由於加速度極心是耦桿平面上瞬時加速度為零之點，若以此點為耦桿點，機構之耦桿點曲線在此加速度極心之鄰域的運動特性，為有限長度的近似直線位移且瞬時等速。對於需要等速地在工作點附近形成一段有限長度的近似直線運動之應用，加速度極心為此應用的最佳選擇。現有文獻指出，輸入桿為等轉速的平面四連桿機構之耦桿點曲線，可通過指定的兩個加速度極心，但迄今為止尚未找到通過三個以上加速度極心之機構。
本研究之目的在於合成可通過三個以上加速度極心的平面六連桿機構，並探討加速度極心之相關特性，所提出之設計方法可同時應用於Watt-I型、Stephenson-III型與Stephenson-I型機構之尺度合成。針對輸入桿為等轉速之三型平面六連桿機構，本文分別推導其加速度極心在固定平面及耦桿平面上之參數式，並將加速度極心曲線分別描繪在上述兩個平面上，再利用耦桿平面上加速度極心曲線的多重點作為耦桿點，其耦桿點曲線即可通過多個加速度極心。綜合所推導的加速度極心之參數式與多重點之存在條件，本文提出一套設計流程，依據指定通過的加速度極心之數目，條列出所須滿足的聯立方程式，並建立包含所有需求方程式的目標函數。然後，以最佳化方法將目標函數值最佳化至零，即可合成所求的平面六連桿機構，使其可在相對應的曲柄角度時通過指定的加速度極心。
本文以數個範例來驗證所提出之設計流程的可行性。針對Watt-I型機構的加速度極心，首先以通過兩個加速度極心的Watt-I型機構與四連桿機構來作比較，再以不同初始值合成通過三個加速度極心的兩個Watt-I型機構，並找到通過四個加速度極心的Watt-I型機構。至於Stephenson-III型機構的加速度極心，藉由所提出的設計流程，推論Stephenson-III型機構最多可通過五個加速度極心，並成功地找到通過四個與五個加速度極心的Stephenson-III型機構。最後，針對Stephenson-I型機構提出另一類設計目標，在加入指定耦桿點通過加速度極心時的速度之條件下，合成通過兩個加速度極心的Stephenson-I型機構。

An acceleration pole is the point on the coupler plane having zero acceleration. If it is chosen as the coupler point, the path of the coupler point has the properties of an approximate straight line within a limited distance and a constant velocity in the vicinity of the acceleration pole. In practical applications, the acceleration pole is the best choice if it is required to design a path generator for tracing an approximate straight line with a constant velocity in the vicinity of the working points. A previous study indicated that the coupler point of a planar four-bar mechanism driven by a crank with a constant rotational speed could pass through two acceleration poles. But the synthesis of planar mechanisms with a coupler point passing through three or more acceleration poles has not been previously reported.
The present study is to synthesize six-bar mechanisms with coupler points passing through three or more acceleration poles and to explore some related characteristics of the acceleration poles. A general synthesis method is proposed for synthesizing the Watt-I, Stephenson-III, and Stephenson-I mechanisms simultaneously. The parametric equations expressing the loci of the acceleration pole on the fixed link and the coupler plane for each mechanism driven by a crank with a constant rotational speed are derived. The desired coupler point of a path generator passing through three or more acceleration poles should be a multiple point on the locus of the acceleration pole described on the coupler plane. Using the parametric equations and the existence conditions for the multiple point on the locus of the acceleration pole on the coupler plane, a synthesis procedure is proposed for solving these equations. According to the number of the specified acceleration poles, the required equations are used to establish an objective function. Then, the value of the objective function is minimized to zero for obtaining the dimensions of each mechanism for generating a coupler curve with three or more specified acceleration poles that accord with the specified crank angles.
Some examples are provided to illustrate the feasibility of the proposed method. First of all, a Watt-I mechanism passing through two acceleration poles is synthesized to compare with a four-bar mechanism. Two Watt-I mechanisms passing through three same acceleration poles are synthesized from different initial guesses. A Watt-I path generator that guides a coupler point through four specified acceleration poles that accord with four crank angles is found. Secondly, a Stephenson-III mechanism for generating a coupler curve with four or five specified acceleration poles is obtained. Finally, a modified procedure is proposed for synthesizing the Stephenson-I mechanism with the specified velocities while the coupler point passing through two specified acceleration poles.

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