KEVOS® MAKEOS · Power Transmission
Roller Chain Sprocket Tooth Form and Hob (ANSI B29.1M Seating Curve, Pressure Angles, Hob Diameter and Lead)
To lay out or check the tooth form of a roller chain sprocket, what are the seating curve diameter, the arc centres and angles, the topping curve and the outside diameters, what pressure angles does the chain run at, and what diameter, helix angle, lead and width does the hob need?
ANSI B29.1M roller chain sprocket tooth form by the formulas the handbook gives: seating curve diameter Ds = 1.005 Dr + 0.003 in and R = Ds ÷ 2, angles A = 35° + 60° ÷ N and B = 18° − 56° ÷ N, ac = 0.8 Dr, M = 0.8 Dr cos A, T = 0.8 Dr sin A, E = 1.3025 Dr + 0.0015 in, chord xy = (2.605 Dr + 0.003) sin (9° − 28° ÷ N), yz, ab = 1.4 Dr, W and V, F, H = √(F² − (1.4 Dr − 0.5 P)²), S = 0.5 P cos (180° ÷ N) + H sin (180° ÷ N), the approximate outside diameter P [0.6 + cot (180° ÷ N)] and the outside diameter when the tooth is pointed, the pressure angles for new chain, minimum and average, and the standard hob: normal pitch 1.011 P, H = 0.27 P, fillet radius 0.03 P, outside diameter 1.7 (bore + Dr + 0.7 P), pitch diameter OD − Ds, helix angle sin M = Pn ÷ π Dh, lead Pn ÷ cos M and the least width.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Chain pitch P | mm | Pitch of the roller chain. |
| Roller diameter Dr | mm | Nominal roller diameter of the chain. |
| Teeth in sprocket N | teeth | Number of teeth in the sprocket. |
| Hob for the sprocket | ||
| Hob bore | mm | Bore of the hob that will cut the sprocket teeth. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Chain pitch P
- What it is
- Pitch of the roller chain, from pin centre to pin centre.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12.7 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the sprocket diameters and the hob pitch.
- Get it right
- Standard pitches run from 1/4 in (6.35 mm) to 3 in (76.2 mm).
What this means: Roller diameter Dr
- What it is
- Nominal diameter of the chain rollers.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7.9248 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the seating curve and every tooth form value.
- Get it right
- Take it from the chain maker’s data or the standard for the chain number.
What this means: Teeth in sprocket N
- What it is
- Number of teeth in the sprocket.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 500 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the tooth form angles and the outside diameter.
- Get it right
- Count the teeth on the drawing or the part.
Hob for the sprocket
What this means: Hob bore
- What it is
- Bore of the hob that will cut the sprocket teeth.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 31.75 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the hob outside diameter and the least hob width.
- Get it right
- Take it from the hob maker; the handbook’s standard hobs use 1.250 to 2.000 in.
Method and formulas
- Ds = 1.005 Dr + 0.0762 mm (0.003 in); R = Ds ÷ 2; A = 35° + 60° ÷ N; B = 18° − 56° ÷ N; ac = 0.8 Dr.
- M = 0.8 Dr cos A; T = 0.8 Dr sin A; E = 1.3025 Dr + 0.0381 mm (0.0015 in).
- xy = (2.605 Dr + 0.0762) sin (9° − 28° ÷ N); yz = Dr [1.4 sin (17° − 64° ÷ N) − 0.8 sin (18° − 56° ÷ N)]; ab = 1.4 Dr; W = 1.4 Dr cos (180° ÷ N); V = 1.4 Dr sin (180° ÷ N).
- F = Dr [0.8 cos (18° − 56° ÷ N) + 1.4 cos (17° − 64° ÷ N) − 1.3025] − 0.0381 mm; H = √(F² − (1.4 Dr − 0.5 P)²); S = 0.5 P cos (180° ÷ N) + H sin (180° ÷ N).
- OD (approx., J = 0.3 P) = P [0.6 + cot (180° ÷ N)]; OD (pointed) = P cot (180° ÷ N) + cos (180° ÷ N)(Ds − Dr) + 2H.
- Pressure angle for new chain 35° − 120° ÷ N; minimum 17° − 64° ÷ N; average 26° − 92° ÷ N.
- Hob: Pn = 1.011 P; H = 0.27 P; E = 0.03 P; OD = 1.7 (bore + Dr + 0.7 P); Dh = OD − Ds; sin M = Pn ÷ π Dh; lead = Pn ÷ cos M; width at least 2 × bore, 6 Dr and 3.2 P.
- Example: the seating curve diameter is 8.0406 mm and the approximate outside diameter 87.805 mm.
Limitations
- The inch constants of the standard (0.003 and 0.0015 in) are converted to millimetres; the seating curve diameter has a plus tolerance only, given in the handbook table.
- The hob outside diameter formula is approximate, as the handbook notes.
- A hob made for a given pitch and roller diameter cuts any number of teeth.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Lay out a roller chain sprocket tooth for a template, wire cut or CNC profile
- Check a sprocket against the standard tooth form
- Specify a hob for cutting roller chain sprockets
Who it is for
- Machinists and gear cutters
- Machine designers
- Toolmakers
What you get
- Seating curve diameter and radius
- Tooth form angles, arc centres and chords
- Topping curve values F, H and S
- Approximate and pointed-tooth outside diameters
- Pressure angles for new chain, minimum and average
- Hob normal pitch, outside and pitch diameters, helix angle, lead and least width
Interpreting the result
- The approximate outside diameter must be smaller than the pointed-tooth diameter, or the teeth come to a point.
- The pressure angle falls from the new-chain value toward the minimum as the chain wears and rides higher on the teeth.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2554–2555. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Useful alongside · Library collection
Belt or chain drive: selecting, installing and maintaining flexible power transmission
In Machine Elements and Mechanical Design
What it covers: Belt and chain drives are simple until they slip, stretch or wreck bearings. How to choose between them, size a drive properly, set tension and alignment, and maintain it for long life.
Useful alongside · KEVOS® original book
Gears and sprockets
In Machine Part Repairs by the Numbers
What it covers: Decide whether a broken gear tooth can be rebuilt, estimate its root bending stress and what a defect there costs, restore the profile, and know when gears and sprockets are replaced in pairs.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.