Cardan齒輪機構是一種知名的齒輪傳動直線機構(straight-line mechanism)，本研究以Cardan齒輪機構為基礎，提出一種新型彈簧式重力平衡器。我們將補償重力用的彈簧安裝在Cardan齒輪機構的直線運動軌跡上，以及透過一速比為2：1的行星齒輪系，將掛有負載的旋轉桿件運動，轉換為彈簧的直線拉伸運動。本設計有幾大創新處：

(1) 本設計概念使用實際彈簧，非理想之零自由長度彈簧；
(2) 彈簧可直接安裝於接頭或某一桿件內，毋須橫跨兩桿件，以避免不必要的干涉；
(3) 全機構僅使用旋轉接頭與齒輪接頭，無摩擦力較大的接頭 (例如：滑行對)；
(4) 機構質量於平衡器運動過程中不影響重力補償效果，即機構為理論上的完美重力平衡 (perfectly gravity balanced)。

我們亦進一步延伸此構想，提供以Cardan齒輪機構為基礎的雙自由度重力平衡器設計概念。此外，我們將所提出之重力平衡器與鎖定機構結合，以避免平衡器因為意外的碰撞而移動。為確認設計構想的正確性，我們使用ADAMS機構運動模擬軟體，驗證整體機構於各位置下之位能皆保持守恆。我們亦對該新型設計進行力量分析，以了解機構內各桿件間之作用力。最後，我們製作實驗模型驗證此設計構想是否可達到重力平衡，並做實驗量測平衡器平衡時所需的摩擦力大小，亦即重力平衡之準確性。

This thesis proposes a novel spring-based gravity balancer by using the well-known Cardan gear straight-line mechanism. The spring for gravity compensation is installed along the straight-line trajectory of the Cardan gear. On the other hand, a planetary gear train with a speed ratio of 2:1 is integrated to the Cardan gear to convert the rotary motion of the payload link to the stretching of the spring. It is interesting to note that the proposed design concept is featured by:

(1) The spring used is practical one. The ideal zero-free-length spring, as adopted in many existing designs, is not considered here;
(2) The spring is installed either in a joint or a link for avoiding the unnecessary interferences;
(3) The mechanism has revolute and gear joints only, where the high-friction joints, e.g., the prismatic joints, are not used;
(4) The link masses of the mechanism do not affect the balancing performance so that the mechanism including the mass itself is perfectly gravity balanced.

We further extended this concept to design a 2-DoF Cardan-gear-based gravity balancer. In addition, we combined the proposed balancer with locking mechanism for avoiding the movement that may be induced by accidentally collision. To validate the proposed concept, we simulated it in ADAMS and confirmed that the total potential energy of the mechanism remains the same in any configuration. Last, we built a test rig for studying the accuracy of the gravity compensation by the prototype of the 1-DoF balancer.

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