Question

The assembly shown below has three teethed circular objects (Pinions) and two teethed flat objects (Racks), which are perfectly mating with each other. Pinions can only rotate clockwise or anti-clockwise staying at its own center. Racks can translate towards the left (\(\leftarrow\)) or the right (\(\rightarrow\)) direction. If the object \(A\) (Rack) is translating towards the right (\(\rightarrow\)) direction, the correct statement among the following is:
\includegraphics[width=0.5\linewidth]{9.png}

• A. Object \(B\) translates towards the right direction.
• B. Object \(B\) translates towards the left direction.
• C. Object \(R\) rotates in the anticlockwise direction.
• D. Object \(Q\) rotates in the clockwise direction.

Hint:

For gear-rack systems, analyze the movement of each component step by step, considering the direction of rotation or translation.

Answer 1

The Correct Option is B

Step 1:
Understanding the Mechanism Racks and Pinions: A rack is a linear gear with teeth, and a pinion is a circular gear. When the rack moves, it causes the connected pinion to rotate. The direction of rotation of the pinion is always opposite to the movement of the rack. \section*{System Analysis} Object A moves to the right (→):
This movement causes Object P (the pinion connected to it) to rotate clockwise. Object P rotates clockwise:
As Object P is connected to a rack (Object B), its clockwise rotation drives Object B to move to the left (←). This happens because the pinion's rotation opposes the rack's movement direction. Object B moves to the left (←):
The leftward movement of Object B makes Object Q rotate in an anticlockwise direction. Object Q rotates anticlockwise:
Finally, the anticlockwise rotation of Object Q causes Object R to move to the right (→). Hence, the correct option is (B).