Error Averaging Effect in Parallel Mechanism Coordinate Measuring Machine
Error averaging effect is one of the advantages of a parallel mechanism when individual errors are relatively large. However, further investigation is necessary to clarify the evidence with mathematical analysis and experiment. In the developed parallel coordinate measuring machine (PCMM), which is based on three pairs of prismatic-universal-universal joints (3-PUU), error averaging mechanism was investigated and is analyzed in this report. Firstly, the error transfer coefficients of various errors in the PCMM were studied based on the established error transfer model. It can be shown how the various original errors in the parallel mechanism are averaged and reduced. Secondly, experimental measurements were carried out, including angular errors and straightness errors of three moving sliders. Lastly, solving the inverse kinematics by numerical method of iteration, it can be seen that the final measuring errors of the moving platform of PCMM can be reduced by the error averaging effect in comparison with the attributed geometric errors of three moving slides. This study reveals the significance of the error averaging effect for a PCMM.
A novel technique for calibration of polygon angles with non-integer subdivision of indexing table
Polygons are basic angle standards for angle measurement, particularly used for calibration of rotary angular indexing, and for measuring equipment such as dividing heads and tables. A main application in daily life is in bar-code readers. Calibration of such angle standards is required for traceability and at the highest accuracy it is a responsibility of national metrology institutes. In order to investigate uncertainty parameters on polygon calibration and to establish the capabilities of national metrology institutes, intercomparision measurements in the name of EUROMET project 371 “angle calibration on precision polygons” between 12 European countries have been carried out. Two precise polygons with 7 and 24 faces have been calibrated by the participants. Difficulties arose for precise calibration of seven-sided polygon for those institutes, which do not have a high-resolution angle comparator or two autocollimators. UME, the National Metrology Institute of Turkey, has applied an alternative technique for precise calibration of seven-sided polygon without using high-resolution angle comparators (i.e., indexing tables or angle dividers) or two autocollimators. The technique is based on the circle closure principle. The pitch and cumulative angles of the polygon are extracted from the angle measurement between some polygon faces (such as one and four (1/4), analogous 2/5, 3/6, 4/7, 5/1, 6/2 and 7/3) the angle of which can be generated close enough by the indexing table. This means that the polygon can be regarded as unfolded in seven 3-pitch angle intervals of 3 × 360◦/7 ≈ 154◦17′, making up 1080 ◦ in total. The method gives the differences between these seven intervals; with the closure condition (the sum must be zero) this gives all absolute angles. A full uncertainty evaluation is given that is based on the model function which relates the measured values to the polygon angles. For the calibration actually carried out, this yielded an uncertainty of 0.24 ′′. Within this uncertainty the measured polygon angles corresponded very well with the reference values of the intercomparison. The method is of use for laboratories which do not have a high-resolution angle comparator (i.e., an indexing table or angle divider) or two autocollimators for the calibration of such angle standards. © 2002 Elsevier Science Inc. All rights reserved.
Self-calibration of precision angle sensor and polygon mirror
Abstract The present paper describes a high-precision angle sensor and a new method for calibrating precision angle sensors absolutely without the use of any accurate reference instruments. Two angle sensors with compensating devices which compensate thermal drift of the light source are developed and calibrated by themselves. The repeatability error of the evaluated mean sensitivity was improved to 0.01% by the compensating device. The repeatability of the calibrated linearity error was reduced to 0.025 s (arc). This paper also describes a new differential method that can calibrate simultaneously the dividing errors of a polygon mirror and angular profile of polygonal surfaces by using the developed angle sensors. Calibration of a 24-sided polygon mirror showed the repeatability error of dividing angle and angular profile to be approximately 0.2 s (arc).