Fig. 1.
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)
Fig. 3.
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)
Fig. 5.
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
Fig. 7.
Reference geometric view
Fig. 8.
View of the robot's workstation when executing predetermined geometries
Fig. 9.
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
Tab. 1.
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 |
Fig. 11.
Value distribution histogram (left side) and distribution of the result values ±3σ (right side) for parallel lines 20 mm apart
Tab. 2.
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 |
Fig. 12.
Relative error robot – reference
Fig. 13.
Standard deviation distribution
Fig. 14.
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
Tab. 3.
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 |
Fig. 16.
Distribution of the relative error (left side) and standard deviation (right side)