Calculate the moment \( M_O \) of the 160-N force about the base point \( O \) of the robot. The moment is positive if counterclockwise and negative if clockwise.

Assume:
- \( F = 160 \, \text{N} \)
- \( a = 560 \, \text{mm} \)
- \( b = 350 \, \text{mm} \)
- \( c = 220 \, \text{mm} \)
- \( \theta = 58^\circ \)
- \( \alpha = 11^\circ \)

Question

10-02-2025
Engineering

College

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Calculate the moment \( M_O \) of the 160-N force about the base point \( O \) of the robot. The moment is positive if counterclockwise and negative if clockwise.

Assume:
- \( F = 160 \, \text{N} \)
- \( a = 560 \, \text{mm} \)
- \( b = 350 \, \text{mm} \)
- \( c = 220 \, \text{mm} \)
- \( \theta = 58^\circ \)
- \( \alpha = 11^\circ \)

Answer :

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azikennamdi azikennamdi · Answer 1 · 2024-12-04T18:05:52-05:00

Since the angle between the force and the perpendicular distance is less than 90 degrees (counterclockwise direction), the moment is positive. Therefore, the moment Mo is 42.22 Nm counterclockwise.

What is the explanation for the above response?

To calculate the moment Mo, we can use the formula:

Mo = F * d

where F is the force, and d is the perpendicular distance from the line of action of the force to the base point O.

First, we need to find the perpendicular distance from the line of action of the force to point O. We can use trigonometry to do this. Let's call this distance "h".

h = a * cos(theta) + c * cos(alpha)

h = 560 mm * cos(58) + 220 mm * cos(11)

h = 263.89 mm

Now we can calculate the moment Mo:

Mo = F * d

Mo = 160 N * 0.26389 m

Mo = 42.22 Nm

Since the angle between the force and the perpendicular distance is less than 90 degrees (counterclockwise direction), the moment is positive. Therefore, the moment Mo is 42.22 Nm counterclockwise.

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