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1. Circular Interpolation
Dr. Belal Gharaibeh
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2. Circular interpolation mode
• The commands for circular interpolation direct CNC servo-
motors to move the tool simultaneously in the X and Y
directions in order to cut a programmed circle or portion of
a circle.
• The actual path followed by the tool is a series of straight
line approximations to follow an arc or a full circle path like:
– circular pockets
– spherical or conical shapes
– Radial recesses
– Grooves
– Corner breaks
– Helical cutting
– Large counterbore
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3. Cutting direction
• A cutting tool may move along an arc in two directions:
– Clockwise (CW)
– Counter clockwise (CCW)
• The motion direction is determined by looking
perpendicular at the plane in which the circular motion is
programmed
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4. Circular interpolation block
• There are two preparatory command associated with
programming an arc direction:
– G02 : circular motion clockwise (CW)
– G03: circular motion counter clockwise (CCW)
• Circular interpolation is executed on a plane. Therefore, the
programmer must first identify this plane before issuing any
circular interpolation commands.
• The plane is based on available combinations of XY, ZX and
YZ for milling operations.
• When G02 or G03 commands is activated by CNC program,
any currently active tool motion command is automatically
canceled. For example G00 or G01.
• All circular tool path motions must be programmed with a
cutting feedrate in effect. If not specified it will take the last
feedrate command (similar to G01)
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5. Radius and arc center vector word addresses
• To move on an arc or a complete circle, a start
and end points are needed as well as the arc
radius for which the tool move about.
• The arc start point is always relative to the
cutting motion and is presented in the
program by coordinates in the block preceding
the circular motion which is the last position
of the cutting tool before the circular
command
• The arc center location or arc radius is needed
for all circular interpolations because there are
unlimited number of arc radii that fit between
the programmed start and end points
• New CNC machines use the word address (R)
to specify the radius of the path
• Older CNC machines require arc center vectors
(I, J, K for the X, Y, and Z axes, respectively)
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6. Arc vectors
• Arc center vector (I) is the distance with specified
direction measured from the start point of the arc
to the center of the arc parallel to the X axis
• Arc center vector (J) is the distance with specified
direction measured from the start point of the arc
to the center of the arc parallel to the Y axis
• Arc center vector (K) is the distance with specified
direction measured from the start point of the arc
to the center of the arc parallel to the Z axis
• The I, J, K vectors are included in the circular block
command and relative to the motion ( +ve or –ve)
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8. Examples
• Write a program to perform circular interpolation
commands for profiling the arc shown in the XY
plane, using the absolute coordinate mode.
• G02 X4.125 Y-3.9486 10. J-2.25 F10.0
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9. Example 2:
• The circular arc shown in Figure is to be cut
using absolute coordinate programming.
• G3 X3.757 Y-1.5625 I-0.875JO
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10. Example 3:
• Incremental coordinates are used when cutting the
circular arc shown in Figure Write the necessary linear
cut, and circular interpolation commands.
• G91
• G1 X1.5 F6.0
• G2 X1.125 Y-4.1986 10.J-2.25
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