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Fig. 11- Angular velocities of links and motors with respect to time After that, maximum allowable dynamic payload has been determined along with the obtained ories in the various simulations. The ob dex, operating time and robot charac maximum payload trajectory. As a resul posed method, the designer can choose priate path among the various optimal o designing necessities. Also, the op payload trajectory obtained using this he closed-loop control of the robot mani optimal trajec- ained results il- ustrate the influences of the problem performance in- eristics on the , using the pro- he most appro- paths according imal maximum method can be used as a reference signal and feed forward command in pulators.

Figure 11 - Angular velocities of links and motors with respect to time After that, maximum allowable dynamic payload has been determined along with the obtained ories in the various simulations. The ob dex, operating time and robot charac maximum payload trajectory. As a resul posed method, the designer can choose priate path among the various optimal o designing necessities. Also, the op payload trajectory obtained using this he closed-loop control of the robot mani optimal trajec- ained results il- ustrate the influences of the problem performance in- eristics on the , using the pro- he most appro- paths according imal maximum method can be used as a reference signal and feed forward command in pulators.

Related Figures (8)

Fig. 1 - A two links mobile manipulator with flexible links and joints.
Fig. 1 - A two links mobile manipulator with flexible links and joints.
n this section, various numerical simulations are pre- sented based on the mathematical model describes in the section 2. In these simulations, the robot optimal trajec- ories and corresponding maximum payloads are de- fined based on various parameters such as operating ime, robot characteristics and the problem performance index. Note that in all simulations, the payload is calcu- ated with the accuracy of 0.1 Kg. Also, in all simula- ions the performance index is defined for minimizing he actuating inputs in addition bounding the joint ve- ocities. For this reason, it form as en
n this section, various numerical simulations are pre- sented based on the mathematical model describes in the section 2. In these simulations, the robot optimal trajec- ories and corresponding maximum payloads are de- fined based on various parameters such as operating ime, robot characteristics and the problem performance index. Note that in all simulations, the payload is calcu- ated with the accuracy of 0.1 Kg. Also, in all simula- ions the performance index is defined for minimizing he actuating inputs in addition bounding the joint ve- ocities. For this reason, it form as en
In this case w is assumed to be constant at w=1. The ro- bot path planning problem is investigated by increasing the payload mass until the maximum allowable payload be determined. The maximum payload is obtained as m,= 8.4 kg (case 4). The obtained angular positions, an- gular velocities and torque curves graphs for a range of m, given in Table 2, are shown in Figs. 4-6. It can be found that increasing the m, results to enlarge the veloc- ity values. Also, as shown in figures, increasing the pay- oad increases the required torque until the maximum payload obtained. So that for the last case the torque curves lay on their limits. Hence, it is the most possible values of the torques and increasing the payload is im- possible, because it leads to violate the boundary condi- ions. n the first case, effects of changing in performance in- dex in the path planning problem are investigated. The payload is assumed to be | Kg and simulation is done for the different values of W=(w, w, 0, 0, w, w) and op- imal paths for a given payload are obtained. Note that in this vector, w refers to the velocities of joints and ac- uators and zero refers to the velocities of mode shapes. The simulations are performed for different values of w as 0, 1, 100 and 1000.
In this case w is assumed to be constant at w=1. The ro- bot path planning problem is investigated by increasing the payload mass until the maximum allowable payload be determined. The maximum payload is obtained as m,= 8.4 kg (case 4). The obtained angular positions, an- gular velocities and torque curves graphs for a range of m, given in Table 2, are shown in Figs. 4-6. It can be found that increasing the m, results to enlarge the veloc- ity values. Also, as shown in figures, increasing the pay- oad increases the required torque until the maximum payload obtained. So that for the last case the torque curves lay on their limits. Hence, it is the most possible values of the torques and increasing the payload is im- possible, because it leads to violate the boundary condi- ions. n the first case, effects of changing in performance in- dex in the path planning problem are investigated. The payload is assumed to be | Kg and simulation is done for the different values of W=(w, w, 0, 0, w, w) and op- imal paths for a given payload are obtained. Note that in this vector, w refers to the velocities of joints and ac- uators and zero refers to the velocities of mode shapes. The simulations are performed for different values of w as 0, 1, 100 and 1000.
Fig. 2 - Angular velocities of joints with respect to time
Fig. 2 - Angular velocities of joints with respect to time
Fig. 5- Angular velocities of joints with respect to time In this case, the maximum payload of flexible mobile manipulator is calculated and corresponding optimal tra- jectory at point-to-point motion is illustrated for differ-
Fig. 5- Angular velocities of joints with respect to time In this case, the maximum payload of flexible mobile manipulator is calculated and corresponding optimal tra- jectory at point-to-point motion is illustrated for differ-
ent values of w given in Table 3. The computed torqueses for these cases are plotted in Fig. 7. As it can be seen, increasing w causes to increase oscillatory be- haviors of the systems that results to reduce the maxi- mum dynamic payload as shown in Table 3. Simulation D The effect of time on the calculating of maximum pay- oad is investigated in this section. w is fixed at w=1. The range of times and corresponding calculated maxi- mum payload are given in Table 4. It can be concluded from table, raising the execution time leads to consider- able increase of the obtained maximum payload value. The reason of this issue is that by increasing the execu- ion time the acceleration and velocity of the system are reduced. Hence, the centrifugal and Coriolis forces which applied to the system are decreased and it causes o increase the maximum payload.
ent values of w given in Table 3. The computed torqueses for these cases are plotted in Fig. 7. As it can be seen, increasing w causes to increase oscillatory be- haviors of the systems that results to reduce the maxi- mum dynamic payload as shown in Table 3. Simulation D The effect of time on the calculating of maximum pay- oad is investigated in this section. w is fixed at w=1. The range of times and corresponding calculated maxi- mum payload are given in Table 4. It can be concluded from table, raising the execution time leads to consider- able increase of the obtained maximum payload value. The reason of this issue is that by increasing the execu- ion time the acceleration and velocity of the system are reduced. Hence, the centrifugal and Coriolis forces which applied to the system are decreased and it causes o increase the maximum payload.
reduced. So, the link flexibility affects the robot vibra- tions significantly. Another simulation is carried out to investigate the effect of joint stiffness in the obtained maximum pay- load of the systems. Simulation is performed for a flexi- ble joint manipulator with different values of joint stiff- ness while EI is remained constant at EI=100 kg.m’/s’. K, and the obtained The values of spring constants, maximum payloads are given in ities of links and motors in the Table 6. hat by increasing the joint stiffness va mum payload is increased. Angular positions and veloc- first cas Figs. 10 and 11. It shows that both the lin! ions and velocities have deviations from their respec- ive motor angular positions and veloci It is observed ue, the maxi- e are given in k angular posi- ies. It can be concluded that link and joint flexibility significantly af- fect on the system oscillation and robot behavior. Hence neglecting of such important affects in modeling and control of robots, results in the considerable and irrepa- rable errors in the applicable usage.
reduced. So, the link flexibility affects the robot vibra- tions significantly. Another simulation is carried out to investigate the effect of joint stiffness in the obtained maximum pay- load of the systems. Simulation is performed for a flexi- ble joint manipulator with different values of joint stiff- ness while EI is remained constant at EI=100 kg.m’/s’. K, and the obtained The values of spring constants, maximum payloads are given in ities of links and motors in the Table 6. hat by increasing the joint stiffness va mum payload is increased. Angular positions and veloc- first cas Figs. 10 and 11. It shows that both the lin! ions and velocities have deviations from their respec- ive motor angular positions and veloci It is observed ue, the maxi- e are given in k angular posi- ies. It can be concluded that link and joint flexibility significantly af- fect on the system oscillation and robot behavior. Hence neglecting of such important affects in modeling and control of robots, results in the considerable and irrepa- rable errors in the applicable usage.
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Mechanical EngineeringRoboticsControl Systems EngineeringComputer Science
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