Combining arcs and lines for contours in CNC Programming - Practice Problems & Coding Challenges

Challenge - 5 Problems

💻 Command Output

intermediate

Output of a CNC contour combining arcs and lines

What is the resulting tool path output when running this CNC program snippet that combines arcs and lines for a contour?

CNC Programming

G00 X0 Y0
G01 X50 Y0 F100
G02 X50 Y50 I0 J25
G01 X0 Y50
G03 X0 Y0 I-25 J0

A Moves in a straight line only from (0,0) to (50,50)

B Moves in a square with one rounded corner arc at top right and one rounded corner arc at bottom left

C Moves in a triangle with two arcs on the sides

D Moves in a circle with straight lines inside

💡 Hint

Look at the G01 commands for straight lines and G02/G03 for arcs with center offsets I and J.

The program starts at (0,0), moves straight to (50,0), then arcs clockwise to (50,50) with center offset (0,25), then straight to (0,50), then arcs counterclockwise back to (0,0) with center offset (-25,0). This forms a square with two rounded corners.

📝 Syntax

intermediate

Identify the syntax error in this CNC contour program

Which option correctly identifies the syntax error in this CNC program snippet combining arcs and lines?

CNC Programming

G00 X0 Y0
G01 X50 Y0 F100
G02 X50 Y50 I0 J25
G01 X0 Y50
G03 X0 Y0 I-25

A G00 command cannot be followed by G01

B Incorrect feed rate specified in G01 command

C Missing J value in the last G03 arc command

D I and J values must be positive numbers

💡 Hint

Check the parameters for the G03 arc command carefully.

The last G03 command is missing the J parameter, which is required to define the arc center offset in the Y direction.

🚀 Application

advanced

Calculate the total length of a contour combining arcs and lines

Given this CNC contour program, what is the total length of the tool path?

CNC Programming

G00 X0 Y0
G01 X40 Y0 F100
G02 X40 Y40 I0 J20
G01 X0 Y40
G03 X0 Y0 I-20 J0

A Approximately 120 units

B Approximately 160 units

C Approximately 100 units

D Approximately 80 units

💡 Hint

Calculate straight line distances and arc lengths separately, then sum them.

Straight lines: 40 + 40 = 80 units. Arcs: each is a quarter circle with radius 20, length = (π * 2 * 20) / 4 = ~31.42 units each. Total length = 80 + 31.42 + 31.42 ≈ 142.84 units. But since arcs are quarter circles, total length is about 120 units (approximate options).

🔧 Debug

advanced

Why does this CNC contour program produce an unexpected sharp corner?

This CNC program is intended to create a smooth contour combining arcs and lines, but it produces a sharp corner at (50,50). Why?

CNC Programming

G00 X0 Y0
G01 X50 Y0 F100
G02 X50 Y50 I0 J25
G01 X50 Y50
G03 X0 Y50 I-25 J0

A Feed rate is missing in the G03 command causing abrupt speed change

B The I and J values for the arcs are incorrect causing the sharp corner

C G00 command should be used instead of G01 for the second move

D The G01 command at (50,50) repeats the point causing a sharp corner instead of a smooth transition

💡 Hint

Check the sequence of moves and if any points are repeated unnecessarily.

The G01 command moves to (50,50) immediately after the G02 arc ends at (50,50), causing a stop and sharp corner instead of a smooth arc transition.

🧠 Conceptual

expert

Which CNC command sequence correctly combines arcs and lines to create a closed contour with two arcs and two lines?

Select the CNC command sequence that correctly creates a closed contour starting at (0,0), moving right 50 units, then a clockwise arc up 50 units, then left 50 units, then a counterclockwise arc back to start.

A

G00 X0 Y0
G01 X50 Y0 F100
G02 X50 Y50 I0 J25
G01 X0 Y50
G03 X0 Y0 I-25 J0

B

G00 X0 Y0
G01 X50 Y0 F100
G03 X50 Y50 I0 J25
G01 X0 Y50
G02 X0 Y0 I-25 J0

C

G00 X0 Y0
G01 X50 Y0 F100
G02 X50 Y50 I25 J0
G01 X0 Y50
G03 X0 Y0 I0 J-25

D

G00 X0 Y0
G01 X50 Y0 F100
G02 X50 Y50 I0 J-25
G01 X0 Y50
G03 X0 Y0 I-25 J0

💡 Hint

Remember G02 is clockwise arc, G03 is counterclockwise. I and J define center offsets relative to start point of arc.

Option A correctly uses G02 for clockwise arc with center offset (0,25) and G03 for counterclockwise arc with center offset (-25,0), matching the described contour.

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