The Numerical Simulation of Forces with High Angular Speed and Low Angular Acceleration in Three and Five Freedoms of Robotic Arm I

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.

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.

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.

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