What motors does a goat-inspired leg need?
Before building a robotic leg you need to know what torque and speed each joint demands. This project computes that for a hindlimb inspired by the domestic goat: it takes joint trajectories from the animal's gait, imposes them on a MuJoCo model and obtains, through inverse dynamics, the torque and speed profiles of hip, knee and ankle. With those requirements, an algorithm sweeps a catalog of commercial motors and gear ratios and ranks the feasible combinations.
Context
Goats move stably over steep, uneven terrain, which makes them an interesting model for exploration and inspection quadrupeds. Copying the shape of the leg is not enough. The performance of a legged robot depends on where the mass sits and on how much inertia and friction the transmission adds: a heavy motor at a distal joint increases limb inertia, and a high reduction delivers torque at the cost of bandwidth and of the ability to sense forces through the motor.
Model
The limb was represented in the sagittal plane as three rigid segments (thigh, shank and metatarsus) with their masses, inertias and centers of mass. The joint angles of one gait cycle were taken from published kinematic data, filtered and interpolated.
Complete flow: gait processing, inverse dynamics and motor selection
The model was validated by checking that the simulation reproduces the input trajectories.
Hip angle: desired and simulated trajectory
Requirements per joint
| Joint | Peak torque [Nm] | RMS torque [Nm] | Nominal speed [rpm] |
|---|---|---|---|
| Hip | 8.12 | 3.13 | 22.6 |
| Knee | 4.35 | 1.59 | 20.7 |
| Ankle | 0.62 | 0.15 | 31.2 |
Demand concentrates at the hip and decreases distally, while speed is highest at the ankle.
Hip torque over one gait cycle
Knee torque over one gait cycle
Ankle torque over one gait cycle
Actuator selection
A database was built with motors from one commercial manufacturer. For each joint, the algorithm evaluates every motor with gear ratios between 1:1 and 50:1, discards the combinations that fail the required torque or speed, and scores the rest by efficiency, gear ratio and mass.
The results follow a consistent pattern. At all three joints the best solutions have low ratios, between 1:1 and 3:1 on top of the motor's own reduction. At the hip and knee, motors with an integrated planetary gearbox win; at the ankle, where torque is low and inertia matters more, the lightest motors in the range win. Efficiency differences between motors affect the score less than mass and gear ratio do.
What is missing
The kinematics come from the literature rather than from the group's own motion capture. The model is rigid-body and leaves out the tendons and passive structures that store energy and absorb impact in the animal, so it likely overestimates the work the actuator has to do. The selection considers mechanical feasibility but not thermal behavior, current limits or closed-loop performance. The analysis covers a single leg in the sagittal plane and a single gait.
How it fits in Robiolab
The project opens a legged-locomotion line in the lab and leaves a reusable tool: the same flow can size the actuators of any articulated mechanism whose trajectory is known, exoskeletons included. The most interesting limitation is also the natural next step. Adding series or parallel elasticity is exactly where bioinspiration stops being geometric and becomes mechanical, and it connects with the group's work on compliant mechanisms.