A gear differential is a compact mechanism that lets two output shafts share drive torque while rotating at different speeds. In a robot drivetrain, this is useful because the outside wheel must travel farther than the inside wheel during a turn. Without a differential, the wheels would scrub against the floor, waste energy, and make steering less predictable.
A bevel-gear differential solves this with a symmetric gear arrangement inside the axle.
Key Facts
- For an ideal open differential, the two wheel torques are approximately equal: T_left = T_right.
- The carrier speed is the average of the two output speeds: omega_carrier = (omega_left + omega_right) / 2.
- If the robot drives straight, omega_left = omega_right and the spider gears do not spin on their own axes.
- During a turn, the spider gears rotate and allow omega_left and omega_right to be different.
- Wheel linear speed is related to angular speed by v = r omega.
- For a turn with track width W and turn radius R measured to the robot center, v_outer / v_inner = (R + W/2) / (R - W/2).
Vocabulary
- Differential
- A gear mechanism that splits input motion and torque between two outputs while allowing the outputs to rotate at different speeds.
- Bevel gear
- A cone-shaped gear that transfers rotation between intersecting shafts, often at a 90 degree angle.
- Spider gear
- A small bevel gear mounted on the carrier that allows the two side gears to rotate at different speeds.
- Side gear
- A bevel gear connected to an output shaft that drives one wheel or one side of a mechanism.
- Carrier
- The rotating frame that holds the spider gears and is driven by the input ring gear.
Common Mistakes to Avoid
- Assuming both wheels always spin at the same speed, which is wrong because the differential is designed to allow different wheel speeds during a turn.
- Thinking the differential sends more torque to the faster wheel, which is wrong for an ideal open differential because both outputs receive nearly equal torque.
- Forgetting to use angular speed units consistently, which is wrong because rpm, rad/s, and wheel linear speed must be converted before using equations.
- Ignoring traction limits, which is wrong because an open differential can only deliver as much useful torque as the lower-traction wheel can support.
Practice Questions
- 1 A robot with wheel radius 0.05 m has a left wheel speed of 12 rad/s and a right wheel speed of 18 rad/s. What are the left and right wheel linear speeds?
- 2 In an ideal differential, the carrier rotates at 300 rpm and the left output rotates at 240 rpm. Using omega_carrier = (omega_left + omega_right) / 2, find the right output speed.
- 3 A robot turns left on a high-traction floor. Explain which wheel should rotate faster and why the spider gears are needed.