在多軸 CNC 加工中，由於多自由度的加工軸向配置常會產生奇異性現 象，當一機構運動接近奇異點 (singular points) 時，會呈現不穩定之狀態，雖 然在應用時可利用適當之路徑規劃或藉由控制方法避開奇異點，或是設計操控 性較佳之機構，使機構較不易接近奇異點，但是最好的方法為選擇機構各驅動 軸之適當位移量，使機構在軸位移空間內可強健地 (robust) 連續經過奇異點。 當刀具加工路徑在CAM 系統中產生時，其所設定的精度是以工件的表面相對 位置為基準，一般是以小直線來表示兩個CL 位置。然而因為驅動機械軸向之 NC 指令是針對刀具旋轉軸心，即使CL 的小段直線為線性的表現，在兩個加 工指令間的路徑相對於工件而言是非線性的路徑。藉由齊次轉換矩陣、D-H 修 正標記法與Jacobian 矩陣，推導求出工具機奇異性發生位置，利用整合於CAM 系統之後處理器產出優化後的串並聯平台五軸刀具路徑，使加工路徑連續，避 免奇異點造成工具機不預期的運動並加工進行驗證。

In multi-axis computer numerical control (CNC) machining, driving axes that are equipped with more degrees of freedom often cause singularities. Approaching singular points may cause the tool path to become unstable, where collisions occur between the tool and parts of the milling machine. Although singular points can be avoided through the rearrangement of appropriate paths and employing control methods to avoid singular points during application, or by designing mechanisms with more feasible handling to prevent the occurrence of approaching singular points, the best way is to generate the appropriate movements for each robust driving axis robustly and continually near singularities during working spaces. As the result of CL data are calculated in the CAM system it is assumed that the tool path between adjacent two CL points is regarded as a straight line relative to the work piece. In fact, due to the rotary axes of the machine, the tool path between two blocks in the NC program will drive the pivot to move non-linearly relative to the work piece, thus reducing the accuracy of the tool path. By using homogeneous transformation matrix, screw theory, modified D-H notation and Jacobian matrix, the kinematics and the singularity algorithm will be implemented in a postprocessor and be integrated directly in CAM system for developing novel postprocessor of the hybrid serial-parallel five-axis machining.