Heavy machineryManufacturing & robotics

Hydraulic excavator

A 20-tonne excavator as one multi-physics model — a planar boom/stick/bucket linkage driven by hydraulic cylinders off a load-sensing pump, from kinematics and workspace through a coupled dig cycle to breakout force and cycle energy.

DjiniousLabModelling & simulation

A DjiniousLab notebook plot of an excavator dig cycle — boom, stick and bucket joint angles with the boom cylinder pressure spiking at dig-resistance contacts

boom · stick · bucket: 3 linksboom · stick · bucket
system pressure: 35 MPasystem pressure
bucket breakout force: 125.3 kNbucket breakout force
energy per dig cycle: 572 kJenergy per dig cycle
design notebooks: 9design notebooks
.djl composition: 1.djl composition

An excavator where fluid power meets multibody.

A 20-tonne excavator's working arm — boom, stick and bucket — as one model that spans two physical domains at once: a planar multibody linkage driven by hydraulic cylinders fed from a load-sensing pump. From forward and inverse kinematics through a coupled dig cycle to breakout force and cycle energy, with the valve-controlled cylinder also composed as a runnable acausal .djl over a brand-new hydraulic domain.

Geometry, hydraulics, and a full dig.

Each subsystem is its own runnable notebook, building from arm geometry up to a coupled fluid-and-multibody dig cycle.

Arm kinematics

Forward kinematics of the 3-link planar arm, swept to trace the bucket-tip reachable workspace — 11.68 m reach and 6.58 m dig depth, rendered as a 3D pose and a 2D envelope.

Inverse kinematics

A closed-form solver places the bucket tip at a target with a 0 mm forward-kinematics round-trip error — exact, not iterative.

Hydraulic cylinder

Chamber compressibility, orifice valve flow and piston dynamics: a commanded cylinder extends to 0.96 m and peaks at 24 MPa, under the 35 MPa relief.

Actuator mapping

The cylinder geometry's nonlinear moment arm — peaking near 1.29 m mid-travel — maps cylinder force to a maximum boom-joint torque of 515 kN·m at system pressure.

Coupled dig cycle

The planar multibody arm, gravity and inertia included, driven by the three cylinders through a dig trajectory — joint angles, cylinder pressures and bucket path as a 46-frame animation.

Pump & flow sharing

One load-sensing pump's flow shared across three simultaneous cylinder commands — pressure compensation keeps the heavy boom section fed where a naive manifold would starve it.

A notebook plot of boom, stick and bucket joint angles through a dig cycle with the boom cylinder pressure spiking at ground contact — A full dig cycle: the boom, stick and bucket joint angles sweeping through the trench while the boom cylinder pressure (dashed) spikes exactly where the bucket meets dig resistance — the coupling between the hydraulics and the multibody arm, in one trace.

A hydraulic actuator on a domain that didn't exist.

The valve-controlled cylinder driving its load is a runnable acausal .djl built on a custom hydraulic domain — pressure as the potential, volumetric flow as the through-variable — that isn't in the block catalog. A load-sensing pump feeds a proportional valve feeds a single-acting cylinder pushing an inertial load against dig resistance, and the same kernel that solves electrical and mechanical networks solves it with no engine changes. It is verified through the production canvas engine: the chamber pressurises to 5.34 MPa — exactly the 60 kN dig load divided by the 0.0113 m² bore area — and the cylinder force converges on 60 kN. Define a connector, write the equations, and fluid power is just another domain.

A notebook plot of dig resistance against the available bucket breakout force through a dig cycle, with margin shaded — Can it dig? The available breakout force at 35 MPa plotted against the soil resistance through the cycle — 125.3 kN of breakout against the peak resistance, with margin to spare. The question every excavator front-end has to answer, settled before any steel is cut.

A notebook plot of hydraulic power and accumulated energy over a dig cycle, totalling 572 kJ — The energy ledger: hydraulic power (pressure × flow) summed across the dig cycle comes to 572 kJ — the number that sizes the pump, the cooling and the fuel burn per cycle, derived from the same coupled run that produced the motion.

Every number is one you can re-run.

The notebooks are gated on worker-verified results, and the hydraulic actuator .djl is confirmed solving through the production canvas engine.

Result

Bucket-tip reach: 11.68 m
IK round-trip error: 0 mm
Max boom-joint torque: 515 kN·m
Bucket breakout force: 125.3 kN
Energy per dig cycle: 572 kJ

Detail

Bucket-tip reach: 6.58 m dig depth
IK round-trip error: closed-form
Max boom-joint torque: at 35 MPa
Bucket breakout force: + margin
Energy per dig cycle: —

Design-grade fluid-power fidelity.

The arm is a planar 3-link model, the hydraulics are lumped cylinder-and-orifice elements rather than a distributed line model, and soil resistance is a scripted profile, not a soil-tool finite-element interaction. The coupled dig notebook uses a pressure-limited cylinder rate servo so the multibody integration stays robust while keeping real inertia, gravity and the hydraulic force ceiling. That is the fidelity machine design needs first: sizing cylinders and the pump, checking reach and breakout, sharing flow across actuators, and budgeting cycle energy — on your own machine numbers, before a full 3D multibody or a CFD hydraulic model.