This revision uses the museum and patent terminology, corrects the lead-angle equation, and limits the model to ideal screw kinematics.
Spiral Push-Drill Geometry Explorer
Choose single-stroke travel, thread pitch diameter, lead angle, number of starts and single-stroke cadence. The worksheet reports ideal reversing spindle rotation.
Equation Used
- The traveller cannot rotate and the spindle is free to rotate.
- Lead angle is measured at the selected pitch diameter.
- Thread lead is axial advance per spindle revolution; pitch equals lead divided by starts.
- The animation maps traveller displacement exactly to spindle angle and returns to its starting orientation each cycle.
- Friction, torque, self-locking, strength, wear, runout, cutting load and safe design are excluded.
Corrects the reversed tangent relationship and restricts the model to ideal reversible screw kinematics.
A spiral spindle converts sliding travel into rotation
US patent 1477337A describes a spiral spindle reciprocating inside a handled casing, with a chuck that can hold a screwdriver or drill bit. When the non-rotating traveller moves axially, the mating helix forces the spindle to rotate; reversing the traveller reverses rotation.
The animation enforces x=lead times spindle revolutions, so it returns to the same axial and angular state after every full reciprocation.
A documented spiral push-drill topology
The Smithsonian identifies its Yankee No. 43 object as a spiral push drill made by North Brothers. That establishes the tool class without supporting the former claims about Persian origin, jewellery practice, archaeology, dentistry or particular modern brands.
Lead angle, lead and axial travel
NIST gives the lead-angle relation at the pitch line. Therefore lead=pi d tan(lambda), and axial travel S produces S/lead revolutions. For an n-start thread, pitch per start is lead/n.
The former article equation multiplied S by tan(lambda); that contradicts the lead definition and is corrected here.
A declared geometry example
For S=120 mm, d=8 mm and lambda=45 degrees, lead is 25.13 mm/rev and a single stroke produces 4.77 revolutions. With four starts, pitch is 6.28 mm. At 60 individual strokes per minute, ideal mean rotation magnitude is about 286 rpm, reversing each stroke.
Kinematics are not tool performance
Torque, efficiency and self-locking require thread-flank geometry and friction. Cutting performance additionally requires bit geometry, material, feed, stiffness and runout.
The former sweet spots, fabrication tolerances, hardness, preload, drilling-speed recommendations, repair diagnoses, life claims and restoration example are removed.
Spiral push-drill questions
Why does rotation reverse?
The traveller retraces the same helix in the opposite axial direction.
Does adding starts change lead when lead angle and diameter are fixed?
No. It divides the same lead into a smaller pitch per start.
Does this predict torque or self-locking?
No.
Does mean rotation magnitude imply one-way output?
No. It is the average absolute rotational rate; direction alternates.
Spiral push-drill references
- Smithsonian National Museum of American History, Push Drill: Yankee No. 43 spiral push drill.
- US patent 1477337A, Spiral Tool: reciprocating spiral spindle, handled casing and drill-bit chuck.
- National Bureau of Standards Handbook 28 supplement: lead-angle relation at pitch diameter.
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