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Required Lift Torque

How much torque a lift actually needs, including the worst case people forget, and whether your motors and gearing supply it.

Inputs

lb

Game objects plus whatever holds them: intake, claw, tray.

in

Horizontal reach when the arm is level, which is where torque peaks. If your lift is a parallel 4-bar rather than a single arm, use the bar length instead: the end effector stays level, so how far forward the load sits makes no difference.

lb

Easy to leave out, and often the larger term on a long arm.

in

Roughly half its length for an even arm.

°

0 is level. Torque is highest here and falls off as it rises.

Results

Can it hold the load?

—

Torque needed, worst case

—N·m

Arm level.

Torque needed at your angle

—N·m

Torque available at the lift

—N·m

Of what the motors can give

—%

Gear ratio

—

Reduction needed to hold it

—

At the worst case, with no margin.

Torque needed, against what the motors give—

Measured at the worst case, arm held level. Past the first mark it holds but will barely lift; past the second it is cooking a motor to stand still.

How this is calculated

Torque is force times the distance it acts from the pivot. An arm holding a load has two of those working against it: the load, and the weight of the arm carrying it.

torque = (load × reach + arm weight × arm balance point) × cos(angle)

The arm's own weight acts at its balance point, which for an even arm is about halfway along. On a long arm that term often beats the game object it was built to carry, which is why a heavy arm costs twice: once in weight, again in the torque needed to move it.

Level is the worst case

The cosine term is the part worth internalizing. At full horizontal extension cos(0) = 1 and torque is at its maximum. Straight up, cos(90) = 0 and the arm needs almost nothing to stay there.

So a lift that seems fine when tested near the top can stall completely on the way through level. Always size for the horizontal case, even if that is not where the arm spends its time.

Getting the torque

available = motors × stall torque × gear ratio

Lifts are where the 100 RPM cartridge earns its place. It gives six times the torque of a 600 for the same motor count, and a lift rarely needs speed. Combined with a large reduction, two motors can hold far more than people expect.

Sources & assumptions

Stall torque is published for the 100 RPM cartridge (2.1 N·m) and derived for the others by scaling inversely with speed. Gear tooth counts are VEX published sizes.

Models a single rigid arm rotating about one pivot. Four bar and DR4B linkages change the geometry, though the peak still lands near horizontal. Ignores friction, which works in your favor for holding and against you for lifting, and ignores rubber band assist, which many lifts rely on. TheRubber Band Assist calculator works out how much of this torque bands can take off you.

Uses motor stall torque, so the answer is what the lift can hold at a standstill, not what it can raise at speed.

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