CNC Circular Interpolation

Confidential
CNC Mc Programming
Circular Interpolation G02 / G03
Presentation By: 22 Century Technologies
Sandeep Adkar
B.E. (Mech.), M.B.A. (Marketing)
Ex Plant Manager / GM – Operations, Cummins Turbo
E mail: support@22centech.com
Web: www.22centech.com
Field: Automobile production, CNC
Machining & Programming
22 Century Technologies, Mfg Skill Develop, support@22centech.com, www.22centech.com 1

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Circular Interpolation
Circular Interpolation G02, G03 Modal
Circular interpolation commands G02, G03 are used to cut circles or
circular arcs. G02 & G03 define clockwise and counter clockwise
motion respectively.
G02-Clockwise G03-Counterclockwise
(CW) (CCW)
Plane selection
12
9
6
3
12
9
6
3

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Format:
Plane Selection + CW or CCW + End Point of Arc Cutting +
Arc/Radius Centre + Cutting Feed Rate;
G17 /
G18 /
G19
G02 /
G03
X_ Y_ /
X_ Z_ /
Y_ Z_
R /
I_ J_ /
I_ K_ /
J_ K_
F_ _;
++++

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The interpolation parameters together with axis commands determine
the circle or arc.
 SP: Start point is determined by previous block
 EP: End point is determined by the axis values in resp plane.
 CP: Circle center point is determined by I, J and K.
EP SP
CP
-I
-J
+R
+X
+Y
-X
-Y
A
+I
+J

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Circular Interpolation G02
G03
G02
G02
G03
G03
Y, 2nd axis
Z, 3rd axis
X, 1st axis
Plane selection is must for circular interpolation.
Dimensions I, J and K:
Command I and J specify the perpendicular distances from the start
point SP of circular arc A to the center point CP. I, J & K must be
specified incrementally whether under ABS or INC mode, adding + or
– sign for the direction of I, J, K. If an interpolation parameter is not
programmed, zero is automatically generated by the control.
I : parallel to X axis
J : parallel to Y axis
K : parallel to Z axis

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•Circle center point is defined either through sign dependent vectors I, J
& K, from a range of 0 to 360 degree. The sign results from the
coordinate direction from the start point to the center point.
•Or directly through the radius R,
R + angle for less than or equal to 180 deg.
R - angle for greater than 180 deg.
R must have negative sign. This is how the machine differentiates when
there are two possibilities.
•The direction in which the arc is traversed is determined by G02 or
G03.
•Circular interpolation is possible in 2 out of 4 axes, both not parallel.
•Radii must not be programmed when the angle to be traversed is 0 deg
or 360 deg. In such cases the full circles must be programmed using the
interpolation parameter I, J and K.

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Eg.1:
Movement in circular interpolation
using interpolation parameters I, J
and K.
60
10
30
30
+Y
+X
A
B
I=0
J=20
Arc center
(X60, Y30)
An arc from A and B in both directions. Under ABS mode:
N5 G17 G02 G90 X30.0 Y30.0 I0 J20.0; Tool moves from A to B
Justification: Here X coordinate is same for both start point and arc
center. Y coordinates are +20mm apart, starting from arc start point to
arc center, in +Y direction. So I=0 and J=+20.
N6 G17 G03 G90 X60.0 Y10.0 I30.0 J0; Tool moves from B to A

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Eg.1:
Movement in circular
interpolation using
interpolation parameters I,
J and K.
An arc from A and B in both directions. Under INC mode:
N5 G17 G02 G91 X-30.0 Y20.0 I0 J20.0;Tool moves from A to B
Justification: Here X coordinate is same for both start point and arc
center. Y coordinates are +20mm apart, starting from arc start point to
arc center, in +Y direction. So I=0 and J=+20.
N6 G17 G03 G91 X30.0 Y-20.0 I30.0 J0;Tool moves from B to A
60
10
30
30
+Y
+X
A
B
I=0
J=20
Arc center
(X60, Y30)

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Eg. 2:
and K. 20
50
10
2010 50
+Y
+X
J=-10
I=-40
B (End of circular arc)
A (Start of circular arc)
C
An arc from A and B in both directions. Under ABS mode:
N3 G17 G90 G03 X20.0 Y50.0 I-40.0 J-10.0 F100; Tool A to B
Distance from point A (start of arc) to the center of arc C with sign.
N4 G17 G90 G02 X50.0 Y20.0 I-10.0 J-40.0 F100; Tool B to A
Distance from point B (start of arc) to the center of arc C with sign.

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Eg. 2:
and K.
An arc from A and B in both directions. Under INC mode:
N4 G17 G91 G03 X-30.0 Y30.0 I-40.0 J-10.0 F100; Tool A to B
Distance from point A (start of arc) to the center of arc with sign.
N5 G17 G91 G02 X30.0 Y-30.0 I-10.0 J-40.0 F100; Tool B to A
Distance from point B (start of arc) to the center of arc with sign.
20
50
10
2010 50
+Y
+X
J=-10
I=-40
B (End of circular arc)
A (Start of circular arc)
C

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•Circular Interpolation by Specifying Radius of Circular Arc, R:
The starting point of the circle or arc is determined by the previous block.
The end point is given by both of the axis values (e.g. X and Y). The
circle center is defined by the signed radius.
The radius of circular arc can be directly specified by R instead of
specifying the center of circular arc by I, J and K. The sign of the radius
value is given according to the size of the traversing angle,
Radius less than or equal to 1800 R+A R+30
Radius greater than 1800 R-B R-60
No radii may be programmed, when the distance between the circle start
point and circle end point is less than or equal to 10µm. That means a
complete circle must be programmed using the interpolation parameters
I, J and K.

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Eg. 3:
Movement in circular interpolation by
specifying the radius.
60
15
45
30
+Y
+X
A
B Arc center
(X60, Y45)
R30
An arc from A and B in both directions. Under ABS mode,
N05 G17 G03 G90 X60.0 Y15.0 R30.0; Tool moves from B to A
N15 G17 G02 G90 X30.0 Y45.0 R30.0; Tool moves from A to B
Under INC mode,
N05 G17 G03 G91 X30.0 Y-30.0 R30.0; Tool moves from B to A
N15 G17 G02 G91 X-30.0 Y30.0 R30.0; Tool moves from A to B

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Eg. 4: Movement in circular interpolation
along an arc from A and B in both
directions with angle >1800.
20
60
20 60
+Y
+X
B
A
End
Start
R40
1800 or
more
An arc from A to B in clockwise direction.
Under ABS mode:
G17 G90 G02 X60.0 Y20.0 R-40.0 F100; A to B
G17 G90 G03 X20.0 Y60.0 R-40.0 F100; B to A
Under INC mode:
G17 G91 G02 X40.0 Y-40.0 R-40.0 F100; A to B
G17 G91 G03 X-40.0 Y40.0 R-40.0 F100; B to A
•When the control range of arc is 180 deg or more, the radius R must
be specified with negative (-) sign.

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A Complete Circle-
•Complete circle can be programmed by using
one block with I, J & K.
+Y
+
X
B
A
R40
A complete circle from point A in clockwise direction,
ABS – G17 G90 G02 (X0.0 Y40.0) I0 J-40.0 F100;
INC – G17 G91 G02 (X0.0 Y0.0) I0 J-40.0 F100;
A complete circle from B in clockwise direction,
ABS – G17 G90 G02 (X40.0 Y0.0) I-40.0 J0 F100;
INC – G17 G91 G02 (X0.0 Y0.0) I-40.0 J0 F100;

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+Y
+X
B
A
R40
•Command in () can be omitted. They are written for easy
understanding.
•The arc radius R programming is not available to a complete circle and
only I, J and K are used.
•If I, J, K and R are specified in the same block R has the priority and I, J
& K are ignored.
•Since the start point and end point are at the same location, it is not
necessary to indicate X and Y coordinate.

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Eg. 5: Start from the zero point, turn
clockwise and return to zero. The
cutting feed rate for straight line is
F200 and for arc is F50.
P2 (X20, Y0)
P1 (X20, Y30)
P4 (X-30, Y0)
P3 (X0, Y-20)
P5 (X0, Y30)
---- Cutting feed
Rapid traverse
O0010;
N1 G90 G54 G17 G00 X20.0 Y30.0 S1000 M03; (0-1)
N2 G01 (X20.0) Y0.0 F200; (1-2)
N3 G02 X0.0 Y-20.0 R20.0 F50.0; (Put R= I-20.0 J0) (2-3)
N4 G01 X-30.0 Y0.0 F200.0; (3-4)
N5 G02 X0.0 Y30.0 R30.0 F50.0; (Put R= I30.0 J0) (4-5)
N6 G01 X20.0 (Y30.0) F200.0; (5-1)
N7 G00 X0.0 Y0.0; (1-0)
N8 M30; (Commands in bracket can be omitted.)

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