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

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

Acta Mechanica et Automatica
Volume 19 (2025): Issue 3 (September 2025)
By: Patryk MIETLIŃSKI,  Michał JAKUBOWICZ,  Lidia MARCINIAK-PODSADNA and  Michał WIECZOROWSKI  
Open Access
|Sep 2025

Figures & Tables

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 1Distance 2Distance 3
84.0 mm121.2 mm204.2 mm
Mean83.883121.393204.587
Max84.518121.446204.763
Min83.490121.352204.400
R1.0270.0940.363
σ0.3780.0270.117
A0.6420.861-0.165
K-1.060-0.526-1.270
U0.950.1350.0100.042

Results of geometric measurements made by the robot and their calculations

10 mm15 mm20 mm25 mm30 mm90°
Mean9.71114.61419.00424.44829.17490.100
Max9.91114.89519.28024.79429.37191.253
Min9.45014.20018.68023.82523.94088.048
R0.4610.6950.6000.9690.4313.205
σ0.1300.1910.1770.2740.1350.819
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
U0.950.0470.0680.0630.0980.0480.293

Results of the reference measurements and their calculations

10 mm15 mm20 mm25 mm30 mm90°
Mean9.12514.35619.28424.06823.90439.876
Max9.39814.60419.68324.31529.14339.938
Min8.74614.14313.85123.73323.62439.803
R0.6520.4560.8320.5820.5240.135
σ0.1780.1400.1890.1770.1320.034
A-0.5890.342-0.093-0.1140.1040.012
K-0.197-0.743-0.042-1.230-0.120-0.412
U0.950.0640.0500.0680.0630.0470.012
DOI: https://doi.org/10.2478/ama-2025-0045 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088
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Language: English
Page range: 380 - 390
Submitted on: Apr 4, 2024
Accepted on: Jun 16, 2025
Published on: Sep 5, 2025
Published by: Bialystok University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
three-axis manipulator,
RRR robot,
training strategies,
3D scanners,
robot programming,
positioning accuracy
Related subjects:
Engineering,
Electrical engineering,
Electronics,
Mechanical engineering,
Mechanics,
Bioengineering and biomedical engineering,
Biomechanics,
Civil engineering,
Environmental engineering

© 2025 Patryk MIETLIŃSKI, Michał JAKUBOWICZ, Lidia MARCINIAK-PODSADNA, Michał WIECZOROWSKI, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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