機器運轉的速度增加常是業界追求的目標，但隨著機器運轉速度增加，其所產生的搖撼力與搖撼力矩也隨之增加，造成機器運轉時的種種問題。為了降低搖撼力與搖撼力矩，平衡器之設計為一重要的研究課題。
本文先建立空間N桿機構的搖撼力與搖撼力矩之分析模式，並以傅立葉級數而得其各頻率項之分量。再對於各種奇異條件發生時的情況加以分類討論，且分別提出其旋轉質量平衡器的設計及旋轉軸的配置。並利用各頻率項搖撼力與搖撼力矩的分量，探討空間機構任一頻率項搖撼力向量端點軌跡圖、均方根值搖撼力矩分佈特性以及搖撼力在任一方向投影之均方根平方值的分佈特性，並討論其間的幾何關係。另外，本文以一空間RCCC機構為例，顯示其各種特性，並驗證理論模式的正確性。
本文證明空間機構任一頻率項搖撼力向量端點軌跡橢圓之主軸，與空間機構任一頻率項之等力矩橢球的兩主軸平行，且向量端點軌跡橢圓之長短軸長度與等力矩橢球之兩長短軸長度成比例關係。另外，本文亦推得空間機構任一頻率項搖撼力在任一方向之投影均方根平方值軌跡為六次曲面，且其對稱軸與向量端點軌跡橢圓之主軸同向且與等力矩橢球之兩主軸方向平行。

Increasing the operation speed of machinery is always a target for the industry; however their shaking force and shaking moment are also augmented. They cause various dynamic problems of machinery. Thus balancing design for reducing the shaking effects is an important issue.
In this study firstly, the model for analyzing the shaking force and shaking moment of spatial mechanisms is introduced, then Fourier transform is applied to get the frequency terms of the shaking effects. Secondly, singular conditions which satisfy the singular equation are classified; then for each condition, an analytical model is proposed to determine its rotating-mass-balancers and their locations. Thirdly, the equation of the root-mean-square (rms) loci of a frequency term of the shaking force along a given direction is derived; the analytical forms of the geometry relations of it, the hodograph of a frequency term of the shaking force, and rms loci of a frequency term of shaking moment are also derived. In addition, a spatial RCCC four-bar linkage is included as the example to reveal the above characteristics and to verify the correctness of proposed models.
The followings are the contributions of this study: (1) for each singular condition, an analytical model is proposed to determine its rotating-mass-balancers and their locations; (2) an analytical form to determine the principal axes of the isomomental ellipsoids of any frequency term of the shaking moment of spatial mechanisms is derived; (3) comparing the geometry of the hodograph of any frequency term of the shaking force and isomomental ellipsoids of any frequency term of the shaking moment, it is proved that their principle axes are parallel and the lengths of their semi-axes are proportional to each other; (4) the equation of the rms loci of a frequency term of the shaking force along a given direction is derived and it is a sixth-order equation, furthermore the principle axes of hodograph of any frequency term of the shaking force are also the symmetric axes of the loci.

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