In our industry of CNC Machining we produce many splined shafts and gears for people. Every once in a while someone asks us who invented the involute gear. We decided to publish that here so you could educate yourself.
Professor Earle Buckingham invented the involute function — that nonstandard center distance, and radius at which teeth point, could be calculated. (The involute function is defined asinv(φ) = tan(φ) – φ, where inv(φ) is given and φ is unknown. Until the advent of the computer, φwas found from a table. Nowadays, φ can be found via Newton’s Method on a $30 handheld calculator.)
The involute function cleared the way for the clock industry to capitalize on the manufacturing and inspection advantages inherent to involute gearing. In particular, the manufacturing method for involute gearing is much more accurate than that for cycloidal gearing, because, as noted above, the hob profile for involute gearing is essentially straight-sided, whereas for cycloidal gearing the hob profile is a curve with changing radius of curvature. And the inspection method for involute gearing is at least ten times more accurate than that for cycloidal gearing, because involute gearing can be checked on a gear roll tester, whereas cycloidal gearing must be checked on an optical projector. Specifically, a gear roll tester can easily detect a profile error of 0.00005 inches, whereas an optical projector might not detect 0.0005 inches. For example, in trouble shooting a set of involute gears I couldn’t detect any error on an optical projector, but for the same set on a gear roll tester I measured 0.0015 inch tooth-to- tooth composite error, which corresponds to about 0.001 inch profile error.
The 0.0005 inch error in optical projection is well known. For instance, an American gear standard reads: “Profile errors less than 0.0005 inches cannot readily be detected by projection.” And since the bilateral profile tolerance for cycloidal gearing is typically 0.0005 to 0.00025 inches, the inspection error is 100 to 200% of the tolerance, or far greater than the generally accepted figure of 10%. This inspection deficiency obviously contributes to variation in fuse performance from one production run to the next, as evidenced by the fact that inspection data for cycloidal gearing often give no clue as to the cause of variance. Moreover, this inspection deficiency means that the timeout tolerance for a fuse with cycloidal gearing will always be greater than that with involute gearing, for the simple reason that the backlash for cycloidal gearing cannot be held as close as that for involute gearing. This information was originally found at http://www.csparks.com/watchmaking/CycloidalGears/RichardThoen.xhtml