由於工廠生產逐漸朝自動化發展，機械手臂取代人工為目前趨勢。而因機械手臂關節出力大，需使用小體積高速比之精密減速機以增加扭矩。因此具有高齒數比、小型、質輕與低噪音等優點的擺線齒輪很常被應用在機器手臂。擺線齒輪的齒形精度要求非常高，本論文目的在於發展擺線齒輪精度評估方式，提出精度評估數學模式。首先讀入量測齒形2D點資料，透過最佳化方法中的共軛梯度法和一維搜索法中的進退法與黃金分割法將所有量測點做中心校正。接著利用B-spline曲線擬合方式將量測點擬合，為了確保擬合曲線的情況，會再進一步計算出擬合誤差。確認了擬合誤差的狀況後利用節圓半徑找出每一齒的左右齒形之節圓點。本論文對於擺線齒輪評估的內容主要分為兩個部分，第一部分為節距誤差評估。利用找出的節圓點後配合DIN所定義的計算方式就能夠評估擺線齒形的節距誤差。依據DIN3960[19]所定義的節距誤差評估計算項目有三種，包含節距誤差、累積節距誤差以及偏擺誤差。將三種節距誤差計算出來後可以進一步利用DIN3962[20]所整理的評估等級做成資料庫，利用此資料庫判斷前面計算出的節距誤差之精度等級。第二部分是做齒形和齒厚誤差的計算。在計算齒形誤差前須先將理論齒形及擬合齒形的節圓點重合，再利用偏移過後的擬合點及對應的理論點作法向上的誤差計算，齒厚誤差則是將理論之齒厚與擬合齒形之齒厚相減而得。利用建立之方法評估市售產品之精度，可做為決定擺線齒輪製造公差依據。

As factory production gradually evolves toward automation, robotic arm replacement is the current trend. Because the mechanical arm joint output is large, it is necessary to use a small volume and high-speed ratio precision reducer to increase the torque. Therefore, cycloidal gears with high gear ratio, small size, lightweight and low noise are often used in robot arms. The purpose of this paper is to develop the accuracy evaluation method of cycloidal gear and propose a mathematical model for accuracy evaluation. Firstly, the 2D point data of the tooth profile are imported, and all the measurement points are center-corrected by the conjugate gradient method, advance and retreat method and the golden section method in the one-dimensional search method. After that, using the B-spline curve fitting method to fit the measurement points, to ensure the fitting curve, the fitting error will be further calculated. After confirming the condition of the fitting error, the pitch radius is used to find the pitch points of the left and right tooth. The content of the evaluation of cycloidal gear in this paper is mainly divided into two parts. The first part is the evaluation of pitch error. The pitch error of the cycloidal gear can be evaluated using the found pitch points and the calculations defined by DIN. There are three calculation items for the pitch error evaluation according to DIN 3960[19], including single pitch error, accumulated pitch error, and run out. After calculating these pitch errors, the database can be further used to make a database using the evaluation level compiled by DIN3962 [20], and the database can be used to judge the accuracy level of the pitch errors. The second part is the calculation of the tooth profile and tooth thickness error. Before calculating the tooth shape error, the theoretical tooth profile and the pitch point of the fitting tooth profile must be coincident, and then the error of the fitting point and the corresponding theoretical point are calculated. The tooth thickness is subtracted from the fitted profile and theoretical one. Using the established method to evaluate the accuracy of commercially available products can be used as a basis for determining the manufacturing tolerance of cycloidal gears.

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