Lesson 3.3: Gear Trains & Cams

Gear Trains and Cams are essential in Theory of Machines. GATE and PSU exams often test gear ratios, velocity ratios, cam profiles, and follower motion.

🔹 1. Gear Trains

• Definition: A combination of gears to transmit motion and torque.

• Applications: Gearboxes, clocks, machine tools, automotive transmissions

• Types of Gears:

  1. Spur Gears: Teeth parallel to axis

  2. Helical Gears: Teeth at an angle → smoother motion

  3. Bevel Gears: Conical gears → change axis direction

  4. Worm Gears: High reduction ratio, non-reversible

• Velocity Ratio (VR):

VR=Speed of driverSpeed of driven=NdrivenNdriver=TdriverTdrivenVR = \frac{\text{Speed of driver}}{\text{Speed of driven}} = \frac{N_{\text{driven}}}{N_{\text{driver}}} = \frac{T_{\text{driver}}}{T_{\text{driven}}}VR=Speed of drivenSpeed of driver​=Ndriver​Ndriven​​=Tdriven​Tdriver​​

Where $N$ = number of teeth, $T$ = torque

• Compound Gear Trains: Multiple gears on same shaft → multiply ratios

• Epicyclic Gear Trains: Central sun gear, planet gears, ring gear → compact design

Example:
Driver gear 20 teeth, driven gear 60 teeth. VR = 60/20 = 3 → driven rotates 3 times slower.

🔹 2. Cams

• Definition: Cam is a rotating or sliding piece that imparts specific motion to a follower.

• Applications: Automobiles (valve operation), presses, textile machines

• Types of Follower Motion:

  1. Uniform Velocity

  2. Simple Harmonic Motion (SHM)

  3. Uniform Acceleration & Retardation (UARM)

• Cam Types:

  • Disc Cam: Flat or radial motion

  • Cylindrical Cam: Rotates around cylinder

  • Translating Cam: Linear displacement

• Follower Types:

  • Knife-edge, Roller, Flat-faced

• Key Design Parameters:

  • Rise, Dwell, Return: Determines motion duration

  • Pressure Angle: Should be < 30° for smooth motion

Example:
Disc cam rotates 180° to lift follower 50 mm with SHM. Max velocity vmax=πh/t=π∗50/(T/2)v_{max} = \pi h / t = \pi * 50 / (T/2)vmax​=πh/t=π∗50/(T/2)

🔹 3. Solved Examples (PYQ Style)

Example 1 (GATE ME 2016):
Simple gear train: Gear A (20 teeth) drives B (40 teeth) → B drives C (30 teeth). Find VR of A to C.

• VR A→B = 40/20 = 2, VR B→C = 30/40 = 0.75

• Total VR A→C = 2 * 0.75 = 1.5 → C rotates slower than A

Example 2 (PSU Exam):
Cam lifts follower 40 mm in 90° rotation with SHM. Max acceleration?

• amax=π2h/(2t2)a_{max} = \pi^2 h / (2 t^2)amax​=π2h/(2t2) (standard formula)

🔹 4. Practice Exercises

1. Calculate velocity ratio for a compound gear train with 4 gears.

2. Draw cam profile for a follower with SHM motion for 50 mm lift.

3. Identify type of follower: roller, knife-edge, flat-faced.

4. Determine maximum pressure angle for given cam-follower system.

5. Design epicyclic gear train for VR = 5.

🔹 5. Summary

• Gear Trains: Transmit motion & torque, VR = teeth ratio, types: spur, helical, bevel, worm, epicyclic

• Cams: Convert rotary motion to reciprocating or oscillating motion

• Follower Motion: Uniform velocity, SHM, UARM

• Applications: Engines, presses, machine tools, automotive systems