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Improvement and Control Trajectory Tracking of a Three-Axis Manipulator for New Training Strategies

Patryk MIETLIŃSKI

Patryk MIETLIŃSKI

Faculty of Mechanical Engineering, Division of Metrology and Measurement Systems, Poznan University of TechnologyPoznań,
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MIETLIŃSKI, Patryk
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Michał JAKUBOWICZ

Michał JAKUBOWICZ

Faculty of Mechanical Engineering, Division of Metrology and Measurement Systems, Poznan University of TechnologyPoznań,
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JAKUBOWICZ, Michał
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Lidia MARCINIAK-PODSADNA

Lidia MARCINIAK-PODSADNA

Faculty of Mechanical Engineering, Division of Metrology and Measurement Systems, Poznan University of TechnologyPoznań,
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MARCINIAK-PODSADNA, Lidia
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Michał WIECZOROWSKI

Michał WIECZOROWSKI

Faculty of Mechanical Engineering, Division of Metrology and Measurement Systems, Poznan University of TechnologyPoznań,
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WIECZOROWSKI, Michał
  
05 wrz 2025
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Data publikacji: 05 wrz 2025
Zakres stron: 380 - 390
Otrzymano: 04 kwi 2024
Przyjęty: 16 cze 2025
DOI: https://doi.org/10.2478/ama-2025-0045
Słowa kluczowe
© 2025 Patryk MIETLIŃSKI et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Fig. 1.

Kinematic diagram of the RRR serial robot
Kinematic diagram of the RRR serial robot

Fig. 2.

Form of the homogeneous transformation matrix; from the left to the right: form of the third joint relative to the robot arm end; form of the arm end relative to the base coordinate system (source: RoboAnalyzer)
Form of the homogeneous transformation matrix; from the left to the right: form of the third joint relative to the robot arm end; form of the arm end relative to the base coordinate system (source: RoboAnalyzer)

Fig. 3.

View of the drawn manipulator trajectory for the maximum extreme position of the robot arm (source: RoboAnalyzer)
View of the drawn manipulator trajectory for the maximum extreme position of the robot arm (source: RoboAnalyzer)

Fig. 4.

Model view of the first manipulator (left side) and view of the finished construction of the first manipulator (right side)
Model view of the first manipulator (left side) and view of the finished construction of the first manipulator (right side)

Fig. 5.

Model view of the second manipulator (left side) and view of the finished construction of the second manipulator (right side)
Model view of the second manipulator (left side) and view of the finished construction of the second manipulator (right side)

Fig. 6.

Control algorithm diagram
Control algorithm diagram

Fig. 7.

Reference geometric view
Reference geometric view

Fig. 8.

View of the robot's workstation when executing predetermined geometries
View of the robot's workstation when executing predetermined geometries

Fig. 9.

Test stand including the Baty Venture XT measuring machine
Test stand including the Baty Venture XT measuring machine

Fig. 10.

View of the test stand during the examination of the second structure using GOM software
View of the test stand during the examination of the second structure using GOM software

Fig. 11.

Value distribution histogram (left side) and distribution of the result values ±3σ (right side) for parallel lines 20 mm apart
Value distribution histogram (left side) and distribution of the result values ±3σ (right side) for parallel lines 20 mm apart

Fig. 12.

Relative error robot – reference
Relative error robot – reference

Fig. 13.

Standard deviation distribution
Standard deviation distribution

Fig. 14.

Variability of measurement results for the analyzed geometries
Variability of measurement results for the analyzed geometries

Fig. 15.

Value distribution histogram (left side) and distribution of the result values ±3σ (right side) for a displacement of 121.2 mm
Value distribution histogram (left side) and distribution of the result values ±3σ (right side) for a displacement of 121.2 mm

Fig. 16.

Distribution of the relative error (left side) and standard deviation (right side)
Distribution of the relative error (left side) and standard deviation (right side)

Calculations of measurement results of element displacement by the robot

Distance 1 Distance 2 Distance 3
84.0 mm 121.2 mm 204.2 mm
Mean 83.883 121.393 204.587
Max 84.518 121.446 204.763
Min 83.490 121.352 204.400
R 1.027 0.094 0.363
σ 0.378 0.027 0.117
A 0.642 0.861 -0.165
K -1.060 -0.526 -1.270
U0.95 0.135 0.010 0.042

Results of geometric measurements made by the robot and their calculations

10 mm 15 mm 20 mm 25 mm 30 mm 90°
Mean 9.711 14.614 19.004 24.448 29.174 90.100
Max 9.911 14.895 19.280 24.794 29.371 91.253
Min 9.450 14.200 18.680 23.825 23.940 88.048
R 0.461 0.695 0.600 0.969 0.431 3.205
σ 0.130 0.191 0.177 0.274 0.135 0.819
A -0.166 -0.171 -0.122 -0.470 -0.381 -0.530
K -0.884 -0.888 -1.127 -0.790 -1.240 -0.336
U0.95 0.047 0.068 0.063 0.098 0.048 0.293

Results of the reference measurements and their calculations

10 mm 15 mm 20 mm 25 mm 30 mm 90°
Mean 9.125 14.356 19.284 24.068 23.904 39.876
Max 9.398 14.604 19.683 24.315 29.143 39.938
Min 8.746 14.143 13.851 23.733 23.624 39.803
R 0.652 0.456 0.832 0.582 0.524 0.135
σ 0.178 0.140 0.189 0.177 0.132 0.034
A -0.589 0.342 -0.093 -0.114 0.104 0.012
K -0.197 -0.743 -0.042 -1.230 -0.120 -0.412
U0.95 0.064 0.050 0.068 0.063 0.047 0.012
Język:
Angielski
Częstotliwość wydawania:
4 razy w roku
Dziedziny czasopisma:
Inżynieria, Elektrotechnika, Elektronika, Inżynieria mechaniczna, Mechanika, Bioinżynieria i inżynieria biomedyczna, Biomechanika, Inżynieria lądowa, Inżynieria środowiska
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