Involute gear simulator built with QT and OpenGL, Part 1

Part 2

I have built a C++ application to provide a high resolution  rendering of a pair of involute gears running together. This post will focus on introducing what it is and what it does. An image of the application is shown below and the source code (along with 32 bit Windows binaries) is available at: https://github.com/wilstep/OpenGL-involute-gears-simulation/releases/tag/v1.3.1
This simulation allows one to slow the gears right down and examine them under great magnification, and from any direction to observe in great detail how the contacts between the gear teeth change in time and how the involute gear form actually works. In effect it lets one examine the gears rotating as if they are being viewed under a high powered microscope, but from any direction and at any chosen speed, and with perfectly sharp edges. So one can view the detailed interaction of the gear teeth with a full virtual reality visualisation.

The simulation is highly realistic and detailed with the correct involute form being calculated to all the standards used in gear specifications including the correct amount of clearance, correct tooth depths and standard pressure angles. There is also a fillet radius at the bottom of the teeth, which was surprisingly difficult to implement. Things are arranged such that one gear drives the other, and the speed at which they rotate may be adjusted. The number of teeth on each of the gears can be changed and the rendering may be zoomed in, shifted and rotated with the mouse. Further the distance separating the two gears may be tweaked and the light source for the rendering may be moved. The above image is shown below after rotating, zooming and moving the light source.

There are two common types of tooth profile systems used in gear design. The first is the cycloidal gear form that is used mainly in horology (mechanical clocks and watches) and the second is the involute form which is far more common. My simulation only deals with involute gears.

An involute is a mathematical curve which is obtained from some generating shape. In the case of gears the generating shape is a circle. Imagine we wrap a string around this circle with a pencil tied to the end, and then draw a spiral as the string unwraps. This spiral is the involute and a very short piece of this forms the profile on the gear tooth. There are several nuances that need to be appreciated to form a gear from the involute curve, which I will discuss in the next post. The special feature of the involute gear form is that the driven gear rotates at constant velocity, regardless of errors in the separation distance between the two gears.

I plan to make a further two posts subsequent to this. The next one discussing more details about the gear profiles, their calculation and also demonstrating some important insights that can be gained from this tool, and then a final one looking at some of the more interesting snippets of the code.

Part 2