以循圓測試法建立HexGlider型平行機構之運動誤差模型與診斷方法

Abstract

本論文主要研究的範疇與目的，係針對Hexglider構型之平行機構的運動誤差，建立其數學模型與診斷方法。 首先，對於所欲研究之平行機構，建立其導致運動誤差的幾何誤差源模型。除了推導該種構型平行機構的驅動滑塊與輸出平台之間運動轉換的關係，同時分析出可能導致其發生運動誤差的幾何誤差源與相關之參數誤差，並利用於運動轉換關係所得到的結果，建構個別誤差源之誤差模型，以瞭解各誤差源在理論上對於該機構之運動精度所造成的影響。 更進一步，以實驗的方式，對此待測之平行機構，進行實機之雙球桿循圓測試，來作誤差診斷。其主要目標，在於找出該機構可能存在之幾何誤差源，並且診斷各誤差源之參數誤差的大小。 在數學上，本論文將利用最小平方法原理，將整個平行機構綜合誤差經循圓測試所量得軌跡，解構為由個別誤差源所對應之循圓運動軌跡的合成，並將針對個別誤差之參數誤差進行估測，以實現該機構之誤差診斷，適當地發展出該機構運動誤差的校驗方法。換言之，只要運用雙球桿量測裝置，正確地對待測之平行機構，量得循圓運動軌跡，即可有效地分析出該機構之各項幾何誤差源，並且診斷其誤差參數之大小。如此，不論是對於該種平行機構之機械本體的精度的改善，或者是終端輸出的位置誤差的補償，都將會有莫大的助益。

This thesis is mainly focused on the study of analyzing and identifying specified motion errors for the hexglider type of parallel manipulator. First, the investigated geometric errors resulting in motion errors for the target parallel manipulator are to be modeled. We begin at deriving the kinematic transformation relationships between the sliders and the end effector of the parallel manipulator. Geometric resources of motional deviations, including translate and angular ones, resulting from the manufacturing or assembly of guideways and linkages are classified and modeled with the analytical results of the kinematics. Next, the double ball bar test is experimentally applied to the desired parallel manipulator for the study of the error diagnosis. We aim to identify geometric errors existing at the manipulator from the measured data. Mathematically, the least square method is adopted in the thesis to the identification of geometric errors. The circular contour of the overall error of the parallel mechanism obtained from the double ball bar test will be fitted by theoretic deviations caused by error sources, and their parameter errors are to be estimated. Based on the results, we will propose a measurement method and evaluating procedure to identify geometric deviations. It can be utilized as a calibration method of the hexglider manipulator. In other words, provided that the double ball bar test is applied to the desired parallel manipulator correctly, geometric deviations existing at the manipulator can be identified. Thus, it will significantly benefit to either the compensation of the position and orientation errors or the improvement of the mechanism accuracy for the hexglider type of parallel manipulator.