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The Open Mechanical Engineering Journal, 2014, 8, 219-223 219
1874-155X/14 2014 Bentham Open
Open Access
Kinematics and Force Analysis of Lifting Mechanism of Detachable
Container Garbage Truck
Shanzeng Liu* and Lianjie Zhang
School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, P.R. China
Abstract: The kinematics and force analysis of the lifting mechanism of the detachable container garbage truck is
performed in this article. First of all, the structural features and working mechanism of detachable container garbage truck
are introduced. Then, for each working condition of the DCG truck, kinematic models are established, and the force
analysis of the lifting mechanism is performed. Finally, the movement of a 20 ton DCG truck is calculated and analyzed
as an example. This study provides a theoretical basis for the optimized design of DCGgarbage truck.
Keywords: Detachable container garbage truck, lifting mechanism, kinematic analysis, force analysis.
1. INTRODUCTION
With the rapid economic and social development in
China, the amount of garbage increases dramatically every
year. Many large cities are besieged by garbage. How to
quickly and efficiently treat the municipal solid waste
becomes a major problem confronted by us. DCG truck is a
high-efficiency waste transfer vehicle which consists of
automobile chassis, lifting mechanism and a garbage
container [1, 2]. The lifting mechanism (namely, link
mechanism) performs the functions of automatic loading and
unloading of the container and garbage dumping. It is now
widely applied in garbage treatment as well as in the loading,
transport and unloading of a variety of commodities [3, 4].
At present, the commercially available DCG trucks on
China's market are small tonnage vehicles (3 ton or 5 ton).
The trucks are usually designed by surveying and drawing or
empirical value setting, which severely restricts the
improvement of the product performance and the promotion
of market application [5, 6].
The structural features of the DCG truck are analyzed,
and its working mechanism is also analyzed. The kinematic
and mechanical models are established corresponding to the
loading and unloading of the DCG garbage truck. Using a 20
t DCG truck as an example, the kinematic and mechanical
models are analyzed and solved.
2. STRUCTURE AND WORKING MECHANISM
The DCG truck is divided into three types, a straight arm
type, swing arm type (Fig. 1) and a slide type. The structural
diagram of the lifting mechanism of the swing arm type is
shown in Fig. (2).
In Fig. (2), point A is the hinge joint between the
auxiliary frame and lifting cylinder 1; point B is the hinge
joint between the guide pulley of auxiliary frame 7 and the
auxiliary frame; point C is the contact point between the
*Address correspondence to this author at the School of Mechatronic
Engineering, China University of Mining and Technology, Xuzhou 221116,
P.R. China; Tel: +8615252026399; E-mail: liushanzeng@163.com
guide pulley of auxiliary frame 7 and the bottom of garbage
container 6; point D is the hinge point between the flip frame
3 and the lifting arm 4; point E is the hinge point between
the lifting arm 4 and the lifting cylinder 1; point F is the
hinge point between the swing arm cylinder 2 and the lifting
arm 4; point G is the hinge point between the swing arm 5
and the lifting arm 4; point H is the hinge point between the
swing arm cylinder 2 and the swing arm 5; point M is the
hinge point between the hook on the swing arm 5 and the
hook on the garbage container 5; point R is the contact point
between the roller on the bottom of garbage container 6 and
the ground 9.
Fig. (1). Detachable container garbage truck.
The DCG truck has four working conditions: loading,
transport, garbage dumping and unloading. The principle of
container unloading for the swing arm type is described as
follows [7]: the swing arm cylinder 2 stretches, then rotates
by a certain angle and pushes the garbage container 6
backwards. After the completion of the action of swing arm
cylinder the lifting cylinder 1 stretches again to lift the lifting
arm 4 and the swing arm 5 so that the bottom of the garbage
container comes in contacts with the guide pulley 7 of
auxiliary frame and moves backwards. When the roller 8 at
the rear of the garbage container gets into contact with
ground 9, the bottom of the garbage container is detached
from the guide pulley of the auxiliary frame. The rear roller
on the garbage container enables the container to roll on the
220 The Open Mechanical Engineering Journal, 2014, Volume 8 Liu and Zhang
ground. In this way, the garbage container is unloaded onto
the ground. The working mechanism of container loading is
identical with that of container unloading, but in a reverse
sequence. To dump the garbage, a locking mechanism locks
the lifting arm and flips frame 3 together. When the lifting
cylinder stretches, the lifting arm rotates around the hinge
point B together with the auxiliary frame. Therefore, the
garbage is dumped.
1. Lifting cylinder, 2. Swing arm cylinder, 3. Flip frame, 4. Lifting arm, 5.
Swing arm, 6. Garbage container, 7. Guide pulley of flip frame, 8. Container
roller, 9. Ground
Fig. (2). Structural diagram of the lifting mechanism.
3. KINEMATIC AND FORCE ANALYSIS
To facilitate the analysis of the system of DCG truck, the
following simplification and assumptions are made:
(a) Due to the large weight of the fully loaded garbage
container, the weight of the lifting mechanism has
little influence on the result of force analysis.
Therefore, the weight of each component of the
lifting mechanism is ignored.
(b) The speed of container loading and unloading is slow,
and therefore the influence of the inertia force of the
container is ignored.
(c) The hydraulic cylinder is considered to make uniform
motion, and the influence of hydraulic power is
ignored.
(d) The deformations of chassis, ground and tires under
stress are ignored.
The unloading process of an ordinary detachable
container garbage truck can be decomposed into two stages.
The first stage involves the placing of the garbage container
onto the guide pulley of auxiliary frame. The second stage is
the detachment of the bottom of container from the guide
pulley and the contact of the roller of the container on the
ground [6, 7].
3.1. Kinematic Model of the First Stage
The working condition of the first stage of unloading is
shown in Fig. (3). In this stage, the flip frame and the
auxiliary frame are tightly combined together via a locking
mechanism. The swing arm has flipped by an angle of ρ° and
is static relative to the lifting arm [6-8]. The lifting cylinder
stretches, and the lifting arm rotates around point D, thereby
pushing the garbage container backwards. At the moment,
the bottom of the container is supported by the guide pulley
of the auxiliary frame. The container slides backwards along
the guide pulley.
Fig. (3). Schematic diagram of the movement in the first stage.
The direction parallel to the ground is taken as the X-axis,
and the direction perpendicular to the ground is the Y-axis.
The rectangular coordinate system is established with the
position of point B along X-axis as the origin. The garbage
container is treated as a standard cuboid, whose geometric
center is the center of gravity O. The coordinates of each
point are shown below:
x
E
=x
D
−l
DE
cos(
α
+
θ
−
β
1
)
y
E
=y
D
+l
DE
sin(
α
+
θ
−
β
1
)
%
&
'
(
'
(1)
x
G
=x
E
−l
EG
cos(
α
-
ϕ
)
y
G
=y
E
+l
EG
sin(
α
-
ϕ
)
$
%
&
'
&
(2)
xF
2
=xG−lF
2
Gcos(
α
+
ρ
)
yF
2
=yG+lF
2
Gsin(
α
+
ρ
)
$
%
&
'
&
(3)
x
M
=x
F
2
+l
MF
2
sin(
α
+
ρ
)
y
M
=y
F
2
+l
MF
2
cos(
α
+
ρ
)
#
$
%
&
%
(4)
x
R
=x
M
+l
MR
cos(
γ
2
+
γ
)
y
R
=y
M
−l
MR
sin(
γ
2
+
γ
)
#
$
%
&
%
(5)
x
P
=x
M
+l
MP
sin
γ
2
y
P
=y
M
+l
MP
cos
γ
2
"
#
$
%
$
(6)
x
O
=x
P
+x
R
2
y
O
=y
p
+y
R
2
!
"
#
#
$
#
#
(7)
α
=ar cos lED
2+lAD
2−lAE
2
2lEDlAD
−
θ
,
γ
2=arcsin yM−yC
lMC
−
γ
1
Lifting Mechanism of Detachable Container Garbage Truck The Open Mechanical Engineering Journal, 2014, Volume 8 221
where (xD, yD), (xE, yE), (xG, yG), (xF2, yF2), (xM, yM), (xR, yR),
(xP, yP) and (xO, yO) are the coordinates of points D, E, G, F2,
M, R, P and O, respectively; α is the angle by which the
lifting arms flips in the first stage; θ and φ are the inclusion
angles of DE and EG segments on the lifting arm with
respect to X axis, respectively, when the lifting arm rotates
by zero degree; γ is the inclusion angle between MR and SR;
γ1 is the inclusion angle between MC and SC; γ2 is the
inclusion angle between the bottom of garbage container and
the X-axis; lDE and lEG are the lengths of DE and EG
segments on the lifting arm, respectively; lMR and lMP are the
lengths of MR and MP, respectively.
The force analysis is made on the lifting mechanism and
garbage container of the truck. The force F1 of lifting
cylinder in the first stage is expressed as follows.
F
1
=
sin
γ
2
+
µ
1
cos
γ
2
( )
y
M
−y
D
( )
y
E
−y
D
( )
cos
β
−x
E
−x
D
( )
sin
β
+
$
%
&
&
(G
I
1
+
µ
1
sin
γ
2
−cos
γ
2
)(x
M
−x
D
)
(y
E
−y
D
)cos
β
−(x
E
−x
D
)sin
β
$
%
&
&
&
&
I
1
(8)
I1=G(xO−xM)
µ
1lMS +xM−xC
( )
2+yM−yC
( )
2−lMS
2
where β is the inclusion angle between the lifting cylinder
AE and X-axis; µ1 is the coefficient of sliding friction
between the bottom of garbage container and the guide
pulley; G is the total weight of garbage container fully
loaded; lMS is the distance from the suspension point M on
the swing arm to the left lower endpoint S of the garbage
container; γ2 is the inclusion angle between the bottom of
garbage container and the X-axis.
3.2. Kinematic Model of the Second Stage
The working condition of the second stage of unloading
is shown in Fig. (4). During the second stage, it is ensured
that there is no collision and interaction between the guide
pulley of the auxiliary frame and the roller R on the garbage
container. This places certain requirements on the parameters
of lifting mechanism [6-8].
Fig. (4). Schematic diagram of the movement of the second stage
The force analysis is carried out on the lifting mechanism
and the garbage container. Thus, the force acting on the
lifting cylinder in the second stage is F2:
F
2
=
µ
2
(y
M
−y
D
)+( G
I
2
−1)(x
M
−x
D
)
"
#
$%
&
'I
2
(y
E
−y
D
)cos
β
−(x
E
−x
D
)sin
β
(9)
I2=G(xO−xM)
xR−xM+
µ
2(yM−h0)
where, µ2 is the coefficient of sliding friction between the
roller on the right lower end of the garbage container and the
ground; h0 is the vertical distance from the roller of the
garbage container to the ground in container unloading [6-8].
3.3. Kinematic Model of Garbage Dumping
The working condition of garbage dumping is shown in
Fig. (5). At the moment, the lifting arm and the flip frame
are combined together and rotate around point B.
Fig. (5). Mathematical model of garbage dumping.
The thrust exerted by the lifting cylinder is F3 when the
garbage is dumped. From the force analysis, it can be
obtained that
F
3
=G(x
B
−x
O
)
I
3
(10)
I
3
=(y
E
−y
A
)x
B
+(x
A
−x
E
)y
B
+x
E
y
A
−x
A
y
E
(y
E
−y
A
)
2
+x
E
−x
A
( )
2
where, (xA, yA) and (xB, yB) are the coordinates of point A and
point B, respectively.
4. CALCULATION ANALYSIS
Based on the analysis with the mathematical model
established above for the swing arm type DCG truck, the
kinematics and force of the 20 T garbage truck are solved.
The technical parameters of a 20 TDCG truck are shown in
Table 1 [8].
The curve of the angle by which the lifting arm rotates is
shown in Fig. (6). When the garbage container is unloaded,
the lifting arm rotates from 0° to 134°. That is, when the
garbage container is unloaded, the lifting arm has to rotate
by 134°. The movement trajectory of the center of gravity is
shown in Fig. (7). It can be seen that the X-coordinate of the
center of gravity of the garbage container changes from -
1467 mm to 3655 mm, while the Y-coordinate changes from
2562 mm to 1219 mm.
222 The Open Mechanical Engineering Journal, 2014, Volume 8 Liu and Zhang
Table 1. Technical parameters of 20 T detachable container
garbage truck.
Item
Parameter
Tonnage
20 T
Rated loading weight (kg)
17750
Dumping angle (°)
≥45
Loading/unloading time (s)
≤60
Size (excluding the container):
Length×width×height (mm)
9525×2500×3150
Wheelbase (mm)
1850+3400+1350
Front suspension/rear suspension (mm)
1500/1425
Angle of approach/departure angle (°)
30 / 15
Height of hook center (mm)
1570
Fig. (6). Variation curve of the angle of lifting arm.
Fig. (7). Curve of the position of the center of gravity of container.
When the garbage container is unloaded, the force acting
on the lifting cylinder in the first stage is shown in Fig. (8).
When the lifting cylinder starts to move, the force acting on
it is -4.61×105 N. When the lifting cylinder stretches, the
force acting on it increases gradually. At 18.3 s, the force
reaches the maximum of 2.83×105 N. The force acting on the
lifting cylinder in the second stage is shown in Fig. (9). At
the beginning of the second stage, the force on the lifting
cylinder reduce sharply from 2.83×105 N by the end of the
first stage (t=18.3 s, the boundary between the first stage and
the second stage) to 4.90×104 N. After that, it increases
gradually again. At t=44 s, the force acting on the lifting
cylinder is the maximum of 7.33×105 N when the garbage
container is dumped onto the ground.
Fig. (8). Force curve of the lifting cylinder in the first stage.
Fig. (9). Force curve of the lifting cylinder in the second stage.
When the garbage is dumped, the rotation angle of the
flip frame and the garbage container is the dumping angle.
The variation curve of the dumping angle is shown in Fig.
(10). During garbage dumping, the dumping angle gradually
increases from 0° to the maximum of 45.5°. The movement
trajectory of the center of gravity of container during
dumping is shown in Fig. (11). The X-coordinate of the
Fig. (10). Variation curve of dumping angle.
Lifting Mechanism of Detachable Container Garbage Truck The Open Mechanical Engineering Journal, 2014, Volume 8 223
center of gravity of container changes from -1396 mm to -
121 mm, while the Y-coordinate changes from 2510 mm to
3147 mm.
Fig. (11). Position curve of the center of gravity of garbage
container.
During garbage dumping, the Y-coordinate of the highest
point of the container (t upper left point) is shown in Fig.
(12). For various working conditions, the highest point is
found during garbage dumping. When the lifting cylinder
stretches completely, the upper left point of the garbage
container has the maximum Y-coordinate of 6028 mm. That
is to say, the maximum height above the ground is 6028 mm.
Fig. (12). Y-coordinate of the highest point of the garbage
container.
The force acting on the lifting cylinder during garbage
dumping is shown in Fig. (13). The maximum force of
5.49×105 N acting on the lifting cylinder occurs at the initial
time during garbage dumping. The force gradually reduces
to 8195 N as the lifting cylinder stretches.
CONCLUSION
(1) The kinematic and mechanical models of the lifting
mechanism are analyzed during the two stages of
unloading and under the working condition of
garbage dumping.
(2) Using 20 T swing arm DCG truck as an example, the
kinematics and force conditions of the lifting
mechanism are calculated and analyzed.
Fig. (13). Force curve of the lifting cylinder.
CONFLICT OF INTEREST
The authors confirm that this article content has no
conflict of interest.
ACKNOWLEDGEMENTS
Project (2014QNB18) supported by the Fundamental
Research Funds for the Central Universities of China.
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Received: July 25, 2014 Revised: August 4, 2014 Accepted: August 4, 2014
© Liu and Zhang; Licensee Bentham Open.
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