Triskelion–Triquetra

 Author: Daniel R Geerman 

 Date of Birth: 25-04-1992 

 This is the personal signed draft by Daniel R Geerman, embedding authorship visibly for attribution


The Triskelion–Triquetra Electromagnetic Engine

An Engineering and Philosophical Exploration

1. Introduction

Ancient symbols such as the Triskelion and the Triquetra encode cycles, balance and interconnection.
This paper re-interprets those forms as a modern electromagnetic device.
Three power sources arranged at 120° form a Triskelion; at the centre a sphere levitates and spins outward; around it two rings spin inward.
The machine is not “magic” but a combination of well-established electromagnetic principles arranged in a sacred-geometry frame.

2. Concept and Geometry

Place three identical electromagnet modules at the vertices of an equilateral triangle (120° apart).
Each module contains a power source, switch, capacitor and coil.
These three coils are driven with currents of the same frequency but 120° out of phase (true 3-phase).
A conductive or magnetic sphere is suspended at the centre.
Two rings are mounted around the sphere on low-friction bearings.
A second set of three coils, also 120° apart, is placed around the rings and driven with the same frequency but reversed phase order.

This geometry mirrors the Triskelion (three arms) and Triquetra (interlaced loops).

3. Physics and Mathematics

3.1 Rotating Magnetic Field

For three coils spaced 120° apart carrying sinusoidal currents:

i1=I0sin⁡(ωt)i_1 = I_0 \sin(\omega t)
i2=I0sin⁡(ωt−120∘)i_2 = I_0 \sin(\omega t - 120^\circ)
i3=I0sin⁡(ωt−240∘)i_3 = I_0 \sin(\omega t - 240^\circ)

the combined magnetic field at the centre is:

B⃗(t)=B0cos⁡(ωt) x^+B0sin⁡(ωt) y^\vec{B}(t) = B_0 \cos(\omega t)\,\hat{x} + B_0 \sin(\omega t)\,\hat{y}

which is a vector of constant magnitude rotating at angular speed ω\omega in the plane of the coils.

3.2 Levitation

A purely static magnetic field cannot stably levitate a permanent magnet or conductor (Earnshaw’s theorem).
Active levitation uses a feedback coil along the vertical axis:

Fz=k Icontrol−mgF_z = k \, I_{control} - m g

with a sensor measuring the sphere’s position and a controller adjusting IcontrolI_{control} so that Fz=mgF_z = m g and the sphere hovers.

3.3 Torque on the Sphere

A conductive sphere of radius rr and conductivity σ\sigma in a rotating magnetic field BB experiences eddy currents and a torque approximately:

τ∝σr5B2ω\tau \propto \sigma r^5 B^2 \omega

spinning it in the direction of the field.
A magnetised sphere couples directly to the rotating field with torque:

τ=μBsin⁡θ\tau = \mu B \sin\theta

where μ\mu is its magnetic moment.

3.4 Counter-Rotation of the Rings

The outer coils driven with reversed phase sequence produce:

B⃗outer(t)=B0cos⁡(−ωt) x^+B0sin⁡(−ωt) y^\vec{B}_{outer}(t) = B_0 \cos(-\omega t)\,\hat{x} + B_0 \sin(-\omega t)\,\hat{y}

which rotates in the opposite direction, inducing currents and torque in the rings the other way.
If the rings have a continuous copper band (a “squirrel cage”), the torque is maximised:

τring≈k B2ωR3\tau_{ring} \approx k \, B^2 \omega R^3

so the rings spin inward while the sphere spins outward.

4. Materials and Components

– Sphere: aluminium (light, conductive, non-magnetic) 20–40 mm diameter, or a small neodymium magnet sphere for stronger torque.
– Rings: soft iron or laminated steel with a brazed copper band to improve flux and torque transfer.
– Coils: enamelled copper wire on soft-iron cores aimed toward the centre.
– Drive electronics: three H-bridge drivers from a microcontroller generating three PWM or sine waveforms 120° apart. Phase order ABC on the inner set (sphere spins outward), ACB on the outer set (rings spin inward).
– Levitation control: vertical coil plus Hall or optical sensor feeding a PID controller.

5. What Happens in the Centre

At the centre a continuously rotating magnetic vector exists.
The sphere experiences eddy currents that spin it and slightly stiffen its position while the control coil actively holds its height.
The rings sit in the outer rotating field and are dragged the other way, orbiting freely around the levitated, counter-spinning sphere.
The visual effect is a physical embodiment of the Triskelion–Triquetra: three inward-driving arms, a sphere spinning outward, and two rings spinning inward.

6. Symbolism and Modern Engineering

The Triskelion arms represent three sources of power converging.
The Triquetra symbolises interconnection and cyclical motion.
This device physically embeds those ideas. It is a modern engineering embodiment of an ancient pattern.

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