Improving machine tool accuracy by a direct position
measurement using a new approach of laser goniometry
Kristian Schröder, Christoph Ament, Stefan Patzelt, Gert Goch
University of Bremen, FB 4, Postf. 330 440, 28334 Bremen, Germany,
k.schroeder@msr.uni-bremen.de
Abstract:
Parallel kinematics machines (PKMs) present a promising new formation of machine
kinematics. But, their application is limited due to insufficient positioning precision,
which follows from errors of the transformation model and an indirect position meas-
urement. To overcome these problems the development of an optical direct position
measurement is presented. Three laser goniometric modules are used to measure
six angles between fixed points and the PKM platform, which characterize the plat-
form position and orientation completely. Each angle is determined with high preci-
sion using an additional reference laser beam and a CCD line sensor.
Introduction
The theoretically attainable machining accuracy of machine tools is decreased by in-
direct position measurements, which are not able to cover many sources of error suf-
ficiently, e.g., dimensional tolerances, loose, wear, distortions. Present machines are
controlled by linear length measurement at the driving end. For this purpose, several
measuring devices based on laser interferometry or linear scales are established. At
the moment, insufficient position measurement and unsolved calibration problems
are the most relevant obstacles concerning the introduction of new machine tools
with parallel or hybrid kinematics.
Description of the problem
The position and orientation {A} (Figure 1) of the tool center point (TCP) of parallelki-
nematic machines (PKM) is not obtainable directly from the knowledge of the strut
lengths li. As a first step of iteration the required strut lengths li is calculated from the
desired set point of the TCP (inverse kinematic problem {B}->{L}). To achieve this, an
accurate PKM model is imperative. Any possible deviation leads to final errors at the
computed set points of the strut lengths li, which cannot be corrected. As a second
step, local control systems of the struts calculate values of the control variables to
obtain the assigned strut lengths li [2, 4].
Figure 1: Coordinate systems of PKM.
The measurement of strut lengths li for the control systems is done at the driving end.
Different measuring principles are taken into account [6, 4]. However, non of these
measuring methods is able to detect occuring errors (thermal expansion, abbe-error)
at high precision [4, 5, 9].
Both steps of the positioning procedure of PKM’s are threatened by errors (Table 1).
A conceptual improvement could be achieved by direct position measurement in car-
tesian coordinates. This method leads to the accuracy-controlled machine (german
project Accomat [1]), which detects and controls its actual position. In [7] Schulz em-
phasises the importance of improved position measurement systems especially con-
sidering high-speed-machining. 3D measurement systems should work independent
from the mechanical line of flux. For that purpose, the measurement must be linked
to the driving-end and not to the axis.
Kinematic model simplifications Physical errors
• Joint DOFs have the same origin • Kinematic errors
• Actuators have one DOF • Manufacturing and assembly
• Actuators acting through joint origins • Deformation by gravity, inertia
• Measurements are accurate • Thermal expansion
• Accuracy of measurement
Table 1: Error due to model simplifications and physical errors.
Possible methods for direct-measuring
Measuring of acceleration – Using acceleration pick-ups, mounted on TCP, it is pos-
sible to measure the acceleration of the TCP. The double integration over time leads
to the position signal of the TCP. Sensors working on basis of MEM achieve a high
accuracy of measurement. However, there is a problem with drift error over the time.
Today a minimal error of 0.1 mikrons over a durance of 40 seconds is achievable [8].
The need of a scheduled recalibration limits the application of this method.
Interferometric methods – Interferometric systems are able to achieve measurement
resolutions in the sub-micrometer range. Using a single monochromatic lightsource
only changes in position are detectable. The laserbeam has to track the TCP move-
ment. For this purpose so called lasertracker are developed [2].
The Laser-µGPS [3] requires no TCP tracking. A first approach using Laser-µGPS for
direct measurement has been made within the project Accomat [7]. Similar to the ra-
dio waves used at the Global Positioning System (GPS) the measuring system works
with IR light. The new method uses the effect of wideband-interferometry. The emit-
ted light is seperated into two beams. The optical path length of the reference beam
is permanently changed. The measuring beam is reflected by a special reflector unit,
which is fixed on the PKM platform. Both beams are superposed resulting in a de-
tectable position signal under the condition of maintenance of the coherence length
criteria [3]. This method is not available with the required accuracy.
New concept of an optical direct position measurement system
The direct measurement of the position of the TCP is based on optical goniometry.
Figure 2 shows the measuring setup.
Figure 2: Enhanced laser goniometry scheme.
Two orthogonally aligned fast mirror actuator modules (FMAM) that are fixed to the
working platform (TCP) deviate a laser beam into the center of a lightsensing position
detector (e.g., 4-quadrants-diode). A movement of the platform and the laser beam
first leads to a deviation from the desired set point at the position detector. The
resulting difference signals (A+B)–(C+D) or (A+C)–(B+D) of the position detector are
used by an inner control system of the FMAMs, to readjust the mirrors. At the same
time, the deviation angles are
measured with high accuracy using
a second laser and a CCD line
sensor (Figure 3). The accuracy of
the whole measuring system is
specified by the accuracy of meas-
uring the mirror angle Θ.
A typical CCD line sensor (ILX 500,
Sony) provides approximately 5000
Pixel, each with a width of 7 mi-
crons. Assuming a distance of 20
cm between the CCD line sensor
and the mirror and taking into ac-
count the angular relations an in- Figure 3: High precision angle measurement.
terpolated resolution of 0.7 arc
seconds can be achieved. The measuring result is independent from systematic er-
rors like loose in the live axle of the galvano-scanner or directional stability of laser
beam, because these errors influence both, the measuring and the reference beam.
The TCP position and orientation can be determined, if three of these goniometric
modules are used, which deliver six linearly independent angle measurements Θx1,
Θy1, Θx2, Θy2, Θx3 and Θy3 in total. The calculated position is unique, as long as the
orientations of the optical axis are not parallel to each other. This can be achieved by
a suitable arrangement of the FMAMs and position detectors. Matlab calculations are
done to estimate the resulting error. Figure 4 shows the result. The error at the
maximum z-position of a simulated Tripod is smaller than 0.021 mm. Based on these
numerical results and on first experimental results of a single axis configuration it
seems to be promising to set up the complete 3D measuring system in the next step.
Figure 4: Estimated accumulated errors.
References
[1] „Project Accomat“: http://www-wbk.mach.uni-karlsruhe.de/Forschung/Projekte/
Accomat/projekt.htm.
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[7] Schulz, H., Versch, A., Fiedler, U., Huerkamp, W.: “Accomat-Accuracy Con-
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