Pitch circle

The term pitch circle has several meanings.

Gear manufacturing

In gear engineering , the pitch circle is the imaginary diameter of a gear on which the pitch circle of the mating gear rolls. Both halved diameters add up to the center distance.

Instrument making

In instrument science and geodesy, a partial circle is a finely divided round disc made of glass , metal or film material, which is used for precise angle measurement . For this purpose, the edge of the disc is evenly subdivided with radially arranged, fine marks ( graduation marks ) or patterns.

With precise instruments, the angle is measured by aiming a measuring telescope and then reading the direction (s) on the pitch circle. Optical aids or photoelectric scanning of the graduation marks are used for reading . Simpler devices and compasses have a sighting device instead of a telescope .

In modern theodolites , the two partial circles for horizontal and elevation angles have a diameter of only about 6-8 cm. The glass circles are divided more precisely than 0.0002 mm and built into a moisture and dust-proof housing. Until about 1930, partial circles made of metal with silver graduation, 10–20 cm in size and freely visible.

Reading of partial circles

The visual reading, which dominated until around 1960, is based on the accuracy of the instrument

• free-eyed , e.g. B. on compasses and simple protractors
• with magnifying glass and vernier , for example on the measuring table and some sextants
• with a scale microscope , e.g. B. the slope knife , scissors telescope or building theodolite
• with reading microscope and micrometer, see seconds theodolite , transit , meridian circle

The photoelectric reading of partial circles is done by automatically scanning the graduation lines or the pattern. The angular measure embodied in the form of even line divisions or by more or less long line traces is converted into light-dark signals during scanning and processed digitally.

Part circles can be open or concealed in a housing; Theodolites , sextants and astronomical meridian circles are equipped with particularly precise partial circles . The graduation marks here are mostly arc minutes or multiples thereof, while the fine reading (to angular seconds or even more precisely) is done by optical micrometers (coincidence with a plane-plate micrometer ).

Partial circles of theodolites

Up until the beginning of the 20th century, precise pitch circles of geodetic instruments were mostly made of brass with a silver inlay . Since the development of the second theodolite (see Wild T2 ), finely etched glass circles with a radius of around 3–5 cm have become established. Their division was initially made mechanically ( using circular dividing machines), later by photographic reproduction (etching), similar to those of today's finest glass scales . With today's measuring accuracies of 0.5 to 1 ", each of the 10 to 20,000 graduation lines must be applied to the glass circle with an accuracy of 0.0001 mm (0.1 µm). The line width is 0.006 mm and the number height of the angle labeling is 0, 1 mm.

In modern electronic theodolites and total stations , the circle reading is optoelectronic replaced process. Their technique of relative angle determination is called the incremental method , in contrast to the code method when using absolute encoders .

Precise pitch circles are produced in a circle dividing machine . The partial circle lines are scratched, etched or applied photo-mechanically into the glass circles.

The lack of accuracy of the circular reading until around 1800 was compensated for by an invention by Tobias Mayer , the repetition circle .

Soccer

In soccer, the partial circle on the penalty area is a marker that tells soccer players where to stand during a penalty kick.

literature

• Franz Ackerl : Geodesy and Photogrammetry. Volume 1: Instruments and methods of measurement and graphical-mechanical evaluation (= technical handbooks for construction practitioners . Vol. 8, ZDB -ID 409611-3 ). Georg Fromme, Vienna 1950.
• Heribert Kahmen : Applied Geodesy. Surveying. de Gruyter, Berlin et al. 2006, ISBN 3-11-018464-8 .