Torque math for desktop quadrupeds: how big the actuators must be

Desktop quadrupeds fail at the actuator spec more often than anywhere else. The failure is arithmetic, not ambition: torque requirements scale brutally with leg length and mass, and demos that dance on a bench stall on a carpet. The math is worth doing in the open.

The square law

Torque at a leg joint scales roughly with the product of the animal’s weight and the lever arm — the distance from the joint to the contact point. Double the leg length and you roughly double the lever arm at the same mass, doubling the torque the joint must supply just to stand. Lengthen the legs and lighten the body at the same time, and the demand compounds.

A worked example

A 2 kg quadruped with 8 cm legs standing on three legs (a conservative pose) puts roughly 0.65 kg-force per loaded foot; with an 8 cm lever arm that is about 0.5 N·m at the hip — before any dynamic margin. Add headroom for a push, a paw lift, and gear inefficiency, and the honest spec lands at 1.5–2x the static number. Quoting the static figure is how actuators get undersized.

Mass beats torque

Every gram saved on the body shrinks the required torque across all joints — the only design lever that improves every axis at once. Battery placement low and central, hollow leg segments, and composite links buy more performance than the next torque tier of actuator, and they cost less.

The demo-versus-reality gap

Bench demos run on smooth surfaces at partial stance. Floors are softer and the animal moves. We size actuators from the worst realistic pose, then test on the surfaces the product will actually live on — which is why our quotes ask where the robot will be used, not just what it should do.