並聯式機構因具有高剛性、各連桿獨立控制、位置誤差能互相平均等特點，適用於高精度和高效生產需求。然而實際應用仍因加工、組裝、熱效應和機械振動等因素導致誤差產生，使得並聯式機構的標稱幾何形狀和實際幾何形狀之間存在偏差而導致精度下降，為了提高工具機的運動精度和定位能力，對機構進行校正有其重要性。本研究針對 3-UPU 平移式並聯機構，運用基於物理模型和無物理模型的校正方法，透過補償方式使經校正後的模型更貼近實際機械結構。
本研究為了在有限的量測點數中提高校正的改善率，安裝了輔助感測器(角度編碼器)於被動接頭，同時透過外部量測方法取得端末點的實際位置，並比較了三種不同的校正方式。第一種基於逆向運動學，透過比較端末點的量測值與運動學標準值，識別出誤差參數進行補償，實現校正；第二種方法不依賴物理模型，而是使用人工神經網路(ANN)，將端末點的量測值和桿長補償量分別作為輸入及輸出進行訓練；第三種方法在第二種基礎上，增加了輔助感測值作為輸入。為貼近真實機台，建立了一個模擬機台，以全面考慮可能的誤差源。模擬結果顯示，第一種方法不論資料筆數多少校正精度最高僅達到 92%，第二種在 28 筆訓練資料時達到 98%的校正精度，而第三種方法則在 21 筆訓練資料時即達到了 98%的校正精度，且最高能將近99%。三種方法均能有效提高並聯式機構的精度，其中第三種方法透過引入更多感測訊息，取得了最佳的校正效果，證明在少量訓練資料點數下，被動關節對於機器學習校正改善的有效性。

Parallel kinematic mechanisms (PKMs), known for their high rigidity, independent control of each link, and mutual averaging of position errors, are suitable for applications requiring high precision and production efficiency. However, practical implementations are often affected by factors such as machine tolerance, assembly, thermal effects, and mechanical vibrations, leading to deviations between the nominal and actual geometrics of PKM and subsequent decreases in accuracy. To enhance the motion precision and positioning capability of machine tools, calibration of the mechanism becomes imperative. This study focuses on the translational 3-UPU PKM, employing both model-based and model-free calibration methods to compensate and align the calibrated model with the real mechanical structure.
To improve the calibration enhancement rate with a limited number of measurement points, auxiliary sensors (angle encoders) were installed on passive joints, and the actual positions of the end effector were obtained through external measurement methods. Three different calibration methods were compared. The first method is based on inverse kinematics, which identifies and compensates for error parameters by comparing the measured values of the end effector with the kinematic standard values, thus achieving calibration. The second method does not rely on a physical model but uses an artificial neural network (ANN), where the measured values of the end effector and the rod length compensation amounts are used as inputs and outputs, respectively, for training. The third method builds on the second method by adding auxiliary sensor values as inputs. To closely replicate a real machine, a simulated machine was established to comprehensively consider possible sources of error. The simulation results indicate that the first method, regardless of the amount of data, achieved a maximum calibration accuracy of only 92%. The second method reached a calibration accuracy of 98% with 28 training data points, while the third method achieved 98% calibration accuracy with only 21 training data points, and a maximum accuracy approaching 99%. All three methods effectively improved the accuracy of the parallel mechanism, with the third method achieving the best calibration results by incorporating more sensor information. This demonstrates the effectiveness of passive joint information in enhancing machine learning calibration with a small number of training data points.

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