Trebuchet Simulator

Physics-based trebuchet simulator with 4 degrees of freedom, symbolic equation derivation via SymPy, and automated design optimization using genetic algorithms.

Built for a virtual trebuchet competition: maximize projectile range under physical constraints (20m machine envelope, 10-ton counterweight limit, 300g max acceleration).

Features

• 4-DoF Lagrangian mechanics with Pseudo-Rigid-Body Model (PRBM) for flexible beam
• Symbolic derivation of equations of motion via SymPy, auto-generated as NumPy code
• 3-phase simulation: sliding start, constrained swing, ballistic flight with air drag
• Cam-driven counterweight with C1-continuous spline profile
• Genetic algorithm optimization (scipy differential_evolution) with constraint handling
• Interactive visualization with real-time animation, energy plots, and angle tracking

Architecture

derive_physics.py      SymPy: symbolic Lagrangian → equations of motion
        ↓
generated_eom.py       Auto-generated NumPy code (mass matrix M, force vector F)
        ↓
trebuchet_model.py     3-phase ODE simulation (slide → swing → ballistics)
        ↓
optimizer.py           Differential evolution + parameter study
        ↓
main_gui.py            Matplotlib animation + energy/angle/tension plots

Physics Model

Generalized coordinates:

Symbol	Description
θ (theta)	Main beam angle from vertical
β (beta)	Flex angle (tip relative to root) — PRBM
γ (gamma)	Counterweight hanger angle
φ (phi)	Sling angle relative to beam tip

Simulation phases:

1. Slide — projectile slides on rail, sling angle locked (φ = θ)
2. Swing — free rotation of all 4 DoF, event detection for release/collision/overload
3. Ballistics — projectile in free flight with quadratic air drag

Constraints:

• Machine must fit in a 20m cube
• Counterweight ≤ 10,000 kg
• Projectile acceleration ≤ 300g
• No ground collision, no rope slack

Optimization Results

Best configuration found (6-hour optimization run):

Parameter	Value
Range	2,840 m
Beam root	5.05 m
Beam tip	6.91 m
Counterweight	9,995 kg
Pivot height	5.22 m
Sling length	9.48 m
Release angle	70.1°

Usage

Run simulation with optimal parameters

python main_gui.py

Run with default parameters

python main_gui.py --default

Show trajectory only

python main_gui.py --trajectory

Compare configurations

python main_gui.py --compare

Run optimization

python optimizer.py           # Full optimization
python optimizer.py --test    # Quick test run
python optimizer.py --study   # Parameter sensitivity study

Regenerate equations of motion

python derive_physics.py

Tech Stack

Python NumPy SciPy SymPy Matplotlib

Requirements

pip install -r requirements.txt