Documentation/Modules/Multi-Pulley Layout

Multi-Pulley Layout

Wrap angles and belt or chain length

Standards catalog

Validation: indicative · Method band: formula

Open calculator

Indicative method: Open/crossed belt length and wrap-angle geometry screening

Assumptions

  • Linear elastic material behavior unless noted otherwise.
  • User is responsible for load combinations and load factors per the selected design code.
  • Design standard (US/EU/ISO) sets unit defaults and screening check labels — not a full code worksheet.

Limitations

  • Does not size belt section or power capacity — use V-belt / timing-belt modules for duty checks.
  • Professional screening — confirm wrap and idler placement for critical layouts.

Engineering checks

CheckINDUSEUISO
Total belt lengthimplemented———
Minimum wrap angleimplemented———

Multi-Pulley Layout (multi-pulley)

Purpose

Compute total belt or chain length and wrap angles for drives with three or more pulleys in a single plane. Supports layout verification before detailed power rating in the V-Belt or Roller Chain modules.

Physics & theory

Multi-pulley drives route a single belt or chain around several shafts. Total length equals sum of straight tangent segments between pulley pairs plus arc lengths on each pulley. Wrap angle on each pulley depends on incoming and outgoing tangent directions, which are determined by pulley centers and diameters in the layout plane.

Minimum wrap angle governs friction capacity on friction belts — values below ~120° require idler pulleys or larger diameters. For timing belts and chains, wrap angle affects chordal action and engagement but not slip. The module treats pulleys as circles in 2D with user-specified center coordinates and diameters.

Power transmission elements operate under cyclic tension, bending, and contact stresses. Service factors account for driver type (motor vs engine), daily operating hours, and shock loading. Belt slip occurs when required friction capacity exceeds available wrap; chain drives depend on proper lubrication and sprocket tooth count for rated life.

Center distance adjustment affects belt length and wrap angle simultaneously — the solver uses the standard open-drive length formula assuming coplanar shafts and parallel pulley grooves.

Governing equations

Numerical method

Geometric layout solver: pulley centers and diameters define tangent lines between adjacent pulleys in the routing order. Arc lengths computed from wrap angles derived from vector geometry. Belt length summed; minimum wrap flagged if below threshold.

Inputs

ParameterDescription
Pulley listCenter coordinates , diameter
Routing orderSequence around which belt wraps
Drive typeOpen belt, crossed, or chain

Outputs

  • Total belt/chain length, per-pulley wrap angle (degrees), minimum wrap angle, tangent segment lengths.

Design codes & checks

  • Indicative: Total belt length, minimum wrap angle screening

Assumptions & limitations

  • Coplanar pulleys only; no 3D skew or quarter-turn twist.
  • Circular pulleys; no crowned or flanged geometry effects.
  • Does not compute power capacity — use with V-Belt or Chain modules.
  • Routing order must be specified correctly by user.

References

  1. Shigley, J. E., & Budynas, R. G. Mechanical Engineering Design, 11th ed., Ch. 17.
  2. Marks' Standard Handbook for Mechanical Engineers, 12th ed.
  3. Gates Corporation. Heavy-Duty V-Belt Drive Design Manual.
  4. ISO 4184:1992. Classical V-belts and pulleys.
  5. PhyCalcPro verification benchmarks in src/data/verification/ where available for this module.
  6. Beer, F. P., et al. Mechanics of Materials, 8th ed. McGraw-Hill — foundational stress and deformation theory.
Maintainer note: Wrap angle and length layout.