Pitch Diameter of Vex IQ gears

I haven’t seen a thorough discussion or knowledge base article of the pitch diameter (PD) of the Vex IQ system. If I have missed it, please share. Otherwise, I may make a video to explain it to the students.

The starter pack is the following:

The Vex IQ gear system is designed to fit within the pitch distance of all the beams. Vex uses the unit of measure of pitch to describe the distance between two holes in a straight beam. One pitch distance is equivalent to 1/2”.

The main gears of 12T (1PD), 36T (2PD) & 60T (3PD) can be stacked in a straight line using various spacing.

When counting spaces, the first and last gear only use half the pitch diameter, a pitch radius if you will. Therefore, two 12T gears can be put in consecutive holes, (1/2P + 1/2P = 1P between gears). If one were to put a 12T gear and a 36T gear in a line, there would need to be 2P between centers (1/2P + 1.5P = 2P)

Vex also has available two intermediate gears. These gears are designed to be placed offset 1/2 a hole down (the diagonal hole in between two holes in a line). These gears of 24T and 48T have PD that are in between their main line gear counterparts. Here is the fun part. When a pitch length is measured across the gear on a line 1/2P offset from the center of the gear, the length of the 24T is 1P and the 48T is 2P. This effectively makes these gears perfect for bridging the gap between other gears.

When a gear is used in the middle of a gear train, you count the full pitch diameter (or in the case of the 24T & 48T gears the offset “diameter”). So a 12T gear and a second 12T gear can have 2P between centers when bridged with a 24T idler gear that has been offset 1/2P.

Hopefully my word salad makes sense and will be of some use to someone in the future.