The final result has smooth tooth profiles. The smoothing logic is explained in this diagram: The step profile occurs in the undercut regions where the backside of the rotated rack tooth profile sticks out as a corner. This can be somewhat alleviated by using finer steps in the simulation but to really get rid of the steps additional smoothing is required. The graphic above shows rough steps in the final output. Finally, the complete gear is assembled from rotated and mirrored half teeth:

These polygons are joined together with the union operator to form one complex 2d shape that is then subtracted from a slice of the outer circle of the target gear to form half a tooth.

Each rack tooth location is calculated and created as a polygon. All of this is accomplished by leveraging the ‘Constructive Area Construction’ capabilities of the csg.js library which is part of OpenJsCad. The complete gear is then assembled by mirroring and rotating the half tooth. In reality the code simulates only one rack tooth and calculates the tooth profile of half a tooth of the matching gear. The code simulates this movement in steps and then for each step subtracts the shape of the rack from the gear.įor illustration purposes the figure below has been calculated based on very coarse steps and only shows two teeth of the rack. When the rack is moved to the right the gear needs to rotate clockwise so that a point on the pitch circle of the gear moves with the same speed as the rack. In the figure below the rack is shown at the top. The advantage of the infinite gear is that it has a very simple trapezoidal tooth form solely defined by the addendum height and the pressure angle. The code behind the online involute spur gear builder determines the tooth profile by simulating how a gear with infinite radius (aka rack) would cut into a smaller gear as discussed by Michal Zalewki. If the undercuts are ignored the resulting gears will jam if machined and assembled precisely. For an elegant description of the issue including a recipe for how to graphically create correct spur gears see Michal Zalewski’s corresponding section in part six of his excellent Guerrilla guide to CNC machining, mold making, and resin casting series.

However, I have not found a freely available tool that correctly caters for undercuts that occur for smaller tooth counts (around 10 or less): An involute curve is fairly easy to calculate and quite a number of freely available tools and scripts exist that use this fact to create involute gear profiles (see e.g., Gear template generator, Parametric Involute Bevel and Spur Gears, OpenJsCad’s gear demo, and many more). Still here and interested in some background? Perfect! Involute gears are by far the most commonly used gears today. For information about version 2 see this post. UPDATE: This post refers to an old version. For the impatient: Just head over to the Online Involute Spur Gear Builder page.

Free wooden gear template generator