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In Figure 11.44 the blue line represents the calculated joint acceleration for arm 2 of the Delta- 3 robot and the red line describes the reference acceleration in EPAS. If one look at the joint velocity of joint 2 there is a smaller percentage deviation (Figure 11.42) between the calculated and the reference value than for joint 1. This is also shown in the acceleration graph for joint 2 where the calculated value match better with the reference value than for joint 1. Figure 11.45, the blue line shows the calculated acceleration and the red line shows the reference acceleration from EPAS. The joint acceleration for the third joint at the Delta-3 robot is shown in Figure 11.45. The blue line represents the calculated joint acceleration with the Jacobian matrix compared with the red line which is the reference acceleration from EPAS. As for joint 1 also the percentage velocity deviation for joint 3 is larger at the time interval where the acceleration deviation is larger. 11.2.4 DISCUSSION When using the Jacobian matrix in EPAS to calculate the TCP velocity respectively the angular velocity for the upper arms one can see a small deviation between the measured value and the calculated value in all three experiments above. The deviation for experiment 1 and 2 is as most 10% and for experiment 2 is the largest deviation around 5%. In general is the arm angle velocity deviation smaller in experiment 2 than for experiment 1 and 3. One reason for this is that the angle velocity of the three arms is smaller than for the two other experiments. If one considers Figure 11.42 (shows the angle velocity deviation in percentage) when looking at the joint acceleration plots for the three arms one can see that where the joint acceleration has a big deviation also the velocity has a larger deviation. Figure 11.44 shows when the calculated velocity has a small deviation also the calculated acceleration will have a very small deviation. A factor which affects the calculated values is the kinematic parameters used in the Jacobian matrix. The kinematic parameters are given from the manufacture of the robot arms and they ______________________________________________________________________________ Public Report ELAU GmbH, Marktheidenfeld 64
also have a small deviation from reality which affects the calculated values. This could be one factor why the calculated value isn’t exact with the reference value from EPAS. Another factor which also affects the results is the singularity of the Jacobian. When the Jacobian becomes more singular the calculated value will also deviate more. These singularities arise when the TCP is near the working surface limits. ______________________________________________________________________________ Public Report ELAU GmbH, Marktheidenfeld 65
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ISSN 0280-5316 ISRN LUTFD2/TFRT--58
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Acknowledgements This Master thesis
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7 Control approach - ELAU GmbH ....
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α1 frame rotation angle for arm at
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2 BACKGROUND 2.1 ROBOTICS The word
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2.2.2 SOFTWARE - ELAU GMBH EPAS-4 i
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3 KINEMATICS - SERIAL ROBOT In the
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3.2 INVERSE KINEMATICS When the for
Page 20 and 21: 4 KINEMATICS & KINETICS - DELTA-3 R
Page 22 and 23: 4.3 Forward Kinematics The forward
Page 24 and 25: Figure 4.5, inverse kinematics tran
Page 26 and 27: where & ⎡x& n ⎤ ⎡− lA sin(
Page 28 and 29: 4.7 ACTUATOR DYNAMICS In most exist
Page 30 and 31: The inertia contribution of each up
Page 32 and 33: According to d’Alembert’s princ
Page 34 and 35: 5 TRAJECTORY A trajectory is a path
Page 36 and 37: 6 TRAJECTORY - ELAU GMBH C600 is th
Page 38 and 39: 6.2 CIRCULAR INTERPOLATION In the E
Page 40 and 41: 7.1 MC-4 DRIVE The MC-4 drive is a
Page 42 and 43: Figure 8.2, Simulink model with mot
Page 44 and 45: 9 PARAMETER ESTIMATION To simulate
Page 46 and 47: 10 EXPERIMENTS For the experiments
Page 48 and 49: Figure 11.2, shows the motion of th
Page 50 and 51: Figure 11.6, shows the current I ef
Page 52 and 53: 11.1.2 SIMULINK EXPERIMENT 2 Figure
Page 54 and 55: Figure 11.13, shows the acceleratio
Page 56 and 57: measured actual value from the real
Page 58 and 59: and are shown over the time in seco
Page 60 and 61: Figure 11.23 shows the x, y and z c
Page 62 and 63: Figure 11.27, the blue line shows t
Page 64 and 65: Figure 11.31, the blue line shows t
Page 66 and 67: In Figure 11.36 the blue line repre
Page 68 and 69: 11.2.3 JACOBIAN EXPERIMENT 3 Figure
Page 72 and 73: 12 CONCLUSIONS In section 11.1 one
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