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 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.
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 | Detail | |
|---|---|---|
| Bucket-tip reach | 11.68 m | 6.58 m dig depth |
| IK round-trip error | 0 mm | closed-form |
| Max boom-joint torque | 515 kN·m | at 35 MPa |
| Bucket breakout force | 125.3 kN | + margin |
| Energy per dig cycle | 572 kJ | — |
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.
Model your own machine.
Book a walkthrough and we'll drop in your linkage, cylinder and pump numbers and run the kinematics, dig-cycle and energy studies live.