本研究的主旨，乃針對考慮接頭間隙(Clearance)的多迴路連桿機構作位置和傳動性能等之誤差分析。而以螺旋理論為基礎，應用互逆螺旋(reciprocal screw)的數學關係去協助求解機構之瞬時構形，建立一套適用於考慮接頭間隙的連桿機構之數學模式。由等值間隙桿(Equivalent Clearance Link)的概念，我們以虛擬間隙桿代替間隙，即把因為間隙多出的自由度，以等效的接頭自由度來取代，如此機構將成為多可動度之非拘束度機構。對受力狀況下之非拘束機構，以螺旋型式表示之虛功原理提出其位置分析之數學模式。在靜力平衡的考慮下，機構將會在任何瞬間構形保持靜力平衡。此時，任何機件所受之外加鈑鉗，將會與其所有接頭傳動鈑鉗保持平衡。

　　本研究首先對考慮接頭間隙(Clearance)的多迴路連桿機構作可解性分析(solvability)，經由分析接頭傳動鈑鉗和接頭扭轉螺旋所產生未知變數之數目，與鈑鉗平衡、接頭傳動鈑鉗和接頭扭轉螺旋互逆關係、位置封閉迴路等所產生方程式之數目相等，肯定的驗證本研究所提方法之可解性。另外，數值方法包括牛頓法和同倫法被用於求解非線性聯立方程組。

　　本研究以具有不同輸入桿之六桿多迴路連桿機構為例，說明本研究所提出之求解方法。並對考慮和不考慮接頭間隙(Clearance)的連桿機構，相互比較其位置和傳動性能。在Watt-I機構例子中，由於傳動鈑鉗作用下機構出現跳躍點構形(Jump point) ，此種跳躍點構形明顯與一般跳躍點構形(停滯點)並不相同。

　　對於傳動中考慮接頭間隙(Clearance)的多迴路連桿機構之位置和傳動性能等，本方法提供了有效的分析求解方式。

　This study introduces a generalized method for error analysis of multi-loop mechanisms with joint clearances. The transmission performance of linkages that have joint clearance is also analyzed. In the study, the joint clearance is treated as virtual link to simplify the study. Equivalent kinematical pairs are used to model the motion freedoms caused by the joint clearances. Under static condition, a mechanism should be in equilibrium at any configuration. The developed methodology uses the properties of reciprocal screws to determine the instantaneous configurations. The joint transmission wrench should equilibrate all externally applied wrenches for each link member. An extra set of constraint equations can be obtained since the joint transmission wrench screw should be reciprocal to the joint twist screw of the member.

　To solve the hyper-freedom linkage problem, we must first assure that the number of independent equations available is at least equal to the number of unknown variables. It has been proved that the number of unknown variables of transmission wrench screws and joint twist screws is equal to the number of wrench equilibrium equations、 reciprocal equations、 positional closed-loop equations and the link-length equations. Then the unknown variables of a mechanism, such as positions, can be solved with the equations simultaneously.

　Six-bar linkages with different specified input links are taken as examples. Positioning error with joint clearance is compared with that of the ideal mechanism. The joint contact “jump point ” configuration under the influence of transmission wrench screw is identified and it may not be at the conventional jump point (stationary) configuration of the mechanism.

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