PMD - Planar Multi-Body Dynamics Simulation Software

PMD is an open-source Python library for modelling, simulating, and post-processing planar rigid-body mechanical systems.

Given a set of rigid bodies connected by kinematic constraints and force elements, PMD assembles and solves the constrained equations of motion numerically, then lets you inspect positions, velocities, accelerations, and reaction forces over time — both programmatically and through an interactive GUI.

---

🏗️ Model definition

A PMD model is built from three building blocks:

Bodies and markers

• Rigid bodies with mass, moment of inertia, and arbitrary body-fixed reference markers
• A singleton ground body acts as the inertial reference frame

Joints (kinematic constraints)

• Revolute, translational, rigid, disc-contact
• Higher-pair composites: RevRev, RevTran
• Relative-rotation and relative-translation constraints
• Analytical driver functions (sine, cosine, polynomial, …) to prescribe any coordinate over time

Force elements

• Gravity (Weight)
• Point-to-point spring-damper (PtpForce)
• Rotational spring-damper-actuator (RotSdaForce)
• Applied forces in local or global frame, torques
• Fully user-defined force laws (UserForce)

---

📐 Analysis and solvers

Analysis	What is computed
Static	Static equilibrium configuration (Newton–Raphson on the force-balance residual, $\ddot{q}=0$, $\dot{q}=0$)
Kinematic	Position and velocity solution for fully driven systems
Dynamic	Full equations of motion — positions, velocities, accelerations, constraint reactions

Integration uses CasADi DAE collocation (Radau IIA) — constraints are satisfied exactly at every step, no constraint drift, no stabilisation parameters needed.

All analyses include automatic Newton–Raphson initial-condition correction.

A configurable UnitSystem (m / mm / cm / in / ft · N / kN / lbf · rad / deg) handles unit conversion transparently.

---

📚 Documentation

Complete documentation is available in docs/source/:

• Getting Started — Installation, first model, core concepts
• User Guide — Detailed walkthroughs on bodies, joints, forces, solvers, GUI
• API Reference — Full class and method reference for pmd.core and pmd.gui

View the docs locally

Build and serve the Sphinx documentation:

cd docs
python -m sphinx -b html source _build/html
python -m http.server -d _build/html 8000

Then open http://localhost:8000/ in your browser.

---

�🖥️ Interactive GUI

PMD ships two optional graphical interfaces (requires PySide6):

PreProcessor — an interactive canvas to build the model visually:

• Create bodies and place markers by click or snap
• Add joints and forces from a ribbon toolbar
• Set initial conditions and launch the solver directly from the UI
• Save and reload models to/from JSON

PostProcessor — a results viewer for one or more simulation sessions:

• Time-history plots of positions, velocities, accelerations, and constraint reactions
• Animated playback of the mechanism motion
• Configurable display units, zoom, and figure export

---

⚡ Quick example

from pmd.core import Body, Marker, RevJoint, Weight, PlanarMultibodyModel, UnitSystem
from pmd.core import Ground

us   = UnitSystem(length="m", force="N")
link = Body(name="pendulum", mass=1.0, inertia=0.01)

A   = Marker(body=link, local_position=[0.0, 0.0])
pin = RevJoint(iMarker=Ground.origin, jMarker=A)
g   = Weight(g=9.81, unit_system=us)

model    = PlanarMultibodyModel(Bodies=[link], Joints=[pin], Forces=[g])
T, uT    = model.solve(analysis="dynamic", t_final=2.0, dt=0.01)

After solve, results are accessible on each Body and Joint object and can be passed directly to the PostProcessor GUI.

---

❓ Support and questions

For questions, ideas, or general discussion please open a Discussion.

For bugs or feature requests please open an Issue describing the problem and, where possible, a minimal reproducible example.

---

🤝 Contributing

PMD is under active development. Contributions, bug reports, and suggestions are welcome. Please open an issue or pull request — all feedback helps.

---

📜 License

MIT