LAS RotaryLock V6 R1 — Engineering & Mathematical Basis

LAS RotaryLock™ V6 R1 — Engineering & Mathematical Basis

Technical Record v1.0 | September 2026

Download the formal V6 R1 Engineering & Mathematical Basis (PDF)

Engineering disposition

PASS — original V6 R1 mathematics, CAD and stored STL are mutually consistent at the tested precision.

The authoritative R1 OpenSCAD master was independently re-exported and compared with the stored original R1 STL. The processed meshes had identical vertex and triangle counts, identical six-decimal vertex-coordinate sets, and a maximum nearest-vertex difference of 0.0 mm.

The 25 × 25 mm × 1/4 in R1 prototype was subsequently physically printed and accepted in hands-on testing for lateral resistance, controlled rotation, stacking, and recessed screw-head accommodation.

Authoritative digital sources

CAD master: LAS_PAD_V6_R1_Rotary_Interlock.scad
SHA-256: 4c66f8625bfe61a24de26959f36576b1b06203644ab81a1784647620b2966eb9
Original STL: LAS_PAD_V6_R1_Rotary_Interlock.stl
SHA-256: 6d0fc7671d433f34f1f1499bd41d2062d32b994f9f7f166fc41ec4f641e7daf0
Independent CAD re-export: V6_R1_CAD_REEXPORT.stl
SHA-256: f87bc9b587ca81e68c79515f66e77de729136cb602d21893aa74f64c3238cc71

Exact V6 R1 radial mathematics

Let r = sqrt(x²+y²) and S = 1 + 1/9 + 1/25.

q(phi) = [cos(phi) + cos(3 phi)/9 + cos(5 phi)/25] / S

For D = 0.75 mm, lambda = 2.40 mm, r0 = 7.35 mm, and r1 = 12.15 mm:

p(r) = D/2 * [1 - q(2*pi*(r-r0)/lambda)]

for r0 ≤ r ≤ r1, with p(r)=0 outside the active annulus. The active annulus contains exactly two complete radial periods.

q range: -1 to +1
p range: 0 to 0.75 mm
max |dp/dr|: 0.7960116521
mean |dp/dr|: 0.6250000000
maximum local surface angle: approximately 38.5202°

Why V6 rotates

The active mating field depends only on radius r, not on polar angle theta. Therefore partial p / partial theta = 0 for the ideal active field. In centered registration, rotating one part about the common Z axis does not require climbing a mathematically defined angular hill.

This does not mean frictionless rotation. Real material friction, preload, print texture, wear, debris and compliance can create rotational torque.

Exact mating identity

At the validated stack increment T = 6.35 mm:

lower top = T + p(r)
upper bottom after translating the second part upward by T = T + p(r)

The active radial surfaces are therefore analytically identical at the intended mating pose.

Collar, groove and fastener geometry

Footprint: 25.00 × 25.00 mm
Corner radius: 1.20 mm
Through hole: Ø5.00 mm
Counterbore: Ø10.40 mm × 3.40 mm deep
Entry chamfer: Ø10.40 → Ø10.80 mm over 0.40 mm
Counterbore floor: z = 2.95 mm
Top collar: ri 6.20 mm; ro 7.00 mm; h 0.90 mm
Bottom groove: ri 6.05 mm; ro 7.15 mm; depth 1.05 mm
Nominal radial clearance: 0.15 mm per side
Nominal axial clearance: 0.15 mm
Minimum wall from 10.80 mm chamfer opening to collar inner wall: 0.80 mm
Active wave annulus: r = 7.35 to 12.15 mm

Original STL verification

Watertight: YES
Winding consistent: YES
Connected components: 1
Processed vertices: 14,112
Triangles: 28,224
Bounding extents: 25.000 × 25.000 × 7.252 mm
Volume: approximately 3553.759756 mm³
Surface area: approximately 2231.367653 mm²

Actual-STL directional check

Independent recomputation from top active-annulus triangle normals produced approximately:

mean-absolute directional-slope spread: 0.06095%
RMS directional-slope spread: 0.00003%
maximum-positive directional-slope spread: 0.14826%

These small spreads are finite-mesh polygonization effects and confirm that the exported mesh preserves the intended near-isotropic lateral engagement.

Physical prototype evidence

The 25 × 25 mm × 1/4 in V6 R1 was physically printed and repeatedly tested by hand. The prototype was accepted for:

strong resistance to X/Y translation under hands-on loading;
controlled/free rotation about the vertical axis;
repeatable stacking;
and recessed screw-head accommodation.

These observations are qualitative prototype evidence, not calibrated torque, lateral-force, structural-load, fatigue, wear-life or code-compliance measurements.

Commercial variant boundary

The validated R1 is specifically the 25 × 25 mm × 1/4 in configuration. LAS Products does not currently expose V6 as the same nine size/thickness selections used for simpler pad families.

A direct 1/8 in substitution is geometrically incompatible with the present R1 fastener zone: 1/8 in = 3.175 mm, while the counterbore alone is 3.40 mm deep, exceeding the nominal body thickness by 0.225 mm before the underside groove/wave geometry is considered.

A 1 in thickness or 4 × 4 / 6 × 6 footprint may be engineerable, but each requires its own CAD/STL and physical validation to preserve the rotation envelope, relief, collar/groove and fastener geometry.

Image provenance

Verified V6 product renders are produced directly from the authoritative original V6 R1 STL. Camera position, lighting and background may be changed for presentation; the product geometry itself is not redrawn or AI-invented.

Claim boundary

No structural load rating, coefficient of friction, calibrated breakout force, rotation torque under preload, fatigue life, universal substrate performance, or building-code approval is established by this record.

Rights and licensing notice

Copyright © 2026 LAS Products. All rights reserved. No license is granted by publication. LAS Products asserts rights, subject to applicable law, in its original written documentation, drawings, graphics, CAD implementation, parameter selection, arrangement, compilation, branding and other protectable material.

Mathematical principles, formulas, algorithms, systems and methods are not protected by copyright merely because they are documented here; patent, design, trademark, trade-secret, contract and other rights may apply. Reproduction or commercial use of LAS Products CAD files, technical documentation, branding, or protectable implementations is not authorized without written permission.