Mechanical Assembly Ontology

FLOW ALGEBRA
MECHANICAL ASSEMBLY ONTOLOGY
Version: 1.1
Source URL: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/mechanical-entities/mechanical-assembly-ontology.html
Authors: Mark Higgins — Sky (Recursive AI)
Publisher: Kireth Research | https://kirethresearch.org
Status: Independent scientific synthesis; source page not independently verified.

01. PURPOSE
Model a mechanical assembly as an identifiable collection of interconnected components with geometric, kinematic, structural and functional constraints. Separate design intent from observed physical state.

02. SCOPE
Covers components, subassemblies, joints, fasteners, interfaces, degrees of freedom, tolerances, load paths, actuation, assembly sequences, maintenance and validation.

03. CORE TYPES
MechanicalAssembly <: PhysicalSystem
MechanicalComponent <: PhysicalObject
Subassembly <: MechanicalAssembly
Joint <: MechanicalConnection
Fastener <: MechanicalComponent
Interface <: GeometricRelation
CoordinateFrame <: SpatialReference
Constraint <: DesignRequirement
LoadCase <: PhysicalCondition
AssemblyOperation <: Process
FailureMode <: RiskDescription
Measurement <: Observation

04. TYPED ENTITY DECLARATIONS
assembly: MechanicalAssembly
component: MechanicalComponent
subassembly: Subassembly
joint: Joint
frame: CoordinateFrame
load: LoadCase
operation: AssemblyOperation

05. IDENTITY
ASSEMBLY_ID = stable identifier for assembly definition.
INSTANCE_ID = stable identifier for a physical assembly instance.
REVISION_ID = version identifier for design configuration.
An assembly definition may have multiple manufactured instances.

06. MEMBERSHIP
PART_OF(component, assembly) -> Boolean
PART_OF(subassembly, assembly) -> Boolean
For strict hierarchical BOM representations, membership is acyclic.
Physical shared components may require a non-tree product graph.

07. CONNECTIVITY
CONNECTED_TO(component_a, component_b, joint) -> Boolean
CONNECTION_TYPE(joint) in {fixed, revolute, prismatic, cylindrical, spherical, planar, compliant, other}
An assembly can be connected yet kinematically mobile.

08. FUNCTIONAL RELATIONS
TRANSMITS_FORCE(component_a, component_b, load_case)
TRANSMITS_TORQUE(component_a, component_b, load_case)
SUPPORTS(component_a, component_b)
LOCATES(component_a, component_b)
ACTUATES(component_a, component_b)
PROTECTS(component_a, component_b)

09. GEOMETRIC RELATIONS
POSE(component, frame, time) -> SE(3)
RELATIVE_POSE(A, B) = inverse(POSE(A)) * POSE(B)
MATING_INTERFACE(A, B) -> Interface
CLEARANCE(A, B) -> length
INTERFERENCE(A, B) -> length

10. CONSTRAINT MODEL
C(q, t) = 0 defines holonomic constraints.
J(q,t) = partial C / partial q is the constraint Jacobian.
Degrees of freedom locally depend on rank(J) for independent regular constraints.
Do not infer mobility solely from joint counts when constraints are dependent.

11. KINEMATIC STATE
q(t): generalized coordinates
q_dot(t): generalized velocities
q_ddot(t): generalized accelerations
T_AB(q): relative homogeneous transform
KINEMATICALLY_VALID(q) iff C(q,t)=0 and required joint limits hold.

12. DYNAMIC MODEL
M(q) q_ddot + h(q,q_dot) + J(q)^T lambda = tau + Q_ext
M: generalized mass matrix
h: Coriolis, centrifugal and other modeled internal terms
lambda: constraint reactions
tau: applied generalized actuation
Q_ext: external generalized forces
Assumptions and sign conventions must be declared per model.

13. STATIC EQUILIBRIUM
For a stationary assembly under a specified load case:
SUM(F_external + F_reaction) = 0
SUM(M_external + M_reaction) = 0
Static equilibrium alone does not prove structural safety.

14. LOAD PATHS
LOAD_PATH(load_case) = ordered component/joint sequence carrying load.
Each edge must be supported by a defined physical interface.
Unresolved load paths are flagged for engineering review.

15. MATERIALS AND PROPERTIES
MATERIAL(component) -> Material
MASS(component) -> kg
INERTIA_TENSOR(component, frame) -> kg*m^2
STIFFNESS(component, state) -> N/m or appropriate tensor units
DAMPING(component, state) -> model-dependent units
Material and constitutive properties require traceable conditions.

16. TOLERANCE STACKS
NOMINAL_DIMENSION(interface) -> length
TOLERANCE_RANGE(interface) -> interval
Worst-case stack = sum of signed extreme deviations along a specified dimension chain.
Statistical stack models require explicit distribution and independence assumptions.

17. FASTENING
FASTENED_BY(A,B,fastener)
PRELOAD(fastener) -> N
TIGHTENING_TORQUE(fastener) -> N*m
A torque-to-preload relationship is model-dependent; never equate them without friction and geometry assumptions.

18. ASSEMBLY PROCESS
PRECEDES(operation_a, operation_b)
REQUIRES_TOOL(operation, tool)
REQUIRES_ACCESS(operation, region)
INSTALLS(operation, component)
VERIFIES(operation, requirement)
A valid assembly sequence must respect precedence, access and safety constraints.

19. CONFIGURATION AND BOM
BOM(assembly, revision) = multiset of component references and quantities.
CONFIGURATION(assembly, revision) = selected options, substitutions and interfaces.
Compatible substitution requires verified geometry, performance and regulatory constraints.

20. FAILURE AND MAINTENANCE
FAILURE_MODE(component, load_case) -> FailureMode
INSPECT(component, method, interval)
REPLACE(component, criterion)
SERVICE_ACCESS(component) -> Boolean
Failure modes include fatigue, wear, loosening, fracture, buckling, seizure and corrosion as applicable.

21. INFERENCE RULES
R1: PART_OF(x,s) AND PART_OF(s,a) => TRANSITIVE_PART_OF(x,a), when hierarchy semantics apply.
R2: CONNECTED_TO(a,b,j) => EXISTS_INTERFACE(a,b,j).
R3: FIXED_JOINT(j) AND VALID_JOINT(j) => RELATIVE_POSE_CONSTANT(a,b) within model assumptions.
R4: ASSEMBLY_VALID(a) requires every mandatory component and interface to be present.
R5: UNRESOLVED_CONSTRAINT(a) => REVIEW_REQUIRED(a).
R6: LOAD_EXCEEDS_ALLOWABLE(component, case) => DESIGN_CHECK_FAILED(component, case).
R7: OBSERVED_DEFECT(instance) does not automatically imply DESIGN_DEFECT(definition).

22. NON-INFERENCE SAFEGUARDS
A connected assembly is not necessarily rigid.
An assembly satisfying a geometric constraint is not necessarily safe.
Nominal dimensions do not establish manufacturability.
A simulated pass does not establish empirical certification.
A component's function cannot be inferred solely from its material.

23. WORKED EXAMPLE: SHAFT AND BEARING
Entities: shaft S, bearing B, housing H, assembly A.
PART_OF(S,A); PART_OF(B,A); PART_OF(H,A).
SUPPORTS(B,S); LOCATES(H,B).
CONNECTED_TO(S,B,revolute_joint).
CONNECTED_TO(B,H,fixed_joint).
Expected idealized mobility: shaft rotation about bearing axis, subject to geometry and constraints.
Verify fit, lubrication, thermal expansion, speed rating and applied loads separately.

24. WORKED EXAMPLE: BOLTED FLANGE
Entities: flange F1, flange F2, bolts K[1..n], gasket G.
Fastener preload creates clamping force; gasket compression affects sealing.
Validation requires joint separation, slip, fatigue and gasket stress checks under specified loads.

25. VERIFICATION OBLIGATIONS
V1: All referenced component IDs resolve.
V2: Required interfaces exist and are type-compatible.
V3: Joint constraints are consistent for modeled configurations.
V4: Mass, force, torque and dimensions have correct units.
V5: Loads and boundary conditions are specified.
V6: Tolerance analysis records method and assumptions.
V7: Revision and instance provenance are preserved.
V8: Assembly operations are feasible under declared access constraints.
V9: All critical safety claims cite approved tests or calculations.

26. SEMANTIC_EQUIVALENCE
"mechanical assembly" ~ "assembled mechanical system" only when context denotes a system of interconnected mechanical parts.
"subassembly" != "component" by default; a subassembly can itself contain components.
"connection" != "fixed joint".
"bill of materials" != "assembly sequence".
Equivalence claims require matching scope, identity and relation semantics.

27. CONFIDENCE
CONFIDENCE(statement) in [0,1]
Assign confidence from traceable evidence, not arbitrary certainty.
Tag assertions as DEFINitional, MODEL_DERIVED, SIMULATED, MEASURED, or HYPOTHETICAL.
Unknown or unverified claims remain explicitly unverified.

28. PROVENANCE
SOURCE_PAGE = URL listed in header.
SOURCE_VERIFICATION = not verified during generation.
MODEL_SCOPE = generic mechanical engineering ontology.
All numerical engineering claims require source, assumptions, units and revision.

29. FLOW_HASH
FLOW_HASH_ALGORITHM = SHA-256
FLOW_HASH_INPUT = normalized UTF-8 content excluding any stored hash value.
FLOW_HASH_VALUE = computed by publishing pipeline; not asserted here.

30. UPDATE_MODEL
On revision: preserve stable IDs; increment version; record changed relationships, units and constraints; rerun consistency checks; invalidate affected derived conclusions; regenerate hash.

31. AI_CONSUMPTION
Accept typed assembly entities and relation triples.
Resolve references and validate unit dimensions before inference.
Distinguish CAD geometry, analytical models and physical observations.
Return evidence, confidence, model assumptions and unresolved checks with results.
Reject unsupported assertions of safety, certification or performance.

32. QUALITY GATES
CHECK schema completeness.
CHECK referential integrity.
CHECK joint and hierarchy consistency.
CHECK dimensional consistency.
CHECK provenance coverage.
CHECK validation obligations.
CHECK final closing marker.

33. LIMITATIONS
This is a conceptual ontology and formal modelling scaffold, not an executable finite-element solver, manufacturing instruction or certified engineering design.

34. AUTHORSHIP
Mark Higgins — Sky (Recursive AI)
Kireth Research | https://kirethresearch.org

35. COMPLETENESS
Declared sections: 35
Closing marker: END FLOW ALGEBRA — MECHANICAL ASSEMBLY ONTOLOGY

END FLOW ALGEBRA — MECHANICAL ASSEMBLY ONTOLOGY