Article Type : Research Article
Authors : Run Xu
Keywords : Numerical simulation; Force and angle; Angular speed and acceleration
In robot design and
application the force and angle with angular speed is important so this study
will model numerical simulation and discuss detail data to investigate their
property. The force may increase as arm 1 angle increases whilst it may
increase if angular speed increases in three freedoms. Meantime it will
decrease if angular acceleration increases. It is found that with the angular
speed increasing all three force may increase whilst the angular acceleration
will cause its increase too in five freedoms. From these value it is observed
that F2 and F1 is prior one to ensure the strength and fatigue life then F3 is
second one to estimate its strength whilst F3 may be neglected. The force may
increase as arm 1 angle increases whilst it may increase if angular speed
increases in three freedoms. Meantime it will decrease if angular acceleration
increases. There is big distance to attain 5KN between the conditions. The
effective factor turn to the force is F1>F3>F2 in three freedoms. The
force may increase from 30N to 18KN and 20KN with F3, F1 and F2 in five
freedoms. Among them F3 is the least one and F1 is the biggest one. The effect
factor turn is F2 >F1 >F3. So the F2 &F1 is important one while F3 is
neglected.
In recent the robotic arm
has been applied to many occasion in factory which can help people to work in
difficult, dirty and dangerous place so its application will be more prevailed
in future which is estimated in this study. China has been the largest country
which can own the largest domestic market in the world, but it has the third
market occupant since it has been not owning the enough advanced condition. So
that we must positively construct the clean and criteria house to meet the
demand for robotic arm to ensure precise work [15]. In robotic design the
force is an important factor to consider since the strength must meet demand no
matter what it may work in factory. So that according to the function it may be
designed to satisfy the no fracture and longer fatigue life for its long life
and high load to work in automatic flow line to be substituted to human worker.
The biggest one will destination in this paper and how to save manufacture cost
is the second one. So it is needed that the mass and load may become first
thing to prepare; secondly for the cost decrease the redundant load shall be
prohibited. In this paper the condition is changed like angular speed and
acceleration to observe the three forces status to ensure security of strength
and save cost status. The three freedoms and five ones are investigated in this
paper detail with parameters like force and angle with angular speed and
acceleration. We try to find the various condition of effective factor in order
to search intrinsic properties relationship which is the destination in this
paper. In short the properties are searched through parameters in detail. We
look forward to finding new change with force and speed & acceleration for
further research.
In Figure 1 there are
three freedoms in mechanical arm that name as 1~3. Meantime there are two other
ones call 4&5which is included in five freedoms as a rotational and
crawling function. In Figure 1 the schematic shows the simplified principle of
robot. The coordinate XAY is three freedoms and X?A?Y it five freedoms. In this
study the five freedoms not three one is deduced since it is complicated
(Figure 1,2).
Figure 1: construction schematic of mechanical arm in series in robot 3hand part; 2wrist part; 1arm part; 4waist part; 5two crawling wheel.
Figure 2: Principle schematic of mechanical arm in series in robot.
(a) F1.
(b)
F2.
Figure
3:
The curve of force and angle with various angular speed and acceleration of 25,
30º/s2 in three freedoms of robot arm.
(a) F1.
(b) F2.
Figure
4:
The curve of force and angle with various angular speed and acceleration of 25,
30º/s2 in five freedoms of robot arm.
As seen in Table 1 the
parameter in robot arm is listed. [6~7] Here ?1, ?2, ?3 is the arm1, arm2, arm3
angle respectively. l1, l2, l3 is arm length. m1, m2, m3 is arm mass. Number is
arm label. According to these parameters the below curves are gained as below
in Figure 3 &4. As seen in Figure 3(a~c) the force of arm1 will increase
with the angular speed and acceleration increasing that expresses the
proportional relation between them fitting to Newton theory well. That says
that angular speed raises the acceleration meantime the later raise the force
too. They all distributes into sinusoidal continuous wave that forms semiwave
with 90º. The force may increase from 30N to 18KN and 20KN with F3, F1 and F2.
Among them F3 is the least one and F1 is the biggest one. The effect factor
turn is F2 >F1 >F3 in Figure 4 in three freedoms. From these value it is
observed that F2 is prior one to ensure the strength and fatigue life then F1
is second one to estimate its strength whilst F3 may be neglected. In contrast
to it in Figure 3 the F1 is 18KN which is main parameter to check the robotic
arm and F3 is second one and finally F2 is 20N which may be neglected in five
freedoms system. The effect turn is F2>F1>F3 here (Table 1).
Table 1: Parameters of robot arms.
items 
Value 
Item 
Value 
l1 /m 
0.55 

30~60 
l2 /m 
0.5 

30~60 
l3 /m 
0.3 

30~60 
m1/N 
7.7 

25,30 
m2/N 
6.6 

25,30 
m3/N 
4.0 

25,30 
As seen in Figure 3 the
force may increase as arm 1 angle increases whilst it may increase if angular
speed increases in three freedoms. Meantime it will decrease if angular
acceleration increases in Figure 3(d). The maximum is 18KN in Figure 3(a) if
angular speed is 35~60º/s and acceleration is 25~30º/s2 so this point will be
checked to ensure the robotic arm strength. There is big distance to attain 5KN
between the conditions. The effective factor turn to the force is
F1>F3>F2 in three freedoms (Figure 3).
In the modeling of five
freedoms in movement of robotic arm the kinetic equation is established
according to Lagrange formula based on three freedoms robotic arm. It
compensates the blank in four freedoms and one impulsion on robot. It is found
that the first and second solution is complicated and long the whole equations
is concise than the traditional equation. This is a blank in five freedoms
which can shorten the whole numerical computation a lot. Referring to the
important occasion the kinetic equation will only be computed on three freedoms
according to this study (Figure 4).
It is suggested that the
big arm happens when angular speed and acceleration is big. So that the
reasonable parameters are chosen to design and estimate their properties is
important. Not to choose big angular speed and acceleration is key in order to
increase the capability and property that may increase the whole cost as well. Overview
the computation is shorter than the five freedoms traditional one. The solution
is easy to use in software like Excel and Origin. The result is satisfactory
and precise to be adopted to numerical simulation so the five freedoms method
based on three freedoms is feasible.