User's Manual ISO TNC 360 (260020xx, 280490xx) - heidenhain

7 Programming with Q Parameters
7.3 Trigonometric Functions
Overview
TNC 360
Sine, cosine and tangent are the terms for the ratios of the sides of right
triangles. Trigonometric functions simplify many calculations.
For a right triangle,
Sine: sin α = a / c
Cosine: cos α = b / c
Tangent: tan α = a / b = sin α / cos α
Where
• c is the side opposite the right angle
• a is the side opposite the angle α
• b is the third side
The angle can be derived from the tangent:
α = arctan α = arctan (a / b) = arctan (sin α / cos α)
Example: a = 10 mm
b = 10 mm
α = arctan (a / b) = arctan 1 = 45°
Furthermore: a 2 + b 2 = c 2 (a 2 = a . a)
c = a 2 + b 2
D06: SINE
e.g. N10 D06 Q20 P01 –Q05 *
Calculate the sine of an angle in degrees (°) and
assign it to a parameter
D07: COSINE
e.g. N10 D07 Q21 P01 –Q05 *
Calculate the cosine of an angle in degrees (°) and
assign it to a parameter
D08: ROOT SUM OF SQUARES
e.g. N10 D08 Q10 P01 +5 P02 +4 *
Take the square root of the sum of two squares, and
assign it to a parameter
D13: ANGLE
e.g. N10 D13 Q20 P01 +10 P02 –Q01 *
Calculate the angle from the arc tangent of two sides or from
the sine and cosine of the angle, and assign it to a parameter
α
c a
b
Fig. 7.3: Sides and angles on a right triangle
7-7