Belt Friction (Capstan Equation) mechanism

Model scope

The core capstan limiting relation is standard, but the specification needs an explicit impending-slip/maximum-ratio label and an exact definition of the alternative "max holding load" output. The empty honest_label is a concern because the equality is a limiting condition, not a universal operating tension ratio.

• T1/T2 = e^(μθ) is the limiting capstan relation at impending slip, not the general tension ratio during static no-slip operation; generally T1/T2 ≤ e^(μθ).
• The claim that the instrument outputs a "max holding load" is underspecified: the loaded side, applied load, anchor condition, and whether T1 or T2 is solved must be defined.
• The formula requires positive tension values and a nonnegative friction coefficient; these input constraints are not stated.

Units and conventions

• θ must be supplied in radians; degrees must be converted using θ_rad = θ_deg × π/180.
• μ is dimensionless and is assumed to be a constant friction coefficient over the contact surface.
• T1 and T2 use the same force units, such as newtons; the ratio is dimensionless.
• The equality assumes a flexible belt or rope, uniform contact, negligible bending stiffness and centrifugal effects, and impending slip under a Coulomb-friction model.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "T2_N": 500,
    "mu": 0.2,
    "theta_rad": 1.5707963267948966
  },
  "expected_outputs": {
    "T1_N": 684.5535
  },
  "working": "μθ = 0.2 × 1.5707963268 = 0.3141592654. e^(μθ) = e^0.3141592654 ≈ 1.369107. T1 = T2 × e^(μθ) = 500 × 1.369107 = 684.5535 N."
}

Failure boundary

• If T2 = 0, the stated ratio T1/T2 is undefined, even though direct evaluation of T1 = T2e^(μθ) gives zero.
• A degree value passed as radians produces an incorrect result; the interface must label the angle unit explicitly.
• Negative θ, negative μ, or negative tensions are physically invalid or reverse the intended tight/slack-side interpretation and should be rejected.
• For very large μθ, e^(μθ) can overflow numerically; an upper input bound or logarithmic handling may be needed.
• The equality should not be presented as an achievable ordinary operating ratio unless impending slip is explicitly specified.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json