
3.INTERPOLATION FUNCTION PROGRAMMING B-63944EN-2/02
- 20 -
Explanation
Involute curve machining can be performed by using involute
interpolation. Involute interpolation ensures continuous pulse
distribution even in high-speed operation in small blocks, thus
enabling smooth and high-speed machining. Moreover, machining
programs can be created more easily, and the size of machining
programs can be reduced.
Yp
Yp
Xp
Pe
0
R
Xp
Ps
Base circle
Pe
Po
Po
R
0
Start
point
End point
End point
I
I
J
Ps
Clockwise involute interpolation (G02.2)
Yp
Pe
Ps
Po
R
0
Pe
0
Yp
Ro
Start point
End
point
I
I
End point
Start point
R
Ps
Xp
Xp
Counterclockwise involute interpolation (G03.2)
J
J
J
Fig. 3.1 (a) Actual movement
- Involute curve
An involute curve on the X-Y plane is defined as follows ;
X (θ) = R [cos θ + (θ - θ
O
) sin θ] + X
O
Y (θ) = R [sin θ - (θ - θ
O
) cos θ] + Y
O
where,
X
O
, Y
O
: Coordinates of the center of a base circle
R : Base circle radius
θ
O
: Angle of the start point of an involute curve
θ : Angle of the point where a tangent from the current
position to the base circle contacts the base circle
X (θ), Y (θ) : Current position on the X-axis and Y-axis