Geometry
Bolt circles, triangles, tapers, chamfers, and programming coordinates.
In short: Geometry
The geometry calculators provide coordinates and dimensions that are often missing when programming and inspecting: bolt circles and hole patterns, triangles, tapers, chamfers, circle segments, ellipses, tangent points, polar and transformed coordinates and sine bar settings. The results are exact calculated values; rounding, zero point and direction of rotation are set by the user.
Frequently asked questions about Geometry
How do you calculate the coordinates of a bolt circle?
For n evenly spaced holes on a pitch circle diameter D, x = D/2 × cos(φ0 + i × 360°/n) and y = D/2 × sin(φ0 + i × 360°/n), with start angle φ0 and i = 0 to n − 1. Six holes on an 80 mm pitch circle are 60° apart and each 40 mm from the centre.
How do you determine the dimensions of a taper?
The taper ratio is C = (D − d) / L and the half taper angle α/2 = arctan((D − d) / (2 × L)). A taper from 30 mm to 20 mm diameter over 50 mm length therefore has a ratio of 1:5 and a half angle of 5.71°.
How do you set an angle with a sine bar?
The required gauge block height is h = L × sin α with the roller spacing L of the sine bar. For 15° on a sine bar with 100 mm roller spacing, 25.882 mm of gauge blocks are needed.
What should you watch out for with chamfer callouts?
A 1 × 45° chamfer has two equal legs of 1 mm; the inclined chamfer face is then 1.414 mm wide. At other angles the legs differ, and a dimension may refer to one leg or to the chamfer width. When in doubt, clarify the drawing callout.