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Belt Joint

In one sentence: Couple two revolving parts so that when one rotates, the other rotates in the same direction at the defined speed ratio — the joint for belt drives, chain drives, and internal gear meshes.

Overview

Workbench: Assembly
Menu: Assembly → Joints → Belt
Shortcut: L

A Belt joint couples two Revolute joints so that rotation of one pulley drives the other in the same direction at a ratio determined by their effective radii. This models belt drives, chain drives, and internal gear meshes — all cases where the coupling preserves rotation direction.

Speed ratio: ω₂ / ω₁ = +R₁ / R₂ (positive because direction is preserved)

Intuition

A coupled joint does not model the physical belt or chain — it only enforces the angular ratio. The pulleys must be positioned correctly by their own Revolute joints; the Belt joint says "when Pulley 1 rotates by X, Pulley 2 must rotate by +(R₁/R₂) × X."

Think of a bicycle: the pedal sprocket turns, the rear wheel sprocket turns in the same direction via the chain. The speed ratio is set by the sprocket sizes (tooth counts, which correspond to pitch radii). A timing belt drive in a 3-D printer works the same way.

When to use it

  • Timing belt drives (3-D printer axes, CNC machines).
  • V-belt or flat-belt drives.
  • Roller chain drives (bicycle, conveyor, motorcycle).
  • Internal gear meshes (ring gear + planet gear, where direction is preserved at the mesh).

When NOT to use it

  • Don't use Belt for external spur gear meshes — external gears reverse direction, use Gears.
  • Don't add Belt before both Revolute joints exist — each pulley must already have its own Revolute joint.

Prerequisites

Both pulleys must each have their own Revolute joint connecting them to the frame.

Step-by-step

  1. Press L or choose Assembly → Joints → Belt.
  2. Click a cylindrical face on Pulley 1.
  3. Click a cylindrical face on Pulley 2.
  4. Set Radius 1 and Radius 2 (effective pulley radii in mm).
  5. Click OK.

The speed ratio is automatically computed as Radius 1 / Radius 2.

Parameters

Parameter Type Default Description
Reference 1 Link — Cylindrical face on Pulley 1
Reference 2 Link — Cylindrical face on Pulley 2
Radius 1 Length — Effective radius of Pulley 1 (mm)
Radius 2 Length — Effective radius of Pulley 2 (mm)

For toothed belt / chain drives, the effective radius is the pitch radius:

pitch_radius = (pitch × tooth_count) / (2π)

For friction belt drives (V-belt, flat belt), use the pulley groove radius.

Choosing Gears vs Belt

Situation Use
External gear mesh — teeth interlock, direction reverses Gears
Belt / chain drive — direction preserves Belt
Internal gear mesh — direction preserves Belt

Python API

Minimal example

import FreeCAD as App

doc = App.ActiveDocument
asm = doc.getObject("Assembly")

joint = asm.Joints.newObject("Assembly::JointObject", "TimingBelt")
joint.JointType = "Belt"
joint.Reference1 = (doc.getObject("MotorPulley"), ["Face2"])
joint.Reference2 = (doc.getObject("DrivenPulley"), ["Face2"])
joint.Radius1 = 15.0   # 15 mm motor pulley
joint.Radius2 = 45.0   # 45 mm driven pulley → 3:1 reduction, same direction
doc.recompute()

Common mistakes and pitfalls

Belt vs Gears direction confusion

External spur gears reverse direction → Gears. Belt and chain drives preserve direction → Belt. Using the wrong joint makes the mechanism rotate the wrong way in simulation.

Belt joint does not model the physical belt or chain

The Belt joint adds only the angular ratio. It does not model belt tension, slip, or physical contact. The pulleys must be correctly positioned by their Revolute joints independently.

Parallel axis assumption

The Belt joint is designed for pulleys with parallel axes (standard belt or chain drive layout). For crossed-belt or twisted-chain configurations, use Gears with appropriate sign conventions.

See also