Chain & Sprockets

Calculate and draw a roller chain drive: two sprockets (Z1 and Z2) with a roller chain, and an idler on the slack strand. Dimensions to ISO 606 / DIN 8187 (chain) and DIN 8196 (sprocket tooth form).

Input

Field	Meaning
Chain	Chain size from the European series B (05B ... 32B), simplex. In brackets the pitch in inches (for example 08B = 1/2"); 05B has an 8 mm pitch and no inch size.
Teeth Z1	Number of teeth of the driving sprocket (left in the drawing).
Teeth Z2	Number of teeth of the driven sprocket (right).
Centre distance a	Distance between the centres of Z1 and Z2 in mm.
Links	Number of links of the chain. 0 = automatic: the smallest even number that fits around the wheels. More links = more slack, which the idler takes up.
Idler teeth	Number of teeth of the idler.
Idler position	Where the idler sits along the slack strand: left = near Z1, right = near Z2. You can also drag the idler in the drawing with the mouse.
Idler outside / inside	Outside the chain (pushes the slack strand inwards) or inside the chain (pushes it outwards).
Bore Z1 / Z2, idler bore	Diameter of the shaft hole in mm (0 = none). It is drawn and exported; a bore larger than 80% of the root circle gives a warning.

Projects

Open... (Ctrl+O), Save (Ctrl+S) and Save as... keep all input in a project file .chs (a readable text file). The title bar shows the project name; a * means there are unsaved changes. When closing or opening another project, the program asks whether to keep the changes. You can also open a project by passing the file as a parameter (or, after installing with the file association, by double-clicking it).

Export (2D)

Export DXF... and Export STEP... write the drive exactly as shown (including the rotation), as separate curves in millimetres, each kind on its own layer:

Layer	Contents
Z1, Z2, IDLER	Outline of the sprocket (with teeth) and the bore
INNER_PLATE, OUTER_PLATE	Outline of every plate
PIN, ROLLER	Circles of the pins (d2) and the rollers (d1)
PITCH_CIRCLE	The pitch circles (only with the tick box "Export pitch circles too")

DXF is version R12 (outlines as closed polylines, circles as CIRCLE). STEP is AP214: every outline (wheel, plate, pin, roller) is one closed curve there (a B-spline that stays sharp at corners such as the tooth tips). The shape deviates at most 0.001 mm (DXF) or 0.003 mm (STEP) from the calculated shape. The STEP file is a few MB.

Export (3D)

With the drop-down list Export you choose what goes into the file: everything as shown, the chain only, or a single wheel (handy for 3D printing a sprocket). This choice also applies to the 2D export.

The 3D model has the middle of the chain in the plane z = 0, the shafts along z:

Part	Shape
Sprocket, idler	Toothed outline, thickness = tooth width bf1, with bore
Inner plate (2 per inner link)	Thickness ti, hole for the bush
Outer plate (2 per outer link)	Thickness to, hole for the pin
Bush	Tube from pin diameter d2 to bush diameter, length b1 + 2 ti
Roller	Tube from bush diameter to roller diameter d1, slightly narrower than b1
Pin	Cylinder d2, sticks out a little on both sides

Every part is its own closed solid; they touch but do not overlap. Plate thicknesses and bush diameter are not in the standard (typical manufacturer values).

3D STEP: true solids (AP214) with flat faces, B-spline side faces and round holes and cylinders.
STL: binary triangle mesh, closed and facing outwards per part.
3D DXF: the same triangle mesh as 3DFACE (R12), a layer per kind of part.

The chord tolerance is the largest distance between the triangle mesh (STL, 3D DXF) and the true shape. A whole chain gives many triangles: at 0.01 mm an STL of 106 links is about 13 MB and a 3D DXF about 50 MB. For a whole chain 0.05 mm is fine; for a single sprocket 0.01 mm is good.

How the chain is laid

The program lays the chain roller by roller: on a sprocket the rollers sit exactly in the tooth gaps (on the pitch circle, exactly one pitch p apart), between the wheels on a straight line. The tight strand is at the top, the slack strand at the bottom. The idler is pushed in just far enough for the chain with the chosen number of links to close exactly, just like in real life.

With Rotate, wheel 1 turns anticlockwise (the tight strand is pulled towards Z1); the chain and the other wheels follow. You can also see the "polygon effect": the idler moves up and down a little.

Formulas

Pitch circle: d = p / sin(180°/z); root circle: df = d − d1.
Tip circle: between d + p(1 − 1.6/z) − d1 and d + 1.25p − d1 (the program takes the middle).
Roller seating radius ri, flank radius re and seating angle α: the middle between the minimum and maximum of the standard.
Tooth width bf1 = 0.93 b1 (p ≤ 12.7 mm) or 0.95 b1 (p > 12.7 mm).
Links without idler (for comparison): X = 2a/p + (z1+z2)/2 + ((z2−z1)/2π)² · p/a.

Warnings

Odd number of links: this needs an offset (cranked) link.
Wrap angle below 120° on a sprocket.
Centre distance outside 30 to 80 × the pitch (recommended: 30 to 50 × p).
The idler touches a sprocket.

Drawing

Mouse wheel = zoom, drag = pan, drag the idler = move it, double-click = fit everything. Inner plates are grey, outer plates yellow. At the end of the line below the drawing you see the scale (px/mm) and how many milliseconds the drawing took.