Arms and pivots

An arm is a lever with a motor at the pivot. It is simple to build — a bar, a bearing, a sprocket — and it can reach up, out and over things in one motion. The catch is gravity: the load on an arm's motor changes as the arm moves, and it is easy to build an arm that holds its weight fine when it is up and cannot lift it when it is out.

Gravity torque

Torque is force times the distance from the pivot — but only the horizontal distance counts when the force is gravity pulling straight down.

gravity torque = mass × g × horizontal distance from pivot
               = m × 9.81 × L × cos(θ)

Here L is the distance from the pivot to the object's centre of mass, and θ is the arm's angle above horizontal.

• Arm straight out (θ = 0°): cos θ = 1. The full length counts. This is the worst case.
• Arm at 45°: cos θ ≈ 0.71. About 71% of the worst case.
• Arm straight up or straight down: cos θ = 0. Gravity pulls straight through the pivot and the motor feels almost nothing.

Every part of the arm contributes, each at its own distance. The bar itself acts at its middle; the claw and the game element act near the end.

Worked example

A 30 cm arm bar weighing 0.3 kg, with a claw plus game element of 0.4 kg at the very end:

bar:   0.3 kg × 0.15 m = 0.045 kg·m   (its centre is halfway out)
claw:  0.4 kg × 0.30 m = 0.120 kg·m
total: 0.165 kg·m
 
torque at horizontal = 9.81 × 0.165 ≈ 1.62 N·m
torque at 45°        = 1.62 × 0.71  ≈ 1.14 N·m

Notice that the claw is responsible for almost three quarters of the load, because it is at the end. Weight at the end of an arm is expensive. Every gram you save on the claw helps more than a gram saved near the pivot.

Why arms need big reductions

Compare that 1.62 N·m with a goBILDA 312 RPM motor, whose listed stall torque is about 2.38 N·m:

Direct-driven, the motor would spend the match working near its limit — hot, sluggish, and stalling whenever anything extra happens. With a 5:1 reduction the load is a small fraction of what the motor can deliver, and the arm can still swing 90° in about a quarter of a second at free speed. (Real gear trains lose a little to friction, so treat 11.9 N·m as a ceiling.)

A big reduction buys three more things:

• Better control. goBILDA lists 537.7 encoder counts per output revolution for this motor. Directly on the arm, that is about 1.5 counts per degree; after a 5:1 reduction it is about 7.5 counts per degree, so position control is far finer.
• Less back-driving. Gravity has a harder time pushing the arm down through a big reduction, so holding position takes less effort.
• A healthier gearbox. Game Manual 0 recommends driving an arm through gears, chain or belt rather than mounting it straight on the motor shaft, partly because of the side loads on the motor and partly to get a larger reduction. Long arms need very large reductions — Game Manual 0's example arm uses 254.5:1.

Counterbalancing

The motor does not have to fight all of gravity alone. A counterbalance pushes the arm upwards so the motor only has to supply the difference.

Common ways to do it in FTC:

• Surgical tubing or springs stretched between the frame and the arm, so they pull the arm up as it goes down. Cheap, light and easy to tune — move the anchor point or change the tubing length.
• A counterweight on the other side of the pivot. Simple, but it adds weight to the robot and makes the arm slower to start and stop.

In the worked example, tubing that provides 1.0 N·m of lift at horizontal leaves the motor to supply only about 0.6 N·m there.

Arms on the end of other mechanisms

Not every arm lifts the whole scoring mechanism. Small arms that flip a claw or tilt an intake are often driven by servos, because the loads are small. The gravity torque calculation is exactly the same — check it against the servo's rated torque, with margin. Because these arms stick out and get hit, support the servo properly so collisions do not land on its output shaft.

Also be realistic about reach. Game Manual 0 points out that a single arm that has to fit in the starting size can only reach about 16 inches, while most games want more than 24. That is why many competitive robots put slides on a pivoting arm: the arm sets the angle, and the slides give the reach.

Next

That completes the mechanisms unit. The last unit is about keeping everything you have built in one piece for a whole season.

Sources and further reading

• Game Manual 0 — Arms (reductions, momentum, reach limits, pivoting slides)
• Game Manual 0 — Linkages
• Game Manual 0 — Motion Mounting (dead axle pivots)
• goBILDA — 5203 Yellow Jacket 312 RPM motor (stall torque and encoder resolution)
• goBILDA — Yellow Jacket planetary gear motors