An involute spline is identified by its tooth count, size system, pressure angle, fit and profile details. A few basic geometry calculations help check a drawing or establish a preliminary model, but they do not fully define a production spline. This reference focuses on calculated pitch geometry and leaves tolerance classes, root form, effective tooth thickness and fit limits to the governing spline standard.

Involute Spline Basic Geometry Reference

Start with the size system

The examples use a metric module and a 30-degree pressure angle. Module m describes the nominal tooth size in millimetres, while tooth count N sets the pitch-circle size. The pitch diameter is d = N × m. The base diameter is db = d × cos(φ), where φ is the pressure angle. The circular pitch is p = π × m, and the basic circular tooth thickness at the pitch circle is half that pitch, subject to the standard and fit definition used for the spline.

These equations are useful for preliminary geometry checks, but the table is not a substitute for a complete spline designation. A valid specification must name the applicable standard, module or diametral-pitch series, pressure angle, tooth count, fit, profile or root form, tolerance class, and internal or external member. A matching pitch diameter by itself does not show that two splines will mate.

Interpret the calculated values

The pitch diameter is a reference circle for the tooth spacing. The base diameter supports construction of the involute flank. Circular pitch is the distance along the pitch circle between corresponding points on adjacent teeth. The basic tooth thickness calculation describes an idealized geometry relationship; actual tooth thickness and space width include the allowance and tolerances required by the selected fit.

Internal and external splines have related but different control dimensions. Root and tip diameters, effective space width, effective tooth thickness, backlash, lead, runout and inspection method matter for the design. A CAD model built only from the pitch and base circles may look correct while being impossible to manufacture or assemble at the required fit.

Keep metric and inch standards separate

Do not combine a module value with diametral-pitch data. Metric and inch spline systems use different size conventions and may use different standard families, profiles and fit rules. Likewise, a 30-degree angle does not identify the complete spline form. Consult the standard named by the drawing and confirm whether the requirement is for an involute spline or another profile such as a straight-sided spline or serration.

Check the model against the drawing

Use the table to verify a few derived values from the tooth count, module and pressure angle. Then compare the complete designation and controlled dimensions with the selected standard or supplier calculation. Ask the spline manufacturer to confirm the proposed hob, broach or shaping process, root clearance, member fit and inspection gauges when the spline carries torque or locates a safety-critical assembly.

For an existing shaft or hub, measure the actual feature with an appropriate method rather than inferring the whole designation from one diameter. Over-pins or measurement across wires may be relevant to some profiles, but require the correct pin size and calculation for the specified standard and tooth form. Do not use the basic tooth-thickness equation as a direct inspection acceptance limit.

Scope and source

The dataset contains computed geometry examples only. It does not claim standard limits, manufacturing tolerances or interchangeable fits. The relationships are summarized from Autodesk Inventor’s published involute-spline dimension references for ANSI metric and ISO spline geometry; confirm the exact notation and standard edition specified for the part before release. A complete production definition must come from the current governing standard and the approved drawing.

Source

Geometry terminology and relationships were checked against Autodesk Inventor’s ANSI metric involute spline relations and Autodesk’s ISO spline nomenclature and relations. These references do not replace the controlled spline standard.