# Constrained Geometric Analysis Protocol

## Purpose

This protocol defines the required analytical framework for evaluating constrained geometric mechanical systems.

The purpose is to ensure that all analysis proceeds from:

1. Geometry
2. Kinematics
3. Force transfer

before any higher-level physical interpretation is introduced.

The mechanism shall first be treated strictly as an ideal constrained geometric system.

---

# Core Principle

This mechanism shall be analyzed as:

[
\boxed{
\text{a constrained geometric system}
}
]

where:

* motion relationships arise from rigid geometric constraint
* relative motion coordinates are physically valid coordinates
* force paths arise directly from geometric constraint
* all members are treated as ideal rigid bodies

---

# Scope of Allowed Analysis

During the derivation stage, analysis is restricted exclusively to:

1. Rigid-body geometry
2. Exact kinematics
3. Direct force transfer relationships

No additional analytical framework shall be introduced during the derivation stage.

---

# Required Order of Operations

Analysis shall proceed strictly in the following order:

1. Geometry
2. Kinematics
3. Force transfer

No later-stage interpretation may be inserted before the previous stage is fully resolved.

---

# Explicit Restrictions

Energy, power, and conservation-based interpretation are deferred until after the geometry, kinematics, and direct force-transfer derivations are completed.

During the derivation stage, DO NOT:

* invoke efficiency arguments
* invoke dynamic effects
* invoke inertia
* invoke elasticity, compliance, or deformation
* invoke losses or friction
* reinterpret internal coordinates into external/lab-frame coordinates
* collapse differential motion into externally observed motion
* replace relative coordinates with absolute coordinates
* reinterpret internal force-transfer coordinates as externally referenced output coordinates

Generalized work and energy interpretations are deferred until after geometric, kinematic, and direct force-transfer relationships are established.

These considerations are explicitly deferred until after:

1. geometry
2. kinematics
3. force transfer

have been completely established.

---

# Coordinate Discipline

All coordinates shall be treated exactly as defined.

Internal relative coordinates are physically valid coordinates and shall not be discarded, substituted, or reinterpreted during derivation.

Relative coordinates arising from constrained motion are to be preserved explicitly during derivation and shall not be reduced to externally referenced coordinates unless explicitly requested.

In particular:

[
\boxed{
\text{ring-to-pin relative motion is a valid differential coordinate}
}
]

and shall not be replaced by:

* ring-to-ground rotation
* carrier-to-ground rotation
* externally observed rotation
* or any equivalent lab-frame reinterpretation

unless explicitly requested in a later-stage analysis.

---

# Constraint Interpretation

All motion relationships shall be interpreted strictly as consequences of geometric constraint.

All force relationships shall be interpreted strictly as consequences of constrained force transfer through rigid geometry.

No higher-level filtering or reinterpretation is permitted during derivation.

---

# Gear Mesh Assumption

At the gear mesh:

* all interaction force is normal to the gear tooth face
* tooth interaction is ideal rigid contact
* no compressive overlap or deformation model shall be introduced
* no frictional tangential force model shall be introduced unless explicitly requested later

---

# Mechanism Definition Requirements

Mechanism definitions shall include:

* all geometric dimensions
* all constraints
* all fixed members
* all allowed motions
* all prohibited motions
* all relative-coordinate definitions

before derivation begins.

---

# Objective

The objective of this protocol is to ensure that:

[
\boxed{
\text{geometry defines the motion}
}
]

[
\boxed{
\text{kinematics defines the relative behavior}
}
]

and

[
\boxed{
\text{force transfer is derived strictly from those constraints}
}
]

before any broader physical interpretation is applied.