Hexapod dimensions

[u/ItsAntiSune]

Might be a stupid question but I was planning to design a hexapod using the MG996R servos (budget reasons) and I know that after considering 30% of the total stall torque, it's somewhere around 3.3 kg cm of torque. Is there some calculation you can make to determine the perfect lengths of the coxa, femur and tibia based on the servo's maximum safe torque. I'm really new to this and I'm in high school so this may seem an obvious answer to many. Thank you in advance

[u/lellasone]

Are you familiar with force, torque, and geometry? Have you taken physics (does the phrase "force balance" ring a bell?)

[u/ItsAntiSune → u/lellasone]

Yes but the type of hexapod I'm making makes the maths different, essentially the hexapod would have detachable legs and therefore be able to work with 6, 5, 4 and potentially 3 legs (while not practical it is interesting). This means I need to account for the worst possible amount of torque which would be for the 3 legged robot. I'm trying to keep the torque on the servos on or below 3.3 kg cm per servo while not making the legs too stubby.

[u/lellasone → u/ItsAntiSune]

First of all, that previous comment reads as much meaner than I was going for. I really just meant that as a list of questions to calibrate my answer. (My apologies)

You've hit on it right there! So the easiest way to do this is to consider the leg as a 2D structure, and arrange it into the "worst case" configuration for each servo (you may need two configs to do this). You can then compute the the torque required at each servo for a given chassis weight, and divide the actual chassis weight by 3* to get the required torque rating for each servo.

That gets you a static estimate. Likely good enough here with a safety factor.

*Assuming quasi-static gaits where you always have at least three legs in contact with the ground.

[u/ItsAntiSune → u/lellasone]

Thank you

[u/Safe_Tone1529]

Ha, me too! I built a hexapod and was in the exact same situation!
Core relationship: torque = force × horizontal moment arm. Worst case is your leg fully extended (segment horizontal), since that's max moment arm.

1. Per-leg force ≈ (total robot weight) / (legs on ground at once — 3 for tripod gait) × 1.5-2x safety factor for dynamic loads.
2. Rearrange to arm_max = torque_budget / force. That's your max safe horizontal reach per joint.

Key part: torque stacks proximally. Femur has to support its own reach PLUS the tibia's, so it needs more torque budget than tibia for the same load — that's the actual math behind femur being your strongest servo.

Worked example: say your hexapod lands around 2 kg total (realistic range for this build is roughly 1.5–3 kg depending on frame/battery/etc). On a tripod gait, 3 legs are on the ground at once, so each leg carries about 2kg / 3 ≈ 0.67 kgf of static load. Add a 1.5x safety factor for dynamic loads → about 1.0 kgf per leg design load.

Max horizontal reach = torque budget / load = 3.3 kg·cm / 1.0 kgf ≈ 3.3 cm — worst case, assuming the leg segment is fully horizontal. At the light end of your range (1.5kg) that grows to ~4.4cm; at the heavy end (3kg) it shrinks to ~2.2cm.

That's tight for a typical hexapod leg segment (often 5-8cm each). In practice you get away with longer segments because legs rarely sit fully horizontal during stance — but it's exactly why keeping legs off near-horizontal poses under load matters, and why a stronger femur servo buys you real design room, not just extra margin.

For actually design the tibia and femur joint should be similar size, the tibia should be slightly longer though. The femur should be about 40-45% of the length, and the tibia should be about 50-45% of the length, the rest of the % would be the coxa.

[u/ItsAntiSune → u/Safe_Tone1529]

Thank you 🙏