正常的成年人有206根骨頭以及超過70個以上的關節，產生了許多可供人利用的自由度。而人在日常生活中的動作或簡單、或複雜，大腦對於不同的動作該如何使用各個自由度在科學界中也沒有定論。其中一種可能為藉由同步多個自由度以簡化控制問題，另外一種可能則是在滿足動作需求後，再使用額外的自由度，以達到其餘效果。
本文針對靜止站立時的狀態做分析，並使用在分析姿勢與步態中常見的測力板當成評估工具。並透過壓力中心傳統指標，加上實驗室的新穎指標，針對不同年齡層或是有無視覺輔助的情況下做比較，而這些指標多數都能夠有效的區分不同族群。
除此之外，本文亦研究人體如何使用地面反作用力的冗力。透過三個必須滿足靜止站立平衡時的限制條件，可以求出地面反作用力的零空間，而實驗結果顯示，此冗力可以減少垂直方向上扭矩的能量以及增加變化速度。從這些結果可以得知，人體控制系統在靜止站立平衡中，除了單純的控制壓力中心追隨質量中心外，更使用了地面反作用力來穩定垂直方向上的旋轉動作。

There are 206 bones and more than 70 joints in an adult’s body, which provides many degrees of freedom (DOFs) for humans to use. People’s motion in daily life can be simple or complex. However, how these large number of DOFs are utilized in performing these daily motions is remain unclear. One possibility is to simplify the motion control problem by synchronizing different DOFs. The other possible is that, after satisfying the task demand of the motion, the extra DOFs should be utilized to achieve additional goals.
In this paper, we study the posture of quiet standing with a force plate which is widely used in the study of postures and gaits. By using conventional center of pressure COP features and newly proposed features, we try to differentiate the quiet standing stability of young and old age groups in in eyes open and closed conditions. The experimental results demonstrate and compare the effectiveness of these features.
Furthermore, this work also studies how humans utilize the ground reaction force (GRF) redundancy. By finding three constraints that must be satisfied during quiet standing, this study determines the null space of GRF. As shown by the experimental results, the GRF redundancy significantly reduces the energy and increases the changing speed of the vertical direction moment. These results demonstrate that during quiet standing, in addition to moving COP to regulate center of mass, the human balance control system also uses the GRF to stabilize the rotational motion in the vertical direction.

論文審定書 i
誌謝 ii
摘要 iii
Abstract iv
目錄 v
圖目錄 viii
表目錄 xii
第一章 緒論 1
1.1 前言 1
1.2 研究動機與目的 3
1.3 文獻回顧 3
1.4 論文架構 4
第二章 實驗流程與方法 5
2.1 實驗對象 5
2.2 實驗流程 6
2.3 實驗設備 8
2.3.1 實驗設備與量測 8
2.3.2 座標軸系統 8
2.4 人機介面 9
第三章 平衡感指標與冗力 11
3.1 壓力中心與質量中心（Center of Pressure and Center of Mass） 11
3.1.1 壓力中心（Center of Pressure） 11
3.1.2 質量中心（Center of Mass） 12
3.2 分析流程與方法 12
3.3 平衡感指標 14
3.3.1 傳統COP指標 14
3.3.2新穎指標 16
3.4 冗力與零空間（Force Redundancy and Null Space） 20
3.4.1 冗力（Force Redundancy） 20
3.4.2 零空間（Null Space） 21
3.5 冗力之計算 21
3.5.1 三軸之冗力 21
3.5.2 一軸之冗力 25
3.5.3 地面反作用力改變時之冗力 25
第四章 實驗結果與討論 26
4.1 視窗相關性 27
4.2 傳統與新穎指標於不同族群間之差異 29
4.3 地面反作用力改變時冗力分析 34
4.4 無效改變量分析 39
4.5 三軸冗力分析 44
4.5.1 全部數據結果比較 45
4.5.2 異常數據移除 47
4.5.3 移除異常數據結果比較 53
4.5.4 跨族群比較 59
4.5.5 移除異常數據後之GRF改變量 64
4.5.6 不同冗力成分項比較 71
4.5.7 其餘特徵分析 72
第五章 結論與未來展望 78
5.1 結論 78
5.1.1 有無使用冗力比較 78
5.1.2 不同族群比較 79
5.1.3 平衡特徵與冗力比例關聯性 81
5.2 結語與未來展望 81
參考文獻 83
附錄 86

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