A rotating shaft carries four unbalanced masses 20, 15, 18 and 10 kg…

Question

A rotating shaft carries four unbalanced masses 20, 15, 18 and 10 kg at radii 50, 60, 70 and 65mm, respectively. The $2^\text{nd}$, $3^\text{rd}$ and $4^\text{th}$ masses revolve in planes 80, 150 and 300 mm respectively measured from the plane of the first mass and are angularly located at $60^\circ$, $130^\circ$ and $270^\circ$ respectively measured anti-clockwise from the first mass looking from this mass end of the shaft. The shaft is dynamically balanced by two masses, both located at 50 mm radii and revolving in planes mid-way between those of first and second masses and midway between those of $3^\text{rd}$ and $4^\text{th}$ masses. Determine the magnitudes of the masses and their respective angular position.

Related pages

• balancing of masses rotating in different planes — topic
• THEORY OF MACHINES syllabus