Thales Tonarm philosophy explained

TRACKING ERROR
While cutting the master disc of vinyl LP, the cutting-tool is hold on a massive support and guided linearly above the disc’s surface. This arrangement keeps the cutter-head rigid, even if high cutting forces occur.
While tracking the LP for playback, it’s totally different properties: the pickup-cartridge should follow the groove as smooth as possible and even tolerate eccentric and wavy vinyl. Therefore, radial pivoted tonearms are established as they allow to reduce unintentional forces at the tracking point tremendously. However, this mechanically preferred solution ends up with a geometrical error, since the cartridge is not guided tangentially to the groove anymore.
This so called tracking error basically distorts the music signal in a non-linear manner. By using non-spherical diamond tips (f. e. elliptical), further consequences as timing error and channel-differences in the frequency-response occur.
GEOMETRY THALES ORIGINAL
The unique Thales-solution combines in an elegant way the advantages of the tried and tested pivoted tonearm with the absolutely tangential tracking. This construction for which a patent was taken out on the 8th of May 2004 reduces the perfectly tangential tracking to pivot points, while the pick-up cartridge is taken and aligned on the Thales’ Circle.
All triangles ABC on the Thales’ Circle around M are rectangular in point C. Thus BC stands rectangular to AC and therefore tangential to the groove (red) with the radius AC. Because the pick-up cartridge is mounted exactly under point C and in the alignment of the straight line BC the tracking is perfectly tangential in every position.
From this completely new solution the following advantages ensue:
No tracking error and no consequential resulting distortions
Minimal friction because of pivot bearings; no linear bearings; no active tracking
Short tonearm with little resonance
Symmetric inertia at the tracking point in all axles
GEOMETRY THALES SIMPLICITY
There is a small but mighty history in finding elegant solutions for tangential tracking of analogue records. Some of the inventors concentrated themselves on tetragon-geometry:
P. W. D. BURNE-JONES 
He announced in 1953 a patent with a tetragon tonearm where the cartridge was mounted in the middle of one side. Burne-Jones sold tonearms under his own name, and his idea was adapted several times.
GARRARD ZERO 100 
This tonearm, published in 1970, is the best known solution working almost tangential. The cartridge tip was mounted exactly below a pivot-point. This idea made it possible to reduce the tracking error to +0.025 / -0.018°
Even if this solutions are not to be mixed up with the Thales-Original Solution – as the Thales is working on a triangle instead of a tetragon – the experience with the Thales geometry made it possible for Micha Huber to even optimize the tetragon solution and reduce the tracking error to 0.006° which is four times less than all solution published so far. This new geometry now made it possible to come very close to the perfect Thales geometry while using less parts and very elegant design.
GEOMETRY THALES EASY
The geometrical basis for the Easy tonearm is a novelty in tonearm-design. It’s the first solution by Thales where none of the bearing-points is located directly above the stylus. The clever arrangement of six bearing points creates three null points for the horizontal tracking error, plus a zero point for the variable offset angle. So, not only the tracking error is reduced, but the skating force as well.
SKATING FORCE
The skating force is so called because it causes the tonearm to glide over the record from the outside to the inside, so to say ‘to skate’. This force which draws the tonearm to the centre of the disc ensues indirectly from the friction between the tracking diamond and the record. This friction force always takes effect in the direction of the tangent line. If the pivot point of the tonearm is not located on the tangent, the friction force is divided into two components: one takes effect in the direction of the pivot point of the tonearm, the other takes effect towards the centre of the disc.
FORCES 
The force Ft results from the friction between the record and the tracking diamond. It acts tangentially. Because the pivot point is not located on the tangent, this force is divided into Fa which acts in the direction of the pivot point and Fs which is the skating force. The value of the skating force is not easily determined. It depends – first of all – on the music signal, further on the tracking weight, the circumferential speed and the tonearm and diamond geometry.
Therefore, even if the Thales-tonearms do track tangentially, their offset angle requiers compensation of the skating force. Since the offset angle for all our tonearms are lower than with normal tonearms, we do preset the compensation and it’s not adjustable for the client. For the different solutions, the compensation mechanism is solved as follows:
Thales Original: compensation-mass on a small lever, decreasing towards the inner groove because of decreasing offset angle
Thales Simplicity II: magnetical compensation between the two arm-tubes, decreasing towards the inner groove because of decreasing offset angle

Thales Easy: no skating compensation required, since the offset angle oscillates around the zero-point (straight arm)

Source: Thales