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ENGR5004 / Week 6
Dynamics L11 Worked example 3TutorialOld spec ENGR2162:210 min

ENGR216 Dynamics L11 worked example 3 (slides 16-18) official answers

In a planetary gear train, the sun gear S (radius 80 mm) is held fixed. Planet gears P (radius 40 mm) mesh with S and with the internal ring gear R (pitch radius 160 mm). The planets are carried on pins of an arm attached to shaft A, which rotates about the common central axis. The ring gear rotates anticlockwise at ωR=3\omega_R = 3 rad/s.

Find the angular velocity of each planet gear and of shaft A.

Planetary gear set: fixed sun gear S (80 mm radius), planet gears P (40 mm radius) on an arm fixed to shaft A, and outer ring gear R rotating at omega_R.
Planetary gear set: fixed sun gear S (80 mm radius), planet gears P (40 mm radius) on an arm fixed to shaft A, and outer ring gear R rotating at omega_R.
Formulas you may need
  • Relative velocity: vB=vA+ω×rB/A\mathbf v_B = \mathbf v_A + \boldsymbol\omega \times \mathbf r_{B/A} (learn this)
  • Meshing gears: the contact points have the same velocity (no slip) (learn this)