Terminology and measurements in this section follow this document. Users should conduct their own characterization with the specific platform weights and weight distributions.

The rotary stage's accuracy and repeatability have been evaluated by recording the angle (°) of the incremental encoder (2400 pulses per revolution) and the angle obtained from the teensystep step counter simultaneously. Figure 1 shows an example test of the stage performance, in this case without the load of the head holder. The stage is repeatedly sent to the set point positions (0 and 360 degrees). The final positions are highly accurate (360.06 ± 0.11° and 0.04 ± 0.07°), suggesting little error accumulation.

Figure 1. Rotary stage performance

Data and code for this characterization are available here.

Minimum incremental motion (MIM) and backlash

The minimum incremental motion reliably measured corresponds to 0.1 degrees. The backlash, in the worst-case scenario corresponding to the offset created by the change in direction of the MIM tests, has been 0.04 degrees.

Figure 2. Minimum incremental motion measurement

Data and code for this characterization are available here.

Accuracy and repeatability

In order to evaluate the accuracy and repeatability of the rotary stage, a sequence of increments of 45 degrees in both rotation directions has been performed, collecting 8 position deviations in each direction (16 per each velocity/acceleration condition). The overall accuracy and repeatability have been calculated from all conditions according to the following equations:

Accuracy:

Repeatability:

Where x_i and s_i are the average inaccuracy and the standard deviation, respectively, at position i. Up and down arrows represent the positive and negative directions.

Figure 3. Accuracy and repeatability test sequence (a) and
average of absolute position deviation in every angular velocity and acceleration condition (b)

Closed-loop characterization

For the closed loop algorithm, the stability of the system response has been evaluated by the analysis of the step response for all previously described conditions (20-100 °·s¯¹ and 200-1200 °·s¯²). A contour plot has been extracted to be used as a map to avoid regions of inaccuracy and instability. Sometimes even achieving a small error the stage can overshoot as shown in Figure 4 (right).

Figure 4. Example step functions (0-90°) at different velocity and acceleration values.
(left) 20 °·s¯¹, 200 °·s¯². (right) 100 °·s¯¹, 1200 °·s¯².

Figures 5 highlight regions in red to avoid errors and instability around the setpoint.

Figure 5. Average (left) and standard deviation (right) of the absolute position deviation.

Data and code for this characterization are available here.

Specifications and characterization of the rotary stage

parameter	value
Resolution stepper motor (°)	0.0024
Resolution of the encoder (°)	0.024
Accuracy (°)	0.37
Repeatability (°)	0.1
Minimum incremental motion (°)	0.1
Maximum angular velocity (°·s¯¹)	100
Maximum angular acceleration (°·s¯²)	1200
Backlash (°)	0.04