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α1 frame rotation angle for arm attached to motor 1 α2 frame rotation angle for arm attached to motor 2 α3 frame rotation angle for arm attached to motor 3 lA length of upper arm lB length of forearm RA radius from base plate centre to one of the three arms RB radius from traveling plate centre to one of the three forearms J Jacobian matrix for a Delta-3 robot Xn column vector, (x,y,z) T of TCP coordinates expressed in {R} Pai point at the centre of the actuator axis Pbi point between the upper arm and the forearm Pci point at the forearms connection with the traveling plate P vector (x,y,z), the forearms lower connection in simplified model mb mass of upper arm mfb mass of forearm mn mass of traveling plate mnt total contribution mass of traveling plate mc mass of elbow between upper arm and forearm rGb τ mass centre point of upper arm column vector, (τ1, τ2, τ3) T of torques kr gear Ratio for transmission between motor shaft and robot axis. MC-4 drive unit Motor KPpos P gain in the position controller KPvel P gain in the velocity controller KIvel I part in the velocity controller KPcurr P gain in the current controller KIcurr I part in the current controller FFcurr current feed forward Fvel time constant for velocity filter FcurrRef time constant for current ref filter Fcurr time constant for current filter CO controller option, on or off CT cycle time at the SERCOS bus ipeak motors maximum current inom motors nominal current RPMmax maximum shaft rotation Km torque Constant Im J_Internal IBrake J_Brake R W_Resistance L W_Inductivity zp pol pairs Fv viscous friction in motor ______________________________________________________________________________ Public Report ELAU GmbH, Marktheidenfeld 4
Fs static friction in motor GRin gear in GRout gear out ILoad moment of inertia of load τload load force CE current equipment ______________________________________________________________________________ Public Report ELAU GmbH, Marktheidenfeld 5
Page 1: ISSN 0280-5316 ISRN LUTFD2/TFRT--58
Page 5: Acknowledgements This Master thesis
Page 8 and 9: 7 Control approach - ELAU GmbH ....
Page 12 and 13: 2 BACKGROUND 2.1 ROBOTICS The word
Page 14 and 15: 2.2.2 SOFTWARE - ELAU GMBH EPAS-4 i
Page 16 and 17: 3 KINEMATICS - SERIAL ROBOT In the
Page 18 and 19: 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 70 and 71:
In Figure 11.44 the blue line repre
Page 72 and 73:
12 CONCLUSIONS In section 11.1 one
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