How to Measure Angular Errors of Plygons

Modern machining systems often utilize rotary tables for tilting and indexing the part. Maintaining an accuracte position of the rotary table is an integral part of ensuring the complete system’s accuracy. For example, if the rotary table is out of place by as little as 10 arc seconds and the part to be machined has a radius of 20 cm (8”), the table can contribute an error of 0.01 mm (0.0004”) to a feature location.


Similarly, when a rotary table is used for inspection and it is located on a CMM, its accuracy remains a strong contributor to the overall accuracy of the system. To ensure system accuracy, it is imperative to verify the angular errors of the rotary table during machine qualification trials.

An autocollimator is a useful and economical tool that can be used to quantify errors of machine tools and CMMs, as it is capable of checking, positioning and encoder errors during these analytical procedures.


An autocollimator is an optical device that is designed to provide high-resolution and highly accurate measurements of the rotary table angles. Autocollimators can be easily operated, and are often used with angle masters, such as polygons, to measure any potential deviation that exists from a nominal angle. Utilizing support software packages also allow for polygon calibration deviations and plot results to be achieved.

When used for the purpose of measuring the angular errors of rotary tables, an autocollimator determines any deviation that exists from the nominal angle through the angular master, which is typically a precision polygon mirror or an index table. When either of these tools is placed on the rotary table to be measured, it must be concentric with the axis of rotation within 0.5 mm (0.02 inch).

Additionally, both of the aforementioned tools are equipped with a reference diameter that can be centered through the use of an electronic indicator. The masters must be parallel to the axis of rotation within 120 seconds or better, thereby allowing an autocollimator to also be useful for measuring parallelism deviation.


Although polygons are available with as many as 72 faces, those that are required for use in rotary tables will typically have 8, 12 or 16 faces. The polygons used for this purpose are regular, which means that the angle between the faces is equal; however, since polygons are not perfectly regular, a list of deviations is supplied in the form of a calibration chart that is typically within the accuracy range of 0.2 seconds.

To ensure proper alignment, the polygon is mounted on the rotary table through the use of the centerline of an inside diameter that is parallel to the faces and square to the base as a reference. Following the alignment of the polygon, one of the mirror faces is rotated toward the autocollimator and zeroed, thereby allowing the readout of the rotary table to also be zeroed.

During inspection procedures, the rotary table is rotated until its readout is the nominal angle of the polygon, which, for an eight-sided polygon, will typically be 45 degree increments. The next face should be aligned to the autocollimator; however, if the next face is not aligned properly, an error can be read on the autocollimator. The table should be therefore rotated to each face of the polygon until all positions are inspected. At zero degrees, the table should return to zero deviation.

Principle of checking an indexing table with Ultra Autocollimator

Principle of checking an indexing table with Ultra Autocollimator

Index Table

The precision indexing table is a useful alternative tool that can be used with a polygon is not available, as this tool exhibits an average angular accuracy of 0.25 seconds and a 360° position resolution of one degree. Indexing tables can be available in numerous different positions per revolution.

To use an indexing table, a plane mirror is placed on the center of the rotary table and parallel to the axis of rotation, which is a similar alignment that is used when a polygon is employed. During inspection the rotary table is rotated to 23 degrees, for example, and the indexing table is counter-rotated 23 degrees.

Similar to when there is a misalignment when a polygon is used, the error can be read on the autocollimator. A similar technique using a high accuracy clinometer, such as the Taylor Hobson TB100, as opposed a precision indexing table, can also be used.

Optical Encoders

Optical encoders are highly accurate devices that are often mounted on the axis of rotation of most machine tool rotary tables. The principal source of error of an optical encoder is the eccentricity and tilt of the grating to the axis of rotation, both of which are sinusoidal in shape, rather than being the lines on the grating. To verify the accuracy of optical encoders, an 8- or 12-sided polygon can be a useful tool.

A second example of an optical encoder is a rotary table that is driven by a gear and worm on the worm shaft. The error pattern is a product of the gear errors, plus the worm errors, plus the encoder errors.

If the pitch on the ring gear is 2 degrees, the periodic worm, which is repetitive in a fixed increment, and encoder errors can be further investigated by testing the table in eight places at time points that are at least 15 minutes apart from each other. The ring can then be checked in increments of 2 degrees. When the table is in use, the error is therefore the sum of the worm and ring errors.

Inductosyn Scales

The Inductosyn rotary scale exhibits two types of periodic error; the first of which is a result of the tilt and/or eccentricity of the scales to the axis of rotation. This first error is similar to those which occur with optical encoders, as these will occur once per revolution and can be visualized by testing eight or more points.

On the other hand, the second type of error is periodic in one pole of the Inductosyn scale in which there are 180, 360 or 720 poles per revolution. For this type of scale, at least eight points in one pole should be tested to limit the amount of errors.

An index table can be used to qualify Inductosyn scales by stacking a 360° position table and a 375 position table. Through the use of counter rotation, the table can move forward by one degree on one table and then backward by 0.96 degree (360/375) on the other, thereby generating multiples of 144 seconds.

Tilt Motions

The aforementioned procedures are capable to work equally well when utilized for tilting tables, as a polygon or index table can be useful tools in verifying the accuracy of the tilt motion of the main axis. It is important to use caution if there is an offset that exists between the point of inspection of a tilt axis and the point of use, as the lack of structure exhibits an infinite stiffness on the offset that can provide a source of error to the entire system.

The use of a precision clinometer for the purposes of verifying the angle of the worktable with part and fixture in place may also be desirable for future use.

Checking a machine tool indexing head using a Taylor Hobson TB clinometer on its back, with a small reflector to enable any position from 0–360° to be measured.

Checking a machine tool indexing head using a Taylor Hobson TB clinometer on its back, with a small reflector to enable any position from 0–360° to be measured.

This information has been sourced, reviewed and adapted from materials provided by Taylor Hobson Limited.

For more information on this source, please visit Taylor Hobson Limited.


Please use one of the following formats to cite this article in your essay, paper or report:

  • APA

    Taylor Hobson. (2019, July 28). How to Measure Angular Errors of Plygons. AZoOptics. Retrieved on August 10, 2020 from

  • MLA

    Taylor Hobson. "How to Measure Angular Errors of Plygons". AZoOptics. 10 August 2020. <>.

  • Chicago

    Taylor Hobson. "How to Measure Angular Errors of Plygons". AZoOptics. (accessed August 10, 2020).

  • Harvard

    Taylor Hobson. 2019. How to Measure Angular Errors of Plygons. AZoOptics, viewed 10 August 2020,

Ask A Question

Do you have a question you'd like to ask regarding this article?

Leave your feedback