Article Type : Research Article
Authors : Run Xu
Keywords : Numerical simulation; Force and angle; Angular speed and acceleration; Robotic arm; Angular Acceleration; Three and five freedoms
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 is prior one to ensure the strength and fatigue life then F2 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 15N to 15KN and 18KN with F3, F2 and F1 in five freedoms. Among
them F3 is the least one and F1 is the biggest one. The effect factor turn is
F1 >F2 >F3. So the F1 and F2 is important one while F3 is neglected. With
increasing speed the torque may be decreased and with angular speed becoming
big the torque may be increased. The biggest torque is 10KNm and 25KNm when
angular speed is 25º/s and 60 º/s respectively. This one needs to be checked
the strength correction when the speed is 1m/s. The ?1~3 is supposed to be same
with ? in addition. The effective turn is v2=1m/s>v1=10.5m/s>v3=1.5m/s.
The robotic arm as a new
mechanism has been wielded in factory for semi conduction etc. transportation
and integration circuit wielding. The auto and artificial intelligence robotic
arm is developed from experimental lab to factory to launch producing. Therefore
grasp the robotic arm kinematic and dynamic will become urgent and necessary in
modern society [1-7]. As a multiple system Lagrange equation may be solved its
dynamics which is a method currently. Due to its precision demand in process
the position defining is very important especially to precise part making.
Through defining a route it may be defined a displacement and then the velocity
and acceleration may be defined through the equation besides the force and
torque properties. For our checking strength and making size the dynamical
properties may be used to it. Such as the motor size and arm shape and size
will be checked out to design it. So in this study the dynamic properties may
be calculated through Lagrange equation according to kinematic constant to
check the feasibility on force to function. To separate three independence
parts the velocity and acceleration will be calculated through displacement and
force may be computed meantime with Lagrange equation separately. So each
resolved resolution may be checked through comparing with others and
literature. This is the destination in this paper to arouse the further
research.
In Figure 1 there are
three freedoms in mechanical arm that name as. 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).
The system kinetic energy is [1, 3]
Substituting two
equations above to equation below
Figure 1: Construction schematic of mechanical arm in series in robot 3-hand part; 2-wrist part;1-arm part; 4-waist part; 5-two crawling wheel.
Figure 2:
Principle schematic of mechanical arm in series in robot.
(a) F1.
(a) F2.
(C) F3.
Figure
3: The curve of force and angle with various angular
speed and acceleration at angular acceleration of 20º/s2 in three
freedoms of robot arm.
(a) F1.
(a) F2.
(a) F3.
Figure
4: The curve of force and angle with various angular
speed and acceleration at angular acceleration of 20º/s2 in five freedoms of
robot arm.
(a) ?=25º/s.
(a) ?=60º/s.
Figure 5: The torque with time and speed v under angular speed ? and acceleration ? ? of 20º/s2.
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 |
|
20 |
m2/N |
6.6 |
|
20 |
m3/N |
4.0 |
|
20 |
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 15N to 15KN and 18KN with F3, F1 and F2
as seen in Figure 4. Among them F3 is the least one and F1 is the biggest one.
The effect factor turn is F1 >F2 >F3 at the angular acceleration of
20º/s2. So the F1 is important one attained 1.8Tons and F2 is second attains
1.5tons while F3 is neglected. From these value it is observed that F1 is prior
one to ensure the strength and fatigue life then F2 is second one to estimate
its strength whilst F3 may be neglected in five freedoms. In contrast to above
in Figure 3 in three freedoms the force F1 is about 18KN ie. 1.8tons which is
the biggest need to be checked the strength estimation and then F3 is 75N and
at last F2 is 16N which are neglected here. The effect turn is F1>F3>F2
(Table 1).
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 20º/s and acceleration is 20º/s2 so this point will be checked
to ensure the robotic arm strength. There is big distance to attain 3~5KN
between the conditions. The effective factor turn to the force is
F1>F3>F2 in three freedoms (Figure 3).
In the modelling 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
(Figure 5).
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. In Figure 5 with increasing speed the torque may be
decreased and with angular speed becoming big the torque may be increased. The
biggest torque is 10KNm and 25KNm when angular speed is 25º/s and 60 º/s
respectively. This one needs to be checked the strength correction when the
speed is 1m/s. The ?1~3 is supposed to be same with angular speed ? and angular
acceleration ? ? of 20º/s2 in Figure 5 in addition. The effective turn is
v2=1m/s>v1=10.5m/s>v3=1.5m/s.
· 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 15N to 15KN and 18KN with F3, F2 and F1 in five freedoms. Among
them F3 is the least one and F1 is the biggest one. The effect factor turn is
F1 >F2 >F3. so the F1 and F2 is important one while F3 is neglected.