Presets
Playback
Ground motion
Peak ground acceleration, frequency and the type of motion (0 = steady harmonic, 1 = sweep from slow to fast, 2 = single pulse).
Building frame
Natural period and damping of the frame; the robot stands on its top floor.
Rescue robot
Foot friction, rubble slope and body geometry set slipping and tipping limits.
Layers
Model checks
The science
The building as a spring-mass
A one-storey frame is modelled as a damped oscillator. With relative displacement x of the roof and ground acceleration a_g, x'' + 2 zeta w_n x' + w_n^2 x = -a_g, where w_n = 2 pi / T is the natural frequency and zeta the damping ratio. For steady shaking at frequency w the drift amplitude is the ground displacement times r^2 / sqrt((1 - r^2)^2 + (2 zeta r)^2) with r = w / w_n. The peak at r near 1 is resonance: slow, long-period motions that match the frame are the dangerous ones. The frequency sweep moves through the resonance on its own.
Robot on a shaking floor
The roof accelerates by a_g + x''. A robot standing on it grips while the friction can supply that acceleration: |a| <= mu g. Above that it slides (Coulomb stick-slip) and accumulates slip distance, which is what the robot status readout and the third graph show.
Climbing rubble
On a slope the wheels grip while tan(theta) <= mu, and the robot tips over backwards when tan(theta) > b / (2 h) (wheelbase b, centre-of-mass height h). The steepest climbable slope is the smaller of the two angles.
Honest simplifications
One degree of freedom, a linear frame, a rigid robot, no rocking, no soil, and idealised harmonic, sweep and Ricker-pulse ground motions. Real structures yield and fail in ways this model does not show; it is a learning tool for resonance and friction limits, not a safety assessment. The roof drift is drawn four times larger than true for visibility.
What to try
- Press Resonant shaking and compare the drift with Off-resonance: the same ground acceleration gives much more sway when the frequencies match.
- Run the Frequency sweep and watch the response grow and shrink as it passes the natural frequency.
- Lower the foot friction below the peak ground acceleration and the robot starts to slip.
- Make the robot taller (raise the centre of mass) and see the tipping limit take over from friction.