齒輪為安裝在軸上的機械元件, 用以傳送兩軸之間的動力, 為重要的
基本元件之一.關於各種齒輪的設計與製造, 在學術界及工業界有不少的
研究. 在當前產業的競爭下, 整合齒輪的設計, 切削與量測實為一重要要
的課題. 本文選取齒條齒輪為例, 對齒輪的設計, 切削與量測做一統
合的研究. 首先利用共軛理論進行齒條與齒輪嚙合的曲線推導, 設計出齒
條齒輪的外型, 並推導三軸工具機的功能函數矩陣, 再規劃切削刀具的位
置矩陣, 令工具機的功能函數矩陣與刀具的位置矩陣相等, 即可求得控制
工具機的三軸參數, 而得到齒條齒輪切削的NC程式, 並進行實作切削. 本
文並推導三次元量床的功能函數矩陣, 規劃量測時的探頭矩陣, 解得三次
元量床的控制參數及自動量測的NC程式, 再於三次元量床上實際量測所切
削的齒輪, 所量得的數據並經過軟體的誤差修正, 使得此量測誤差最小.
以期達成齒輪的設計, 切削與量測的整合.

This thesis presents an analytical methodology on the NC
data generationfor maching of spur gear meshed with spur rack on
3-axis machine tools, andautomation measurement of the spur gear
on coordinate measuring machine. Theability function of the
machine tool and the coordinate measuring machine arederived by
the Denavit-Hartenberg notation. The desired cutter and probe
locations are also derived by the Denavit-Hartenberg notation.
The cutting NCdata equations are obtained by solving the link
variables of the machine tool through equations of its ability
function and the desired cutter location matrix. The measuring
NC data equations are obtained by solving the link variables of
the coordinate measuring machine througt equations of its
abilityfunction and the desired probe location matrix. To verify
the developed methodology, this gear is machined on a 3-axis
machine tool, and measured on a coordinate measuring machine
then. The measuring data will be localized through a program
designed to get a better measuring result. This methodology is a
general one and is applicable for various gear manufactures and
measurements. It also combine the activities of gear design,
manufacturing, and measurement.