. Cloth Pickup and Folding
Head; Patent Number: 4,444,384; Date
of Patent: Apr. 24, 1984.
3. Fort J. Darnieulles, France: Gripper for
Textile Layer or The Like; Patent Number: 4,697,837; Date of Patent: Oct. 6,
1987.
4. Stasik K. Mathematical Model of a Mechatronic Pinch-Type Gripper for Textiles. Fibres & Textiles in Eastern Europe
2005; 13, 1, 49: 67-70.
5. Stasik K. Mathematical Model of a Mechatronic Parallel Finger Gripper for Textiles. Fibres & Textiles in Eastern Europe
2005; 13, 2, 50: 73-75.
6. Stasik K. Method of Separating Fabric
from a Stack – Part 1. Fibres & Textiles
in Eastern Europe 2014; 22, 1, 103: 103107.
7. Zajączkowski J. Modelling of Dynamical
Properties of Textiles Under Compression. Fibres & Textiles in Eastern Europe
2000; 8, 1, 28: 57-58.
8. Robak D.: Dynamics of Transport Fabric in the Process of Sewing (in Polish), Ph. D. Thesis, Technical University
of Łódź, Department of Mechanics of Textile Machines, 2003.
9. Zajączkowski J, Stasik K. Device
for Gripping a Single Layer from the
Material Stack (in Polish), Patent PL
197 340, 31.01.2008.
Received 23.05.2012
Reviewed 04.07.2013
83