本研究提出一基於幾何約束方法(Geometric Constrain Programing)的彈簧式靜力平衡機構設計方法，期望解決現有靜平衡技術之問題，使機構構型與尺寸能夠快速生成，以及避免實現零自由長度彈簧所產生之問題。首先，檢索與分析現有靜平衡設計，歸納其特性，再於靜力平衡機構基本原理的基礎上，提出一種基於幾何約束方法之創新彈簧式靜力平衡機構設計方法。其中藉由「彈力位能同心圓」的作圖，使彈力位能以視覺化的方式呈現於圖面上，以快速生成近似靜平衡的機構尺寸。本研究將此方法應用於坐站姿轉換輔具，以滿足高齡社會對輔具的需求。經由實驗收集受試者於坐到站時的設計規格參數，將其帶入本研究提出的方法中，以生成機構構型與尺寸。依輔助使用者之腿部肌力強度的不同，提出兩種類型的設計實例，又根據不同的負載假設情況，共分為五個設計實例。利用機械系統動力分析軟體ADAMS分析這五個設計實例之總位能與省力效果。在這些設計實例中最小的總位能平均誤差為0.69%。在軟體中加入虛擬馬達，馬達扭矩之最佳的平均省力效果達85%；而若無虛擬馬達、以加入外力方式模擬看護者操作作站姿轉換輔具，最佳的平均省力效果達82%。經過分析這些設計實例的數據，歸納出在幾何約束編程中，設定越多桿件必須通過的精確位置，可降低其總位能誤差，以及總位能誤差與省力效果呈負相關的結論。此外，也認知到此設計方法之侷限，無法達成人體坐到站姿態轉換中，人體質量逐步由椅面轉移至地面、導致機構系統中負載隨運動而減少的情形。最後，選用一組穩定度較高的設計實例製作原型機後，以實驗驗證利用本研究提出的方法所生成的機構，其施加外力平均省力效果高達73%。並且驗證利用本研究提出的創新設計方法所生成的機構，具可行性與近似靜平衡效果。

This study proposes a spring-based static balancing mechanism design method based on Geometric Constraint Programming, aiming to address issues with existing static balance techniques. The method allows for rapid generation of mechanism configuration and dimensions while avoiding problems associated with implementing zero-length springs. Initially, existing static balance designs are retrieved and analyzed to deduce their characteristics. Then, building upon the basic principles of static balancing mechanisms, an innovative spring-based static balancing mechanism design method based on Geometric Constraint Programming is proposed.
By plotting the "elastic potential energy concentric circles," the elastic potential energy is visualized on the graph, facilitating the rapid generation of approximate static balancing mechanism dimensions. This method is applied to the design of assistive devices for sit-to-stand transitions to meet the needs of an aging society. Experimental data on design specification parameters during sit-to-stand transitions is collected from participants and incorporated into the proposed method to generate mechanism configurations and dimensions.
Two types of design examples are presented based on the strength of the user's leg muscle, further divided into five design examples according to different loading assumptions. The total potential energy and energy-saving effects of these five design examples are analyzed using the mechanical system dynamics analysis software ADAMS. The average minimum total potential energy error among these design examples is 0.69%. By integrating virtual motors into the software, the average optimal energy-saving effect of motor torque reaches 85%. Without virtual motors, simulating caregiver-operated sit-to-stand transition assistive devices through external force addition achieves an average energy-saving effect of 82%.
After analyzing the data from these design examples, we concluded that in Geometric Constraint Programming, setting more precise positions that the members must pass can reduce the total potential energy error and that the total potential energy error is negatively correlated with the energy-saving effect. In addition, we are also aware of the limitations of this design method. It cannot achieve the situation where the human body's mass gradually transfers from the chair surface to the ground when the human body changes from sitting to standing, causing the load in the mechanism system to decrease with movement.
Finally, a set of design examples with higher stability is selected to create prototype machines. Experimental verification demonstrates that mechanisms generated using the proposed method achieve an average energy-saving effect of up to 73% when subjected to external force. The feasibility and approximate static balance effect of mechanisms generated using the innovative design method proposed in this study are confirmed through experimentation.

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