Mechanical Systems

Planetary Gear Simulator

Examine the kinematic states of an Epicyclic Gear Train (Planetary System). Set Sun/Planet teeth ratios, select which component is held locked, and adjust input speed to study speed ratios, torque magnification, and planet rotation.

Gearset

Epicyclic

Planetary train

Ring Teeth (Nr)

64T

Ns + 2*Np

Out Power

1.52 kW

Net Net Output

Parameters

Kinematic Lock Mode

Sun Gear Teeth (Ns)24 teeth

1080

Planet Gear Teeth (Np)20 teeth

1060

Input Shaft RPM150 RPM

10500

Input Torque100 N·m

101000

Mesh Efficiency97 %

80100

Input Speed Sweep

Epicyclic Kinematics Model

Velocity Relationship

Ns * w_s + Nr * w_r - (Ns + Nr) * w_c = 0

Ring Teeth Formula

Nr = Ns + 2 * Np

Planet Velocity about Carrier Pin

w_p_rel = (w_c - w_s) * Ns / Np

Output Power Conversion

P_out = P_in * eta_efficiency (P = 2*pi*N*T / 60000)

Locking the Ring Gear yields a transmission ratio of 3.667:1.

Mechanical efficiency losses dissipate 0.05 kW of power.

Epicyclic Mesh Visualizer

Gear Ratio

3.667: 1

Output Speed

40.9RPM

Output Torque

355.7N·m

Output Power

1.52kW

Output RPM & Output Torque vs Input Speed

Kinematics Data Grid

Input RPM	Output RPM	Output Torque (N·m)
20	5.5	355.7
100	27.3	355.7
180	49.1	355.7
260	70.9	355.7
340	92.7	355.7
420	114.5	355.7
500	136.4	355.7