Combining arcs and lines for contours in CNC Programming - Step-by-Step Execution

Concept Flow - Combining arcs and lines for contours

Start at point

↓

Draw line to next point

↓

Draw arc to next point

↓

Draw line or arc to next point

↓

Repeat until contour complete

↓

End contour

The flow shows starting at a point, then alternating drawing lines and arcs step-by-step to form a contour until complete.

Execution Sample

CNC Programming

G00 X0 Y0
G01 X10 Y0 F100
G02 X15 Y5 I0 J5
G01 X15 Y15
G03 X10 Y20 I-5 J0

This CNC code moves to start, draws a line, then an arc clockwise, another line, and an arc counterclockwise to form a contour.

Execution Table

Step	Command	Action	Position After	Notes
1	G00 X0 Y0	Rapid move to start point	(0, 0)	Start position set
2	G01 X10 Y0 F100	Linear move to (10,0)	(10, 0)	Draw line segment
3	G02 X15 Y5 I0 J5	Clockwise arc to (15,5) with center offset (0,5)	(15, 5)	Draw arc segment
4	G01 X15 Y15	Linear move to (15,15)	(15, 15)	Draw line segment
5	G03 X10 Y20 I-5 J0	Counterclockwise arc to (10,20) with center offset (-5,0)	(10, 20)	Draw arc segment
6	End	Contour complete	(10, 20)	Finished contour

💡 All commands executed, contour path completed.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5	Final
Position	(unknown)	(0, 0)	(10, 0)	(15, 5)	(15, 15)	(10, 20)	(10, 20)

Key Moments - 3 Insights

Why does the position change after each command?

Each command moves the tool head to a new position, updating the current coordinates as shown in the execution_table rows.

How do I know if an arc is clockwise or counterclockwise?

The G02 command means clockwise arc, G03 means counterclockwise, as shown in steps 3 and 5 in the execution_table.

What do the I and J values mean in arc commands?

I and J specify the center of the arc relative to the start point, guiding the arc's curve direction and radius.

Visual Quiz - 3 Questions

Look at the execution_table, what is the position after step 3?

A (15, 5)

B (10, 0)

C (15, 15)

D (0, 0)

💡 Hint

Check the 'Position After' column for step 3 in the execution_table.

At which step does the tool draw a counterclockwise arc?

A Step 3

B Step 5

C Step 2

D Step 4

💡 Hint

Look for G03 command in the 'Command' column of the execution_table.

If the G01 command at step 4 changed to move to (20, 15), what would be the new position after step 4?

A (15, 15)

B (10, 20)

C (20, 15)

D (15, 5)

💡 Hint

The position after a G01 command is the coordinates specified in that command.

Concept Snapshot

Combining arcs and lines for contours:
- Use G01 for straight lines
- Use G02 for clockwise arcs
- Use G03 for counterclockwise arcs
- I and J define arc center offsets
- Sequence commands to form complex shapes

Full Transcript

This lesson shows how CNC programs combine line and arc commands to create contours. The tool starts at a point, then moves in straight lines (G01) or arcs (G02 clockwise, G03 counterclockwise) to new positions. The I and J values specify the arc center relative to the start point. Each command updates the tool's position, building the contour step-by-step until complete.

Practice

1. Which G-code command is used to move the tool in a straight line when combining arcs and lines for contours?

easy

A. G01

B. G02

C. G03

D. G00

Solution

1. Step 1: Understand G-code commands for movement

   G01 is the command for linear interpolation, which moves the tool in a straight line.

2. Step 2: Differentiate from arc commands

   G02 and G03 are used for clockwise and counterclockwise arcs, respectively, while G00 is rapid positioning without cutting.

3. Final Answer:

   G01 -> Option A

4. Quick Check:

   Straight line move = G01 [OK]

Hint: Remember: G01 = line, G02/G03 = arcs [OK]

Common Mistakes:

• Confusing G01 with G02 or G03
• Using G00 for cutting moves
• Mixing arc commands for straight lines

2. Which of the following is the correct syntax to program a clockwise arc from the current position to X10 Y10 with center offset I5 J0?

easy

A. G02 X10 Y10 I5 J0

B. G03 X10 Y10 I5 J0

C. G01 X10 Y10 I5 J0

D. G00 X10 Y10 I5 J0

Solution

1. Step 1: Identify arc direction commands

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

2. Step 2: Check parameters for arc center

   I and J specify the center offset relative to the start point, which is correct here.

3. Final Answer:

   G02 X10 Y10 I5 J0 -> Option A

4. Quick Check:

   Clockwise arc = G02 [OK]

Hint: G02 = clockwise arc, G03 = counterclockwise arc [OK]

Common Mistakes:

• Using G03 for clockwise arcs
• Using G01 or G00 with I and J parameters
• Forgetting I and J for arc centers

3. What is the output position of the tool after executing the following G-code sequence starting at X0 Y0?

G01 X10 Y0
G02 X10 Y10 I0 J5

medium

A. X10 Y5

B. X0 Y10

C. X10 Y10

D. X5 Y10

Solution

1. Step 1: Execute the linear move

   G01 X10 Y0 moves the tool straight from X0 Y0 to X10 Y0.

2. Step 2: Execute the clockwise arc

   G02 X10 Y10 I0 J5 draws a clockwise arc from X10 Y0 to X10 Y10 with center offset 0 in X and 5 in Y, forming a quarter circle.

3. Final Answer:

   X10 Y10 -> Option C

4. Quick Check:

   Arc ends at X10 Y10 [OK]

Hint: Arc ends at specified X and Y coordinates [OK]

Common Mistakes:

• Confusing arc center offsets
• Assuming arc ends at center point
• Ignoring the final X and Y in arc command

4. Identify the error in this G-code snippet intended to create a smooth contour combining lines and arcs:

G01 X5 Y5
G02 X10 Y10 I5 J0
G03 X15 Y5 I5 J-5

medium

A. Missing G00 command before arcs

B. Incorrect use of I and J values for arc centers

C. Using G03 instead of G02 for clockwise arc

D. No error, code is correct

Solution

1. Step 1: Analyze arc center offsets

   For the first arc G02 X10 Y10 I5 J0, the center offset I5 J0 is correct relative to start X5 Y5.

2. Step 2: Check second arc offsets

   G03 X15 Y5 I5 J-5 is suspicious because the center offset I5 J-5 does not correctly define a smooth arc from X10 Y10 to X15 Y5.

3. Final Answer:

   Incorrect use of I and J values for arc centers -> Option B

4. Quick Check:

   Arc center offsets must match start/end points [OK]

Hint: Verify I and J match arc start/end points [OK]

Common Mistakes:

• Assuming any I/J values work
• Confusing clockwise and counterclockwise arcs
• Forgetting arcs need correct center offsets

5. You want to program a contour that starts at X0 Y0, moves straight to X20 Y0, then follows a counterclockwise arc to X20 Y20 with center offset I0 J10, and finally moves straight back to X0 Y20. Which sequence of G-code commands correctly achieves this?

hard

A. G01 X20 Y0
G02 X20 Y20 I0 J10
G01 X0 Y20

B. G01 X20 Y0
G03 X20 Y20 I10 J0
G01 X0 Y20

C. G00 X20 Y0
G03 X20 Y20 I0 J10
G00 X0 Y20

D. G01 X20 Y0
G03 X20 Y20 I0 J10
G01 X0 Y20

Solution

1. Step 1: Move straight from start to X20 Y0

   Use G01 X20 Y0 for a linear cut from X0 Y0 to X20 Y0.

2. Step 2: Program counterclockwise arc to X20 Y20

   G03 is for counterclockwise arcs; center offset I0 J10 matches the arc center 10 units above start point.

3. Step 3: Move straight back to X0 Y20

   Use G01 X0 Y20 for a linear move back along Y axis.

4. Final Answer:

   G01 X20 Y0 G03 X20 Y20 I0 J10 G01 X0 Y20 -> Option D

5. Quick Check:

   Line + CCW arc + line = sequence B [OK]

Hint: Use G03 for CCW arcs with correct I/J offsets [OK]

Common Mistakes:

• Using G02 instead of G03 for CCW arc
• Wrong I/J values for arc center
• Using G00 for cutting moves