A capstan drive is a cable transmission used in robots when a joint needs smooth, precise motion with very little looseness. A motor turns a small capstan drum, and a tensioned cable wrapped around it drives a larger output pulley connected to the joint. This arrangement can multiply torque, reduce speed, and avoid the backlash often found in gear trains.
It is especially useful in haptic devices, surgical robots, and lightweight robot arms.
Key Facts
- Speed ratio for a capstan drive is approximately omega_out / omega_in = r_capstan / r_pulley.
- Torque ratio is approximately tau_out / tau_in = r_pulley / r_capstan, ignoring losses.
- Cable speed is v = omega r for both the capstan drum and the output pulley if there is no slip.
- Friction grip follows the capstan equation T_high / T_low = e^(mu theta), where theta is in radians.
- Output torque from cable tension is tau_out = (T_tight - T_slack) r_pulley.
- A properly tensioned cable drive can have near zero backlash because the cable stays in continuous contact with the pulleys.
Vocabulary
- Capstan drum
- A small rotating cylinder that grips a wrapped cable by friction and transfers motor motion to the cable.
- Output pulley
- The larger wheel connected to the robot joint that is driven by the moving cable.
- Cable tension
- The pulling force in the cable that allows the drive to transmit torque without going slack.
- Backlash
- Backlash is unwanted looseness or delay in motion when a drive changes direction.
- Wrap angle
- Wrap angle is the total angle of contact between the cable and drum, measured in radians.
Common Mistakes to Avoid
- Using diameter ratio backward, which gives the wrong speed and torque change. The larger output pulley reduces angular speed and increases torque compared with the smaller capstan drum.
- Forgetting to convert wrap angle to radians, which makes the capstan equation incorrect. In T_high / T_low = e^(mu theta), theta must be measured in radians, not degrees.
- Assuming more cable wraps always remove all slip, which is not guaranteed. The cable also needs enough friction, proper pretension, and a clean drum surface.
- Treating cable tension as the same on both sides when torque is being transmitted. Output torque depends on the difference between tight-side and slack-side tension.
Practice Questions
- 1 A motor drives a capstan drum of radius 8 mm connected by cable to an output pulley of radius 40 mm. If the motor spins at 300 rpm and there is no slip, what is the output speed in rpm?
- 2 A capstan drive has a tight-side tension of 45 N and a slack-side tension of 15 N. If the output pulley radius is 0.06 m, what output torque does the cable produce?
- 3 A robot designer chooses a capstan drive instead of gears for a haptic joystick joint. Explain why low backlash, smooth frictional contact, and cable tension are important for the feel of the device.