🔧 Given

• Gear A = 10 teeth (input / driver)
• Gear B = 20 teeth
• Gear C = 8 teeth (mounted on the same shaft as B)
• Gear D = 24 teeth (output)

So the train works like this:

A → B (shaft 1)
C → D (shaft 2)
(B and C rotate together)

⚙️ Stage-1: Gear A → Gear B

Speed ratio$$\text{Speed}_B = \text{Speed}_A \times \frac{T_A}{T_B} = \text{Speed}_A \times \frac{10}{20} = \frac{1}{2}\,\text{Speed}_A$$SpeedB​=SpeedA​×TB​TA​​=SpeedA​×2010​=21​SpeedA​

👉 Gear B rotates at half the speed of Gear A.

Torque ratio$$\text{Torque}_B = \text{Torque}_A \times \frac{T_B}{T_A} = \text{Torque}_A \times 2$$TorqueB​=TorqueA​×TA​TB​​=TorqueA​×2

👉 Torque doubles at Gear B.

🔗 Compound effect (B & C)

• Gear B and C are rigidly connected
• So:
  • Speed of C = Speed of B
  • Torque of C = Torque of B

⚙️ Stage-2: Gear C → Gear D

Speed ratio$$\text{Speed}_D = \text{Speed}_C \times \frac{T_C}{T_D} = \text{Speed}_C \times \frac{8}{24} = \frac{1}{3}\,\text{Speed}_C$$SpeedD​=SpeedC​×TD​TC​​=SpeedC​×248​=31​SpeedC​

Torque ratio$$\text{Torque}_D = \text{Torque}_C \times \frac{T_D}{T_C} = \text{Torque}_C \times 3$$TorqueD​=TorqueC​×TC​TD​​=TorqueC​×3

📉 Overall Speed Ratio (A → D)

$$\text{Speed}_D = \text{Speed}_A \times \frac{10}{20} \times \frac{8}{24} = \text{Speed}_A \times \frac{1}{6}$$SpeedD​=SpeedA​×2010​×248​=SpeedA​×61​

👉 Final speed = 1/6 of input speed

💪 Overall Torque Ratio (A → D)

$$\text{Torque}_D = \text{Torque}_A \times 2 \times 3 = 6 \times \text{Torque}_A$$TorqueD​=TorqueA​×2×3=6×TorqueA​

👉 Final torque = 6× input torque

Why Compound Gears Matter

So far, we’ve seen how compound gear trains work and why they are such a powerful step up from simple gear pairs. By combining multiple gear stages on shared shafts, we can achieve large speed reductions and high torque multiplication without making the system excessively large.

This is why compound gear trains are widely used in:

• Mechanical gearboxes
• Machine tools
• Robotics mechanisms
• Multi-stage speed reducers

But here’s the catch.

Even compound gear trains have limits.

As gearboxes become more compact and torque requirements increase, designers start facing problems like:

• Longer shaft lengths
• Higher bearing loads
• Alignment challenges
• Limited space for further gear stages

This is exactly where planetary gear systems shine.

In Part 2, we’ll explore:

• What a planetary gear system really is
• How it achieves massive torque in an extremely compact layout
• Why modern EVs, automatic transmissions, and robotic joints rely heavily on planetary gearboxes
• And most importantly — when you should choose planetary gears instead of compound gear trains

👉 Part 2 is where things get really interesting.
Bookmark this page and move on when you’re ready.

RenderWrench Insight:

Compound gear trains teach you how torque multiplies. Planetary systems teach you how engineers cheat space itself.

Happy making 🔧