機械手臂的關節間隙是由製造等過程產生的自然結果，雖然許多研究中假設沒有關節間隙，但關節間隙的存在是難以避免的，因此其影響需要被評估。 隨著機械設備精度提升的趨勢，關節間隙所造成的誤差漸漸成為重要的議題。
本研究評估機械手臂因為關節間隙的而造成偏離目標加工位置的誤差。偏離目標位置的誤差可以經由適當的加工路徑選擇而降低。最佳路徑的產生是在目標加工位置下先將目標參數化，相關的控制輸入，亦即速度、角速度以及加速度可由逆向運動學計算，關節間隙再加入其中，而產生路徑的偏差。最佳化的架構以路徑參數為設計變數，並最小化結果的誤差。本文展示這個建議的最佳化架構，在不增加額外設備成本或控制的情況下提升精度並減低能量消耗。以並聯式五連桿機械手臂示範所提出的方法。

Manipulator joint clearance is a natural consequence of manufacturing processes. Although most studies in the literature have assumed zero joint clearance, its existence is unavoidable and thus its impact needs to be evaluated. With the miniaturizing trend in engineering products, errors due to joint clearance have become an increasingly important issue. This study investigates how manipulators deviate from the desired working sites due to joint clearance. Deviations from the target locations can be reduced by properly selecting the working path. The optimal path is obtained by first parameterizing the path based on the required target task locations. Corresponding controlling inputs, namely linear and angular velocities as well as their accelerations, are calculated using inverse kinematics. Joint clearances are then added to obtain the deviations a path will make. An optimization framework with path parameters as the design variables is then formulated to minimize the resulting deviations. The proposed framework is shown to improve accuracy without additional equipment cost or control effort. A five-bar parallel manipulator is used to demonstrate the effectiveness of the proposed method. Results show that paths without considering joint clearance could have larger errors with higher energy requirements. Systematically bringing joint clearance uncertainty into initial path planning could achieve better results for both objectives without additional cost.

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