AppRotary Tables Angular vs Linear Accuracy
The relationship between angles and linear dimensions is defined by trigonometry. Sine, cosine and tangent functions allow to calculate these relationships. Because an angle diverges as distance from the origin increases, so too, increases the tangential component. Therefore, it is not appropriate to specify a rotary tables accuracy in linear values, unless a maximum envelope (diameter) is also specified.
It is not difficult to determine the linear relationships to their respective angles, within a specific envelope. Let's equate 1 arc second (see definition in Glossary) to some common linear measurements. For our discussion, we'll use 0.000004848 as the tangent of 1 arc second. Since the trig functions provide dimensionless ratios, 0.000004848 (usually rounded to (0.000005) applies to any unit of linear measure, just be consistent.
To use the charts below, locate your required linear tolerance, and the maximum radius to be worked, the resulting intersection shows the corresponding nominal index accuracy, in arc seconds (unless specified, i.e., [°] = deg.; ['] = min.), required for the application. If your tolerance zone or working radius falls between two values, use the tighter requirement.
Tolerance 
Working Radius (Inches)  

1 
2 
3 
4 
5 
6 
10 
12 
18 
20 
24 
30 
36 
40 
48 
0.010" 
½° 
¼° 
10' 
8' 
6' 
5' 
3' 
2' 
2' 
1' 
1' 
1' 
30 
30 
30 
0.005" 
¼° 
10' 
5' 
4' 
3' 
2' 
2' 
1' 
1' 
30 
30 
30 
20 
20 
15 
0.003" 
10' 
5' 
4' 
3' 
2' 
2' 
1' 
1' 
30 
30 
30 
20 
20 
15 
10 
0.002" 
5' 
3' 
2' 
2' 
1' 
1' 
30 
30 
30 
20 
15 
10 
10 
10 
10 
0.001" 
3' 
2' 
2' 
1' 
30 
30 
20 
20 
15 
10 
10 
10 
5 
5 
5 
0.0005" 
1' 
1' 
30 
30 
20 
15 
10 
10 
5 
5 
5 
5 
2 
2 
2 
0.0003" 
1' 
30 
20 
15 
10 
10 
5 
5 
5 
3 
3 
3 
2 
1 
1 
0.0001" 
20 
10 
5 
5 
3 
3 
2 
2 
1 
1 
1 
0.5 
0.5 
0.2 
0.2 
0.00005" 
10 
5 
2 
2 
2 
1 
1 
1 
0.5 
0.5 
0.5 
0.2 
0.2 
0.2 
0.1 
0.00001" 
2 
1 
1 
0.5 
0.2 
0.2 
0.2 
0.1 
0.1 
0.1 
* 
* 
* 
* 
* 
Table 2 [metric values]
Tolerance 
Working Radius (Millimeters)  

25 
50 
75 
100 
125 
150 
200 
250 
375 
500 
750 
1000 
1500 
0.25 mm 
½° 
¼° 
10' 
8' 
6' 
5' 
4' 
3' 
2' 
1' 
1' 
30 
30 
0.1 mm 
10' 
5' 
4' 
3' 
2' 
2' 
1' 
1' 
30 
30 
15 
15 
10 
0.05 mm 
5' 
3' 
2' 
1' 
1' 
1' 
30 
30 
20 
15 
10 
10 
5 
0.025 mm 
2' 
1' 
1' 
30 
30 
30 
15 