01From observation to a mechanical question
A movement trace is one part of what we can observe in an articulator. Interpreting it also requires attention to the instrument’s arrangement: its guides, contacts, and constraints. The selected studies explore different aspects of this question and offer a concrete entry point into Frame-Bound Mechanics.
Laboratory observation, geometric analysis, and theoretical description meet here. Each text is introduced through its own question and method. The short introductions can be read on their own; references lead to the complete texts and specific sections for closer study.
The articulator research index also includes the sources on Artex CN, Dentatus ARD, SAM 3, primitive closure and CROR. Each original work retains its own place, with a separate continuation when new analysis is added.
02Five starting points
The reading order follows guide position, adjustability and traces, then the independent structural questions of Hanau H and Artex CN.
Guide position and functional neutrality
How does the contact position on the incisal table relate to the behaviour of the arrangement? Is a nominal “zero” position enough to describe how it functions?
A geometric and laboratory study using a fixed-condyle articulator. It uses maxillary and mandibular wax rims and a magnetic plate, examining different positions on the anatomical incisal table and a reversed flat arrangement.
It raises the question of how geometric position relates to functional response. The text on partial adjustability explicitly names it as its fixed-constraint baseline.
Connection: partial adjustability ↓Source, edition, and reading locations
Functional Neutral-Guide Behavior in Anatomical Incisal Tables of Fixed-Condyle Articulators: A Geometric Analysis Using a Reference Instrument
§2.1 Reference Instrument and Configuration; §2.2 Mounting Protocol; §3 Results; §4 Discussion.
Open the source fileNo date or version number is stated in the file examined.
“Functional neutrality” is read within this study’s arrangement and claims. Its wax-rim setup differs materially from the trace study below, which uses no mounted casts or wax rims.
What changes with partial adjustability?
When some parameters become adjustable, how do we describe behaviour in relation to the constraints that still apply?
A conceptual and qualitative analysis of partial adjustability, parameter perturbations, and the limits of interpretability. It does not present quantitative experimental validation.
It explicitly connects the fixed arrangement studied above with the question of adjustable systems. It offers a way to consider an adjustment in relation to the overall arrangement of constraints.
Read the full study and worked example →Source, edition, and reading locations
Mechanical Behaviour under Partial Adjustability in Articulator Systems
Scope & Positioning; §1 Baseline Reference; §§4–6; §7 Non-Extension Statement.
Open the source fileNo date or version number is stated in the file examined.
It is read as an analysis of mechanical interpretation. The text itself excludes application instructions, optimization procedures, and clinical recommendations.
Trace similarity, contact, and stability
When two states produce similar traces, what else needs to be observed in contact, motion, and repeatability?
The draft presented here compares Hanau H2-type, Dentatus ARD-type, and Artex CN-type instruments. It describes primitive articulator closure without mounted casts, wax rims, prosthetic specimens, or occlusal records.
It examines traces alongside categorical observations of contact, movement behaviour, and reproducibility. It offers concrete material for asking what an observation supports and what further evidence its interpretation requires.
Source, edition, and reading locations
Mechanical Interpretation of Articulator Traces: A Laboratory Study of Trace Similarity, Contact Continuity, and Mechanical Stability
§§2.1–2.3 Study design / primitive closure / unmounted condition; §2.5 Equipment information; §2.12 Statistical and categorical analysis; §4 Discussion and limitations.
Open the source fileEdition examined: JPD_articulator_trace_paper_v0_6.pdf. The v0_6 label comes from the filename.
This introduction concerns the particular v0_6 draft identified by its filename. It contains equipment details still to be completed and no continuous force or displacement measurements. This description does not assign a status to other versions of the work.
Hanau H as a system of constraints
How can Hanau H be described through its constraints and equilibrium selection? What can their projection into an observed trace reveal?
A short theoretical note presenting a formal description of Hanau H. It considers an admissible set, weighted equilibrium selection, reciprocal guide dominance, and non-unique interpretation of traces.
It moves the reading from the arrangement of a particular instrument to explicit theoretical objects. It helps distinguish observing a trace from the assumptions used to interpret it.
Read the independent Hanau study →Source, edition, and reading locations
Hanau H as a Frame-Bound Mechanical System
§§1–3, p. 1; §§4–9, p. 2; §§10–12, p. 3. Regime: §7.
Open the source fileNo date or version number is stated in the file examined.
In §7, “regime” is defined as an equilibrium state and is retained here as the note’s local usage. It is not automatically treated as equivalent to definitions elsewhere in the corpus. The note is not a laboratory validation.
Artex CN: realization of the anterior constraint
What changes when the anterior constraint is realized differently within the same frame?
The April 2026 note declares posterior, anterior and coupling constraints, joint admissibility and equilibrium selection. It attributes channel-type behaviour to the anatomical incisal table and considers flat or reversed anterior realizations.
The independent study develops two conditional comparisons: when an anterior change affects joint admissibility, and when an existing minimizer is preserved under a restriction. Each result states its assumptions; applying it to a particular CN configuration requires that configuration’s own relations.
Read the independent Artex CN study →Source, edition, and reading locations
Artex CN as a Frame-Bound Constraint System
April 2026 · §§1–3.2, p. 1; §§3.3–11, p. 2.
Open the source fileThe original symbolic note retains its own identity. The site analysis is dated 4 November 2026 and does not establish quantitative CN predictions or bench validation.
03From the application domain to the corpus
In Constraint Theory of Frame-Bound Mechanical Systems, the author locates the first formalization in the analysis of articulators and jaw-motion simulators. The text distinguishes this historical origin from the axioms’ logical foundation.
The consolidated technical supplement identifies two texts as extensions of that theory and places them within the broader FBMS/GBST corpus. It references the three canonical monographs and the Manifest, while stating that it does not replace those records. These statements document a connection between the initial mechanical inquiry, axiomatic formulation, and organisation of the corpus.
Generalized Frame-Bound Systems Theory (GBST) formulates a framework independent of particular applications. It is connected here as a generalised theoretical direction. The relationship between this particular edition and other editions in the corpus remains unresolved.
Sources for this connection
Constraint Theory of Frame-Bound Mechanical Systems — A Structural Axiomatization
First Domain of Application / Historical Origin of Formalization / Domain as Application, Not Foundation.
Open the source fileConstraint Topology, Regime Formation, and Structural Validation Operators in Frame-Bound Mechanical Systems — A Public Technical Supplement to the Frame-Bound Mechanics Corpus
Front Matter, p. 3: Historical and Corpus Positioning Note; p. 4: Public Canonical Roots / DOI Anchors.
Open the source fileGeneralized Frame-Bound Systems Theory (GBST) — A Structural Axiomatization of Constraint-Defined Systems
Abstract; §1 Introduction; §2 Core Entities; §7 Falsifiability and Scope.
Open the source fileFor the current organisation of the corpus, the Manifest identifies three distinct roles:
- Theory
The conceptual framework and the relationships between constraints, regimes, and projection.
- Mathematics
The formal objects and mathematical relationships of the corpus.
- Atlas
The empirical study of articulators and the classification of mechanical behaviour.
Roles and bibliographic identities: Corpus Manifest v1.0, §§3.1–3.3, pp. 2–3; §§5.1–5.3, p. 4.
04Continue with the study chapters
- What can a trace tell us?
Comparing articulator traces leads to a general question: how many different descriptions can be compatible with the same observation? The chapter uses a simple geometric example to show the role of the observation channel.
- Which constraints define what is admissible?
Guide position and available adjustments draw attention to the arrangement of constraints. The chapter introduces an admissible set through elementary inequalities and shows what changes when another constraint is added.
- When is an interpretation supported by evidence?
The observation, the comparison criterion, and the candidate interpretations each need a clear description. The chapter shows why compatibility with an observation is not, by itself, enough to identify a system’s structure uniquely.
05Sources and editions
This page is an introductory synthesis of the specific files cited. Titles and locations lead to the sources used for this presentation; the selection is not a complete chronology or publication catalogue.
Google Drive files open according to the reader’s existing access permissions.
Open Corpus Manifest v1.0