本文針對一種按摩機構做分析及合成，首先針對現有按摩椅中之按摩機構專利做搜尋，並找出其中含連桿機構之專利，分析其機構構型、作動方式及桿件和接頭之連接方式。將搜尋到之6篇專利分類，發現絕大多數之專利皆是使用一種空間六連桿雙自由度機構來驅動按摩滾輪，所以本文將以此型機構來做後續分析及合成。先對其做位移分析，以空間迴路方程式推導出其位移方程式，為一4次方程式，表示此型機構最多可有4組分支構型。因為此型機構具有2個自由度，所以將此按摩機構分成搓揉及搥打兩部份運動分開合成，分別推導出其合成方程式，以循環座標下降法與牛頓法求解。最後提出一組按摩機構之數值範例，再以Pro/ENGINEER軟體繪製出各桿件及接頭再以軟體之機構模組模擬其運動，以驗證合成出之機構實際運行出之曲線與欲設其通過之軌跡是否相近。

This thesis deals with the displacement analysis and dimensional synthesis of a spatial massaging mechanism. A patent search for the massaging mechanisms currently in use is first conducted and the kinematic structure of six such mechanisms are identified and analyzed. It is found that most of which can be classified as two degree of freedom spatial linkages. Therefore this thesis is focused on the study of this type mechanism. Based on the use of spatial rotation matrix, the loop closure equation of the mechanism is first derived and then reduced to a fourth order polynomial equation in terms of the input and output angles. This indicates that the mechanism can have at most four branches. In addition, the equations for synthesizing the dimensions of the links for generating the kneading and punching motions with respect to the two input angles are derived. A numerical algorithm based on the cyclic coordinate descent method and the Newton-Raphson method for solving these equations is presented. The proposed methods are verified by a numerical example and a solid model representation of the synthesized mechanism is conducted by using Pro/Engineer computer software.

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