Arc programming with I, J, K (center) in CNC Programming - Step-by-Step Execution

Concept Flow - Arc programming with I, J, K (center)

Start at current point

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Read G02/G03 command

↓

Read target end point (X,Y,Z)

↓

Read center offsets (I,J,K)

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Calculate arc center = current point + (I,J,K)

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Move tool along arc to end point

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Update current point to end point

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End

The CNC reads the arc command with center offsets I, J, K, calculates the arc center from the current point, then moves the tool along the arc to the target end point.

Execution Sample

CNC Programming

G02 X5 Y5 I5 J0
G03 X0 Y10 I-5 J0

Two arc moves: first clockwise arc to (5,5) with center offset (5,0), then counterclockwise arc to (0,10) with center offset (-5,0).

Execution Table

Step	Command	Current Point (X,Y)	I,J Offsets	Arc Center (Xc,Yc)	Move Direction	End Point (X,Y)	Action
1	Start	(0,0)	-	-	-	-	Set current point to (0,0)
2	G02 X5 Y5 I5 J0	(0,0)	(5,0)	(5,0)	Clockwise	(5,5)	Calculate center (0+5,0+0)=(5,0), move arc CW to (5,5)
3	Update current point	(5,5)	-	-	-	-	Current point updated to (5,5)
4	G03 X0 Y10 I-5 J0	(5,5)	(-5,0)	(0,5)	Counterclockwise	(0,10)	Calculate center (5-5,5+0)=(0,5), move arc CCW to (0,10)
5	Update current point	(0,10)	-	-	-	-	Current point updated to (0,10)
6	End	(0,10)	-	-	-	-	Program ends

💡 Program ends after executing all arc moves and updating current point.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 5	Final
Current Point (X,Y)	(0,0)	(0,0)	(5,5)	(5,5)	(0,10)	(0,10)
I,J Offsets	-	(5,0)	-	(-5,0)	-	-
Arc Center (Xc,Yc)	-	(5,0)	-	(0,5)	-	-
Move Direction	-	Clockwise	-	Counterclockwise	-	-
End Point (X,Y)	-	(5,5)	-	(0,10)	-	-

Key Moments - 3 Insights

Why do we add I and J to the current point to find the arc center?

Because I and J represent the offset from the current point to the arc center, so adding them locates the center relative to where the tool currently is, as shown in steps 2 and 4.

What happens if I or J is zero?

If I or J is zero, it means the arc center lies directly horizontally or vertically aligned with the current point, like in step 2 where J=0 means center is horizontally offset only.

How does the program know which direction to move along the arc?

The command G02 means clockwise and G03 means counterclockwise, so the program uses these to decide the arc direction as seen in steps 2 and 4.

Visual Quiz - 3 Questions

Look at the execution table at step 2. What is the calculated arc center?

A (0,5)

B (10,10)

C (5,0)

D (0,0)

💡 Hint

Check the 'Arc Center (Xc,Yc)' column at step 2 in the execution table.

At which step does the current point update to (5,5)?

A Step 3

B Step 2

C Step 4

D Step 5

💡 Hint

Look for 'Update current point' actions in the execution table.

If the command at step 4 changed from G03 to G02, what would change in the execution table?

A End Point would change

B Move Direction would be Clockwise instead of Counterclockwise

C Arc Center would change

D Current Point would not update

💡 Hint

Check the 'Move Direction' column at step 4 in the execution table.

Concept Snapshot

Arc programming with I, J, K:
- G02 = clockwise arc, G03 = counterclockwise arc
- I, J, K specify center offsets from current point
- Arc center = current point + (I, J, K)
- Tool moves along arc to target end point (X, Y, Z)
- Current point updates to end point after move

Full Transcript

Arc programming with I, J, K uses commands G02 or G03 to move the tool along a circular arc. The I, J, and K values give the offset from the current tool position to the center of the arc. The CNC calculates the arc center by adding these offsets to the current point. Then it moves the tool along the arc in the specified direction (clockwise for G02, counterclockwise for G03) to the target end point. After the move, the current point updates to the end point. This process repeats for each arc command until the program ends.

Practice

1. What do the letters I, J, and K represent in CNC arc programming with G02/G03?

easy

A. The feed rate values for the arc movement

B. The center point offsets of the arc relative to the start point along X, Y, and Z axes

C. The end point coordinates of the arc

D. The tool diameter compensation values

Solution

1. Step 1: Understand the role of I, J, K in arc programming

   In G02/G03 commands, I, J, and K specify the center of the arc relative to the start point along the X, Y, and Z axes respectively.

2. Step 2: Differentiate from other parameters

   They are not end points, feed rates, or tool compensation values, which are specified differently.

3. Final Answer:

   The center point offsets of the arc relative to the start point along X, Y, and Z axes -> Option B

4. Quick Check:

   I, J, K = center offsets [OK]

Hint: I, J, K always mean center offsets in arc commands [OK]

Common Mistakes:

• Confusing I, J, K with end point coordinates
• Thinking I, J, K are feed rates
• Mixing I, J, K with tool diameter values

2. Which of the following is the correct syntax to program a clockwise arc from (10,10) to (20,20) with a center offset of I=5 and J=0 using G-code?

easy

A. G03 X20 Y20 I5 J0

B. G01 X20 Y20 I5 J0

C. G02 X20 Y20 I0 J5

D. G02 X20 Y20 I5 J0

Solution

1. Step 1: Identify the correct G-code for clockwise arc

   G02 is used for clockwise arcs, while G03 is for counterclockwise.

2. Step 2: Check the center offset syntax

   I and J specify the center offset along X and Y axes respectively. Here, I=5 and J=0 is correct.

3. Final Answer:

   G02 X20 Y20 I5 J0 -> Option D

4. Quick Check:

   Clockwise arc uses G02 with correct I, J offsets [OK]

Hint: Use G02 for clockwise arcs with I, J center offsets [OK]

Common Mistakes:

• Using G03 instead of G02 for clockwise arcs
• Swapping I and J values
• Using G01 which is linear move

3. Given the G-code command G03 X40 Y40 I10 J0 starting from (20,40), what is the radius of the arc?

medium

A. 10 units

B. 20 units

C. 30 units

D. 40 units

Solution

1. Step 1: Understand the center offset and start point

   The start point is (20,40). The center offset I=10 means the center is at (20+10, 40+0) = (30,40).

2. Step 2: Calculate the radius

   The radius is the distance from center (30,40) to start point (20,40), which is |30-20| = 10 units. Also check distance to end point (40,40) to (30,40) is |40-30| = 10 units, so radius is consistent with start point offset.

3. Step 3: Verify end point

   End point is (40,40), distance from center (30,40) is 10 units, matching the start point offset.

4. Final Answer:

   10 units -> Option A

5. Quick Check:

   Radius = center offset I = 10 [OK]

Hint: Radius equals distance from start to center (I, J offsets) [OK]

Common Mistakes:

• Confusing radius with distance from center to end point
• Ignoring that I, J are relative to start point
• Calculating radius as distance between start and end points

4. Identify the error in this G-code arc command: G02 X50 Y50 I20 J

medium

A. X and Y coordinates are invalid

B. Incorrect G-code for clockwise arc

C. Missing value for J parameter

D. I and J should be absolute coordinates, not offsets

Solution

1. Step 1: Check the syntax of I and J parameters

   The command has I20 but J is given without a value, which is a syntax error.

2. Step 2: Verify other parts of the command

   G02 is correct for clockwise arc, X50 Y50 are valid coordinates, and I, J are offsets, not absolute coordinates.

3. Final Answer:

   Missing value for J parameter -> Option C

4. Quick Check:

   J must have a numeric value [OK]

Hint: Always provide numeric values for I, J, K parameters [OK]

Common Mistakes:

• Leaving I, J, or K without values
• Using wrong G-code for arc direction
• Confusing offsets with absolute coordinates

5. You want to program a counterclockwise arc from (0,0,0) to (10,10,10) in 3D space using G03 with center offset I=5, J=5, K=5. Which statement about this command is true?

hard

A. I, J, K are relative offsets from the start point, so center is at (5,5,5) relative to (0,0,0)

B. I, J, K specify absolute center coordinates, so the center is at (5,5,5)

C. G03 cannot be used for 3D arcs with I, J, K offsets simultaneously

D. The arc will move in a perfect 3D circular path centered at (5,5,5)

Solution

1. Step 1: Understand I, J, K offsets in 3D arc programming

   I, J, K represent center offsets relative to the start point, not absolute coordinates.

2. Step 2: Analyze the center position

   Since start is (0,0,0), center is at (0+5, 0+5, 0+5) = (5,5,5).

3. Step 3: Confirm G03 usage for 3D arcs

   G03 supports 3D arcs with I, J, K offsets to define the center in 3D space.

4. Final Answer:

   I, J, K are relative offsets from the start point, so center is at (5,5,5) relative to (0,0,0) -> Option A

5. Quick Check:

   I, J, K = relative center offsets in 3D [OK]

Hint: I, J, K always offset from start point, not absolute [OK]

Common Mistakes:

• Thinking I, J, K are absolute coordinates
• Assuming G03 can't handle 3D arcs
• Believing arc center is at origin always