How thick must a printer rod be to keep carriage ringing small at a given acceleration?

What it found

Follow-up to selfrep-alufreq: the rod diameter is derived from an acceleration and a 50 µm ringing tolerance (one-mode oscillator, assumed 0.3 kg carriage and damping ratio 0.01) instead of a bare frequency target. At 3 m/s² with abrupt steps steel needs 7.3 mm, aluminium 9.6 mm and hardwood 15.5 mm; ramping the force over 20 ms cuts aluminium at 5 m/s² from 10.9 to 8.9 mm. Stylised: one mode, assumed damping, nothing measured.

A figure from its own output

Paper, code and results

• README and method
• Experiments and results
• Code
• Tests

More in Self-replicating manufacturing

• Which assumed input of the replicating-printer growth model does the doubling time depend on most?Which assumed input of the replicating-printer growth model moves its doubling time (Sobol indices, stylised, assumed ranges): budget and vitamin cost together carry ~90% of the variance when imports bind; when machine time binds, failure, print rate, budget and price are comparable.
• How does a resale value for the finished fleet move the switch from copies to goods?A resale value s per machine at the horizon shortens the goods phase from one e-folding time 1/k to 1/k − s/a; at s ≥ a/k the shop never switches. Grid optimum matches the closed form. All inputs assumed. Stylised.
• Does a resale value for the finished fleet still end copying late when the goods market saturates?A resale value s per machine with a saturating goods market (DP): at capacity c = 1000 machine-hours per hour the copy phase runs to the horizon once s is 12.5 (a quarter of a/k), and the policy that ignores s earns 14% of the optimum; the DP loses to bang-bang by under 1% where the fleet is large, so it is a lower bound there; stylised, preliminary.
• Is the dynamic-programming table for the replicating shop with a resale value converged, and can its policy be trusted?Grid-convergence check of the terminal-value DP: the policy's value is stable to about 0.15% from 800 to 1,600 grid points while the table value rises from 8–13% (400 points) to 2–3% (1,600) below it; a stylised fluid model, preliminary.
• How much does a smooth copy-then-sell policy beat a single switch for the replicating shop, certified without interpolation?An interpolation-free DP (the table equals its own policy's value to 1e-14): with no resale value and a saturating market a three-phase policy beats the best single switch by 4.7% (c = 1e4) to 7.1% (c = 1e3), while a resale value of 50 makes one switch optimal; a stylised fluid model, preliminary.
• How does a falling resale price for the finished fleet change when the shop stops copying?A resale price for the finished fleet that falls with market depth m (stylised): with an unsaturated goods market the switch moves from 574 h (linear) to 549 h (m = 1e3) and a single switch matches the DP; with a saturating goods market the DP beats the best switch by up to 14%.

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Proper scoring & elicitation28Effort & peer prediction9Verification games & slashing19Detection & tolerances14Markets as routers13Prediction-market design9Paying contributors8Decentralised training systems23Digital twins & sim-to-real164LLM chip design loops40Robot manufacturing loops53Ambient AI assistant46Self-replicating manufacturing34Simulation-first design64Engineered clothing45Task-specific AI accelerators40Algorithmic chip-design loops42Open-source purpose-built robots44The software-engineering loop43Adversarial human imitation41Open-source residential construction41Autonomous multi-angle capture34Sensing, imaging and 3D31Energy supply and dense energy storage39Robot societies among people31Agentic co-design of low-cost robots27Laundry-hanging robots25Machine learning on qualitative data23Robots on the building site27Civilizations & group psychology1History & human sciences1

Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.