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John Palmateer


Dual T-Mac Performance on a Large NC Machine

Published: Thursday, February 20, 2014 - 14:34

This article estimates the uncertainty for measuring a tool tip using dual Leica T-Mac sensors set up on opposite sides of an NC machine head and measured with tracking interferometers at opposite ends of a machine bed. Performance testing compares the estimated and measured uncertainties and comments on the nature of the setup.


The T-Mac is a special sensor for the Leica tracking interferometer, relying on a camera mounted on the tracking interferometer head to watch the sensor and estimate its angular orientation. (T-Mac “sensor” is used rather than T-Mac “target” because the T-Mac is a hybrid of a cooperative target, a corner cube for determining positions, and a set of active LEDs that strobe to determine orientation.) The tracking interferometer laser ADM simultaneously measures the distance to the sensor. Proposed applications include measuring and correcting NC head locations, in-process inspection, and augmenting inspection equipment on a machine head or robot with certifiable location and orientation information. The benefit of using T-Mac technology is that calibration and certification of the T-Mac is simpler than calibration and certification of all linkages making up the NC machine.

Figure 1 ultimately shows the 2-sigma confidence interval for the dual T-Mac sensors whose tracking interferometers are 400 in. apart, and where the distance from the T-Mac sensor to tool tip is 24 in. This confidence interval was built in several stages. Estimates of maximum permissible error (MPE) for dual trackers show that the increasing MPEs of individual trackers are mitigated by averaging measurements from opposite directions across a volume. The MPE confidence interval is the average MPE value divided by the square root of the number of instruments2, in this case square root of 2. The tracker plus T-Mac sensors are then combined, which also shows individual increases in the uncertainty are again flattened out via the use of dual instruments. The distance from the T-Mac sensor to the tool tip (24 in.) is added to the results: approximately 24 in. × tan(0.01 deg) = 0.0042 in.

Clearly, the angular uncertainty of the T-Mac, 0.01 degree, distinctly increases the overall tool tip uncertainty as seen in figure 1, going from “Dual Tracker & T-Mac MPE Confidence Interval” to “Tool Tip Dual MPE Confidence Interval.” Finally, the MPE estimate for the tool tip uncertainty is converted to a 2-sigma value using the Leica rule that the 50 percent of the MPE covers 90 percent of the Gaussian distribution3. The result shows that the confidence interval is smallest at the center of the machine, gradually getting slightly larger toward the ends of the machine volume.

Figure 1. Estimated dual T-Mac tool tip uncertainties. Click here for lager image.

The overall uncertainty when using a T-Mac needs to include the uncertainty of the workpiece to the tool tip. The workpiece can have its coordinate frame defined using a group of spherically-mounted retroreflectors (SMRs), which the tracker also measures. In general, more than the minimum three SMRs along with a conformal transformation into the workpiece coordinate frame should be used. Typically at Boeing seven or more transformation points are used for robust results. The following assumes the workpiece is on the order of the size of a 787 fuselage mandrel and has 12 reference targets. Figure 2 shows a typical reference target measured by laser radar4. The least squares fit5 of the laser radar to mandrel nominal fit was 0.005 in. (see Table 1). The 1-sigma confidence interval is approximately 0.0014 in., which is the value used in the uncertainty computation. Figure 3 shows the combination of tool tip and workpiece 2-sigma uncertainties. The graph assumes independence between the measurements of the T-Mac sensor and workpiece coordinate frames. The tracker will measure the workpiece coordinate frame, so there may be some dependencies that will increase the overall process confidence interval.

Figure 2. Typical fuselage region for trim and drill


Table 1. Typical measured to reference fit. Click here for larger image.


Figure 3. Estimate of total process uncertainty. Click here for larger image.


Testing of the predicted T-Mac tool tip performance was performed on a large gantry NC machine (see figures 4 and 5). Dual T-Mac sensors were attached on opposite sides of the NC machine head with their respective trackers at opposite ends of the machine bed. For this test, a third tracker measured an SMR at the tool tip, and this value was compared to the NC machine values and T-Mac tool tip values. Typically the third tracker would not be used in a production scenario.


Two AT901 trackers with T-Cam were set on the bed of the NC machine such that they could see the T-Mac sensor placed on opposite sides of the NC head. A third API T3+ tracker was set up halfway between the AT901 trackers and at the edge of the bed for monitoring the SMR in the chuck of the machine.

T-Mac to tool tip offset and NC machine coordinate frames
The tool tip offset and coordinate frame of the NC machine was determined using seven positions of the NC machine head. Only XYZ translations without head rotations were used at this juncture. Each NC machine position was recorded. The coordinate frame origins for both T-Mac sensors were recorded along with AT901 measurements of the SMR at the tool tip. And the SMR at the tool tip was recorded by the API tracker. Figure 6 shows the flow diagram where measurements by the two T-Mac systems define the offset between the T-Mac sensor and tool tip, as well as the transformation into NC machine tool tip coordinate frame.

Figure 4: NC machine with dual trackers


Figure 5: NC machine head with T-Mac sensor and tool tip SMR


The positions from the NC machine were used for a least squares transform into the NC machine coordinate frame with respect to the T-Mac tool tip location. The difference between the T-Mac corner cubes and AT901 measurements of the tool tip were averaged and became the offset for the T-Mac to tool tip. In each coordinate frame of the T-Mac, the offset to the tool tip SMR is recorded. Note that there are two possible modes for offset calculation: 1) the difference between T-Mac origin and tool tip in the NC machine coordinate frame; and 2) the distance to the tool tip in the T-Mac coordinate frame. The former is preferred because the uncertainties of tracker-only measurements are smaller than the uncertainty of the measurements in the T-Mac coordinate frame.

Figure 6: Flow diagram for computing T-Mac sensor tool tip offset and transformation. Click here for larger image.


Data collection
Forty NC machine positions were used for each test. The NC machine head axes A and B were also moved. The position and orientation of the NC machine was recorded. The AT901 trackers only recorded the T-Mac coordinate frames, while the API tracker only measured the tool tip SMR. A measurement plan (MP) was written that combined the tool tip offset for each T-Mac coordinate frame and created a point at the tool tip. These values were compared with the API tracker tool tip values.

Figure 7. Dual T-Mac measurement process flow. Click here for larger image.



The separation of the AT901 trackers was approximately 35 ft. The separation was limited by the length of wiring from the T-Mac sensor to the AT901. During the setup phase we had a difficult time attaching the T-Mac to the NC machine head. Hot glue adhered to neither the T-Mac sensor nor 30 years of coolant residue on the NC machine head. Double-backed tape ultimately was used.

NC machine coordinate frame
The transformation of tracker tool tip coordinates to NC machine nominal values are shown in tables 2 through 4. Measurement integration time was set to 2 seconds per target. The B and C axes were not moved during this portion of the test. A bit surprising was that the average RSS (root sum of squares) difference for the API tracker was 0.004 in., even though it was less than half the T-Mac distance to the spindle. The average RSS difference between NC machine and AT901 trackers were approximately 0.003 in. North and south T-Mac data measurements track, with differences of 0.0015 in. or less (data not shown). The tracker-to-tracker vs. trackers to machine differences might indicate some slight inaccuracy of the NC machine.

Table 2: NC machine to API. Click here for larger image.

Table 3: NC machine to north T-Mac. Click here for larger image.

Table 4: NC machine to south T-Mac. Click here for larger image.

Figure 8 graphically shows the residual errors from the API and north and south T-Mac measurements of the drill tip SMR. Noticeable is that any X, Y, and Z measurement component (groups of blue, red, green) seem to track. And the X, Y, and Z values for the T-Mac values seem to more closely track. This tracking of values from three independent measurement systems would seem to indicate that there is an accuracy degradation of the NC machine, up to 0.003 in.

Figure 8: NC machine to tracker fit. Click here for larger image.


T-Mac offset
As noted, the estimated uncertainty for the T-Mac sensor to tool tip is approximately 24 in. × tan(0.01 deg) = 0.0042 in. The origin of the T-Mac sensor frame to the tool tip is the offset value. The T-Mac to tool tip SMR offsets are shown in tables 5 and 6. The standard deviation values for the offsets, 0.0035 in. and 0.0043 in., seem a bit larger than expected. This could indicate the need for improvement to the calibration method (this computation was performed in T-Mac coordinate frame and may have a slightly different result in world coordinate frame), or for T-Cam compensation improvements.

Table 5: North T-Mac offset


Table 6: South T-Mac offset


Data collection
Two sets of data were collected by arbitrarily moving and rotating the NC machine head as allowed by visibility of the T-Mac sensors and tool tip SMR. The variation in horizontal rotation (C axis) was +20 /–27 degrees, while the elevation (B axis) was +32 / –7 degrees. For this portion of the test, the AT901 trackers only measured the T-Mac sensor while the API tracker only measured the tool tip SMR. An unknown error, either data collection or numerical, occurred during the first of two data sets where the API data would not correlate with the T-Mac target.

So, after the first data collection, only the AT901 T-Mac data could be compared. As noted, an MP combined the T-Mac coordinate frame with the tool tip offset and created points at the tool tip. Table 7 and figure 9 show the comparison between the north and south T-Mac tool tip points. As part of a dual T-Mac process, these two T-Mac values would be averaged and used as the NC machine position. The average RSS difference was 0.0031 in.

Table 7: North and south T-Mac comparison. Click here for larger image.


Figure 9. T-Mac to T-Mac fit. Click here for larger image.


For the second set of data collection (after lunch break), the unknown error in the API tracker data was not observed. This set of data collection used the original seven-point coordinate frame transformation for determining the relationship between the T-Mac sensors and tool tip SMR, as well as the transformation into NC machine coordinates. Again, the MP operated on the T-Mac coordinate frames and created tool tip points. The T-Mac data sets were averaged and then compared (i.e., difference without six-degree-of-freedom fitting) to the API tool tip measurements (see table 8). The average RSS error was 0.003 in. while the maximum RSS error was 0.0062 in. The standard deviation is a 1-sigma value, so the estimated 2-sigma RSS measurement uncertainty for this process, excluding the fit to the object being measured, is 0.0056 in. This is significantly higher than predicted by the specification sheet data shown in figure 1.

Table 8: Difference between API Quill and north and south T-Mac average. Click here for larger image.

The average for the second set of T-Mac data was also 6 DoF least square fit to the API tool tip data. This also showed smaller fitting errors: average RSS error was 0.002 in. while the maximum RSS error was 0.0044 in. (see table 9). The standard deviation is a 1-sigma value, so the estimated 2-sigma RSS measurement uncertainty for this process, excluding the fit to the object being measured, is 0.0044 in.

Table 9: 6 DoF transformations between API Quill and north and south T-Mac average. Click here for larger image.

The slight discrepancy between tables 8 and 9 indicates that a better job of initially fitting to the NC machine coordinate frame could have been done. The reason this is needed is that in general the measurement process will require all the necessary transformations up front so that data collection can proceed without any post-processing. This could be accomplished by measuring more reference locations. And as seen in tables 5 and 6, the coordinate frame transformation from T-Mac to tool tip needs improving.

Lastly, the graphical comparison between the difference and 6-DoF fit as a function of position on the machine bed is shown in figure 10. The difference method shows a trend line similar to that of the dual T-Mac shown in figure 1, whereas the trend line for the 6-DoF curves in the opposite direction. This opposite curve could be caused by uniform weighting of the least squares calculation and the fact that data collected at the machine ends had larger uncertainties than at the machine center. In effect, the least squares method weighted the ends more heavily, bringing those errors closer to zero, and the center weighted less, allowing those errors to be larger.

Figure 10. Dual T-Mac to tool tip method comparison.



This test shows that use of T-Mac for monitoring the tool tip of an NC machine is possible. One aspect of the test showed slight errors (about 0.003 in.) of the NC machine that the use of optical machine control could improve. Another aspect of the testing indicated that there appeared to be a compensation problem with the T-Mac and or T-Cam. The measured values when applying the angular orientation of the T-Mac to tool tip had a 2-sigma uncertainty for the measurement and was approximately 0.005 in. without taking into account the relationship between the AT901 trackers and the object being manufactured. There are clearly areas of improvement in processes, including recompensation of the T-Mac and T-Cam, as well as increasing the measurement time for improved average values, which could make this a usable in-process measurement method.

Further work

Specification results and Tables 5 and 6 show errors related to T-Mac pointing uncertainty that can negatively impact the total error budget. The factory calibration file was used: recalibrate the T-Mac. And we have since learned how to set the measurement and averaging processes for the T-Mac sensor. Point measurements were 2 seconds to average out air turbulence. The T-Mac measurements were less than 2 seconds.

Improve the initial distribution of points to improve the estimate of the NC machine coordinate frame.

Need to increase the separation between AT901 trackers to approximately 600 in., which was limited in this test by the length of wiring connecting the T-Mac sensor to the AT901 tracker.

Rather than ad hoc movements by the machine operator, NC program the moves so that the various regions of the machine volume are measured uniformly.

Determine if it is possible to make a master-slave MP for creating tool tip points from the coordinate frame and offset. When a new coordinate frame from the T-Mac is detected (after initialization) the computation for the tool tip should automatically run.


Thanks to Rick Breitzman (A-3790), who patiently operated the NC machine. Thanks also to the crew at Boeing Optical Services for assisting with setting up the T-Mac configuration files, assisting with the trial run, and fixing the uninterruptable power supply on short notice. Thanks also to Chris Prestholt and Jim H. Henderson at Boeing Computer Aided Measurements Group.


Sources cited

1. This graph does not attempt to optimize the uncertainty via knowledge of the geometry.

2. The statistic for confidence interval: the computation for the confidence interval is valid for any distribution and for distributions in more than one dimension.

3. Private communication: dividing the MPE by 3.29 produces a 1-sigma value.

4. Admittedly, the correspondence to the proposed process is not exact. The laser radar is slightly less accurate than the tracking interferometer (14 ppm vs. 10 ppm, respectively), and the number of targets on the older mandrel used in this example is probably greater than for the new mandrels that would be measured by the dual T-Mac process. Nonetheless, the evaluation gives a starting point for the total uncertainty analysis.

5. Software used is the BR&T developed functions for Excel: Least_sq_win7.xlsm


About The Author

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John Palmateer

John Palmateer, a Technical Fellow for the past 14 of his 35-year career at The Boeing Co., focuses on developing and implementing metrology systems, which include computer-aided theodolites, tracking interferometers, laser projectors, AM/FM laser radar, as well as calibration and certification of these devices and accreditation of metrology software. Currently he is working on extending metrology systems from tooling applications to in-process measurements for control and inspection during fabrication and assembly. Palmateer has bachelor’s degrees in physics and mathematics, a master’s degree in electrical engineering, and a Juris Doctor in law.