Free Involute Gear Generator - True Involute Profile Calculator, Simulator & DXF Export
GearDXF is the internet's most accurate free online involute gear generator. Built on the mathematical foundations of kinematic geometry, our tool calculates true involute tooth curves, base circle diameters, line-of-action contact paths, and trochoidal root fillets for external spur gears, internal ring gears, and straight racks. Export mathematically precise closed-path DXF, SVG, and 1:1 scale printable PDF files for CAD modeling, CNC milling, laser cutting, and 3D printing.
The Mathematics of the Involute Tooth Curve
The involute curve is generated by tracing a point on a taut string as it unwinds from the base circle (r_b = r × cos(α)). The parametric Cartesian formulation is expressed as x(t) = r_b × (cos(t) + t × sin(t)) and y(t) = r_b × (sin(t) - t × cos(t)). Along the involute flank, the involute function is inv(α) = tan(α) - α. This geometric curve guarantees that the common normal at any contact point passes through the pitch point, satisfying the Fundamental Law of Gearing and keeping angular velocity strictly constant.
Center Distance Insensitivity: A Critical Advantage
Unlike cycloidal or circular-arc gear profiles, true involute gears possess the unique property of center distance insensitivity. If shaft mounting tolerances or thermal expansions shift the center-to-center distance, the velocity ratio remains perfectly constant. The operational pressure angle simply increases slightly, while the line of action remains a straight tangent line between the two base circles.
Pressure Angles: 14.5°, 20°, and 25° Analysis
Pressure angle (α) dictates base circle size and tooth flank inclination:
- 20° Standard: The optimal balance between tooth bending strength, contact ratio, and minimal undercutting (minimum 17 teeth).
- 14.5° Low Pressure Angle: Produces a higher contact ratio and lower radial bearing loads, favored in quiet clocks, but prone to undercutting below 32 teeth.
- 25° High Pressure Angle: Delivers maximum tooth root thickness and heavy impact load resistance, permitting tooth counts as low as 12 without undercutting.
Root Fillets & Trochoidal Clearance Geometry
Because the involute profile terminates at the base circle, the tooth dedendum transition down to the root circle must be smoothly blended. GearDXF constructs realistic trochoidal root fillets that relieve stress concentrations and prevent premature bending fatigue failure during high-torque operation.
High-Fidelity CAD DXF & SVG Polylines
Rather than rough polygonal approximations, GearDXF samples hundreds of high-precision mathematical points along each tooth flank to produce dense, ultra-smooth closed polyline paths. Import directly into Autodesk Fusion 360, SolidWorks, AutoCAD, Rhino, FreeCAD, and Mastercam with zero geometry errors or open contour warnings.
Frequently Asked Questions (Involute Gears)
What is an involute gear generator? An engineering web tool that calculates exact involute curve coordinates and exports ready-to-manufacture 2D CAD files (DXF, SVG, PDF).
What is the base circle? The base circle is the foundational cylinder from which the involute curve is generated: Base Diameter = Pitch Diameter × cos(α).
Why do involute gears run smoother than other shapes? Because the common normal to tooth contact always intersects the fixed pitch point, guaranteeing constant speed transmission without vibrations.
How do I prevent undercutting on low-tooth pinions? Increase the pressure angle to 20° or 25°, or maintain at least 17 teeth on a 20° spur gear.
- Precision Machinery: Design industrial gearboxes with verified contact ratios and high load ratings.
- Robotics & Drones: Create lightweight, high-efficiency involute gear reductions.
- CNC Milling & EDM: Generate closed vector toolpaths for wire EDM and 2D CNC contouring.
- Engineering Education: Visualize base circles, pressure lines, and conjugate action in real-time simulation.
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