Circular arc on a part profile is being machined on a vertical CNC milling machine. CNC part program using metric units with absolute dimensions is listed below:
--------------------------------
N60 G01 X 30 Y 55 Z – 5 F 50
N70 G02 X 50 Y 35 R 20
N80 G01 Z 5
--------------------------------
The coordinates of the centre of the circular arc are :
a)
(30, 55)
b)
(50, 55)
c)
(50, 35)
d)
(30, 35)
Correct answer is option 'D'. Can you explain this answer?

Question

Circular arc on a part profile is being machined on a vertical CNC milling machine. CNC part program using metric units with absolute dimensions is listed below:
--------------------------------
N60 G01 X 30 Y 55 Z – 5 F 50
N70 G02 X 50 Y 35 R 20
N80 G01 Z 5
--------------------------------
The coordinates of the centre of the circular arc are :

a)
(30, 55)
b)
(50, 55)
c)
(50, 35)
d)
(30, 35)

Correct answer is option 'D'. Can you explain this answer?

Answer

Given:
CNC part program using metric units with absolute dimensions:
N60 G01 X 30 Y 55 Z 5 F 50
N70 G02 X 50 Y 35 R 20
N80 G01 Z 5

To find:
The coordinates of the center of the circular arc.

Solution:
The given CNC part program consists of three lines. Let's analyze each line to find the coordinates of the center of the circular arc.

Line N60:
G01 - This command specifies linear interpolation.
X 30 - This command moves the tool in the X-axis to the coordinate 30.
Y 55 - This command moves the tool in the Y-axis to the coordinate 55.
Z 5 - This command moves the tool in the Z-axis to the coordinate 5.
F 50 - This command sets the feed rate to 50.

So, the tool moves to the point (30, 55, 5) in three-dimensional space.

Line N70:
G02 - This command specifies circular interpolation in a clockwise direction.
X 50 - This command moves the tool in the X-axis to the coordinate 50.
Y 35 - This command moves the tool in the Y-axis to the coordinate 35.
R 20 - This command specifies the radius of the circular arc, which is 20.

The center of the circular arc can be found by moving 20 units perpendicular to the line joining the current position (30, 55, 5) and the target position (50, 35, 5). The direction of the movement is determined by the circular interpolation direction, which is clockwise (G02).

Since the target position is (50, 35, 5), the center of the circular arc is the point that is 20 units away from the line joining (30, 55, 5) and (50, 35, 5) in the clockwise direction.

Line N80:
G01 - This command specifies linear interpolation.
Z 5 - This command moves the tool in the Z-axis to the coordinate 5.

This line doesn't affect the coordinates of the center of the circular arc.

Final Answer:
The coordinates of the center of the circular arc are (30, 35). Therefore, the correct answer is option 'D'.

Answer

D

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