Arms, Torque and Gear Reduction

A pivoting arm rotates around a joint, called the shoulder, that is mounted on the robot. Instead of moving in a straight line like a lift, the end of the arm moves in an arc. Arms can reach over the robot, flip a game element from front to back, or reach down to the floor and up to a scoring zone with a single motor. They are often simpler to build than multi-stage slides, but they come with one big challenge: torque.

Pivoting arms

A basic arm is a rigid beam on a shaft, driven by a motor through gears, sprockets or a belt. At the far end you usually mount a claw or a small intake, sometimes on a servo-driven wrist that keeps the element at the right angle as the arm rotates. The longer the arm, the further it reaches, and the harder the shoulder has to work.

Torque at the shoulder

Torque is a turning force. It equals the force multiplied by the distance from the pivot: torque = force x distance. Gravity pulls every part of the arm straight down. When the arm points straight up or straight down, that pull runs through the pivot and creates almost no torque. When the arm is horizontal, the full weight acts at its full distance from the pivot, so the torque is at its highest. That is why arms often struggle or droop when held level, and why heavy items at the far end matter so much.

1Force from gravity = mass (kg) x 9.81 (m/s^2)
2Torque = force (N) x distance from pivot (m)
3
4Arm itself:   0.60 kg, centre of mass 0.20 m from pivot
5              0.60 x 9.81 x 0.20 = 1.18 N*m
6Game element: 0.15 kg, held 0.40 m from pivot
7              0.15 x 9.81 x 0.40 = 0.59 N*m
8
9Total at horizontal          ~ 1.77 N*m
10With a 3:1 external reduction, the motor
11must supply about 1.77 / 3   ~ 0.59 N*m (before friction)

Gear reduction

Gear reduction trades speed for torque. When a small gear (the driver, on the motor) turns a large gear (the driven gear, on the arm shaft), the arm turns slower but with more torque. The ratio is the driven gear's teeth divided by the driver gear's teeth. A 20-tooth gear driving a 60-tooth gear gives a 3:1 reduction: roughly three times the torque and one third of the speed, minus some friction losses. Reduction also makes small motor movements into even smaller arm movements, which makes the arm easier to control precisely.

Counterbalancing

Counterbalancing means adding something that pushes back against gravity so the motor does not carry the whole load. Common options are springs, surgical tubing or elastic bands stretched so they pull the arm up, or a small counterweight on the opposite side of the pivot. A well-counterbalanced arm almost floats: it stays roughly where you leave it with the motor unpowered. Because the gravity torque changes with the arm's angle, a counterbalance will never be perfect at every angle, so tune it for the angles where the arm spends the most time. In code, teams also add a small holding power that depends on the angle, largest when the arm is horizontal.

• Keep heavy parts (motors, servos) close to the pivot and use light materials towards the end.
• Support the shoulder shaft on both sides with bearings so it does not bend or wobble.
• Add hard stops so the arm cannot swing past its safe range.
• Watch for backlash (play in the gears); it makes the end of a long arm wobble.

Arm or lift? An arm is usually lighter and can reach in an arc with one motor, but it is hard to hold steady at long reach. A lift moves in a straight line and keeps the element level, but adds stages and rigging. Many teams combine them, putting a short arm or wrist on top of a lift.