G01 linear interpolation (cutting feed) in CNC Programming - Time & Space Complexity

Time Complexity: G01 linear interpolation (cutting feed)

O(n)

Understanding Time Complexity

We want to understand how the time to complete a G01 linear move changes as the distance or number of moves increases.

How does the program's execution time grow when cutting longer or more lines?

Scenario Under Consideration

Analyze the time complexity of the following CNC program snippet using G01 commands.

N10 G01 X10 Y0 F100
N20 G01 X20 Y10
N30 G01 X30 Y20
N40 G01 X40 Y30
N50 G01 X50 Y40

This code moves the tool in straight lines from one point to the next at a set feed rate.

Identify Repeating Operations

Each G01 command moves the tool along a straight line.

• Primary operation: Executing each linear move command (G01).
• How many times: Once per line segment, so the number of moves equals the number of G01 commands.

How Execution Grows With Input

As you add more G01 commands, the total execution time grows roughly in direct proportion to the number of moves.

Input Size (n)	Approx. Operations
10 moves	10 linear moves executed
100 moves	100 linear moves executed
1000 moves	1000 linear moves executed

Pattern observation: Doubling the number of moves doubles the execution time.

Final Time Complexity

Time Complexity: O(n)

This means the time to complete all moves grows linearly with the number of G01 commands.

Common Mistake

[X] Wrong: "The time to execute G01 commands stays the same no matter how many moves there are."

[OK] Correct: Each G01 command requires the machine to move along a line, so more commands mean more moves and more time.

Interview Connect

Understanding how execution time grows with commands helps you write efficient CNC programs and shows you can reason about machine performance.

Self-Check

What if we combined multiple linear moves into one longer G01 command? How would the time complexity change?

Practice

1. What does the G01 command do in CNC programming?

easy

A. Moves the tool rapidly without cutting

B. Changes the tool automatically

C. Stops the machine immediately

D. Moves the tool in a straight line at a controlled cutting speed

Solution

1. Step 1: Understand the purpose of G01

   The G01 command is used for linear interpolation, meaning it moves the tool in a straight line.

2. Step 2: Recognize the feed rate role

   G01 moves the tool at a set feed rate, which controls cutting speed, unlike rapid moves (G00).

3. Final Answer:

   Moves the tool in a straight line at a controlled cutting speed -> Option D

4. Quick Check:

   G01 = Linear cutting move [OK]

Hint: G01 means straight line move with cutting feed [OK]

Common Mistakes:

• Confusing G01 with rapid move G00
• Thinking G01 stops the machine
• Assuming G01 changes tools

2. Which of the following is the correct syntax for a G01 command to move to X=10, Y=5 at feed rate 150?

easy

A. G01 X10 Y5 150F

B. G01 X10 Y5 F150

C. G01 F150 X10 Y5

D. G01 X=10 Y=5 F=150

Solution

1. Step 1: Identify correct order and format

   The standard syntax places G01 first, followed by coordinates and feed rate with no equal signs.

2. Step 2: Check feed rate format

   Feed rate is specified as F followed by the number, no equal sign or reversed order.

3. Final Answer:

   G01 X10 Y5 F150 -> Option B

4. Quick Check:

   Correct G01 syntax = G01 X10 Y5 F150 [OK]

Hint: Coordinates then feed rate, no equal signs [OK]

Common Mistakes:

• Using equal signs (=) in commands
• Placing feed rate before coordinates incorrectly
• Writing feed rate as number then F

3. What is the result of this CNC code snippet?

G01 X20 Y10 F100
G01 X30 Y10

medium

A. Moves to (20,10) at default feed, then moves to (30,10) at feed 100

B. Moves to (20,10) at feed 100, then moves to (30,10) at default feed

C. Moves to (20,10) at feed 100, then moves to (30,10) at feed 100

D. Syntax error due to missing feed rate in second line

Solution

1. Step 1: Analyze first line

   G01 moves to X20 Y10 at feed rate 100, setting feed rate for subsequent moves.

2. Step 2: Analyze second line

   Second G01 moves to X30 Y10 without feed rate, so it uses the last set feed rate 100.

3. Final Answer:

   Moves to (20,10) at feed 100, then moves to (30,10) at feed 100 -> Option C

4. Quick Check:

   Feed rate persists until changed = Moves to (20,10) at feed 100, then moves to (30,10) at feed 100 [OK]

Hint: Feed rate stays until changed explicitly [OK]

Common Mistakes:

• Assuming feed rate resets each line
• Thinking missing feed causes error
• Confusing feed rate with rapid move

4. Identify the error in this CNC code:

G01 X50 Y25 F200
G01 X60 Y30 F

medium

A. Missing feed rate value after F in second line

B. Coordinates are invalid

C. G01 command cannot be repeated twice

D. Feed rate must be before coordinates

Solution

1. Step 1: Check second line syntax

   The second line has 'F' with no number after it, which is invalid syntax.

2. Step 2: Validate other parts

   Coordinates are valid, G01 can repeat, and feed rate can come after coordinates.

3. Final Answer:

   Missing feed rate value after F in second line -> Option A

4. Quick Check:

   F must have a number after it [OK]

Hint: F must always have a number after it [OK]

Common Mistakes:

• Ignoring missing feed rate value
• Thinking feed rate order matters
• Assuming repeated G01 is wrong

5. You want to cut a straight line from (0,0) to (50,50) with feed rate 120, then move rapidly to (0,0). Which code sequence is correct?

hard

A. G01 X50 Y50 F120
G00 X0 Y0

B. G00 X50 Y50 F120
G01 X0 Y0

C. G01 X50 Y50
G00 X0 Y0 F120

D. G01 X50 Y50 F120
G01 X0 Y0 F0

Solution

1. Step 1: Use G01 for cutting move

   Cutting move with feed rate 120 requires G01 to move from (0,0) to (50,50).

2. Step 2: Use G00 for rapid move back

   Rapid move back to (0,0) uses G00 without feed rate.

3. Final Answer:

   G01 X50 Y50 F120 G00 X0 Y0 -> Option A

4. Quick Check:

   Cut with G01, rapid with G00 [OK]

Hint: Cut with G01, rapid return with G00 [OK]

Common Mistakes:

• Using G00 for cutting moves
• Setting feed rate on rapid moves
• Using feed rate zero to stop feed