PYTHON · NUMPY

From geometry to toolpath

Generate a valid roughing + finishing toolpath for a pocket and explain how tool diameter and stock define what the path can and cannot reach.

01Challenge

Select a tool and generate a toolpath (or paths) for the pocket (30×20×8 mm with 4 mm internal corner radii), then Run Cut and clear it fully: flat floor, walls in place, corners matching the 4 mm radius. Pick a tool too big and the corners stay full; skip roughing and the middle never clears; pick ∅3 and it works but takes forever. Try to clear it on purpose.

02Model

A milling machine can't draw. It can only spin a round tool and drag it through metal, so the real question is what shapes a round tool can leave behind. Subtractive manufacturing is erasing: the empty region is the sweep of the tool's circle along its path.

Here's the limit: a tool can never cut a corner sharper than its own radius. Say you need a 4 mm internal corner. Your tool radius must be ≤ 4 mm (a ∅8 end-mill or smaller). So we split the job: roughing hogs out the bulk fast with a bigger tool leaving a little stock; finishing takes one light pass with a tool small enough for the corners. Fast and accurate.

The tool sweeps the stock; its radius leaves corners.

03Guided practice

Step A (worked): ∅6 rough (3 mm radius ≤ 4 mm corner) with stock_to_leave=0.4, then ∅6 finish to nominal → cleared 100%, corners OK.
Step B (fade): switch the rougher to ∅10 to reproduce the corner failure, then pick a corner-capable finisher to recover.
Step C (independent): the tab_slot (5 mm wide, smallest radius 2.5 mm) means tools wider than 5 mm return ENTRY_BLOCKED; author a rough+finish plan from scratch.

04Feedback

PASS WHEN On the assigned feature, cleared_pct ≥ 99.5%, corner_radius_ok True, gouge False, entry_ok True, and sim_time ≤ 1.8× par on seed 2101.

If your run fails, check:

CORNER_NOT_CLEARED: 4 leftover crescents, tool radius 5.0 mm > corner radius 4.0 mm. Choose a finishing tool with diameter ≤ 8 mm.
POCKET_INTERIOR_NOT_CLEARED: ~38% remaining at center. A FINISH_CONTOUR only cuts the boundary; add a ROUGH_POCKET pass.
ENTRY_BLOCKED: a ∅6 tool cannot enter a 5.0 mm-wide slot. Required tool diameter < 5.0 mm.
SLOW: sim_time = 4.1× par. A ∅3 tool clearing the whole bulk is correct but wasteful; rough with a larger tool, finish with the small one.

05Retrieve & space

From M1.1: why can no end mill produce a 0 mm (sharp) internal corner, and what is the cheapest fix? → it always leaves its own radius; accept a min-tool-radius fillet.
From M1.2: a 2.5 mm radius slot 6 mm deep is a 2.4:1 ratio. Is that comfortable for milling or a hint to reconsider the process?
Forward link: predict what halving stepover does to cleared %, finish, and sim_time (sets up 2.2's triangle).

06Mastery & project

On the unseen tab_slot part, a rough+finish plan grades to cleared_pct ≥ 99.5, corner_radius_ok True, gouge False, entry_ok True, sim_time ≤ 1.8× par, and answer 'a tool can't cut a corner sharper than its own ____' (radius).

Where each machined feature gets its tool + toolpath; in M5 the factory runs many back-to-back, so a badly chosen tool here becomes a yield/finish defect there. Banks the bracket pocket toolpath + the tab_slot plan.

← Designing for the process (DFM)Process parameters →

PYTHON · NUMPY

From geometry to toolpath

The full Bench is a WebGL voxel cutter; here it is a numpy voxel sim. Pick tools and stepover, then run the cut. The autograder checks cleared %, corners, gouge, entry, and time.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you