分支型態與匯流型態鉸接式靜平衡平面機構之分擔系數概念及應用

Abstract

本論文提出了分支型態與匯流型態之鉸接式靜平衡平面機構之設計。靜平衡機構是可以在任何姿態下平衡自身重力之機構。藉由安裝彈簧於機構之桿件上指定位置上，使其彈力位能隨著桿件運動增減，進而使系統重力位能及彈力位能總合為固定值，從而保持機構之靜平衡。本文首先定義分支型態與匯流型態鉸接式靜平衡平面機構。對於分支形態機構，選擇與地桿相連最多的開環連續桿件為主幹部分(Main Part)，較少的為分支部分(Branch Part)，兩者間重疊桿件之靜平衡由主幹部分和分支部分共同承擔。同理，將匯流形態機構分為擁有重疊桿件的主幹部分(Main Part)和匯流部分(Confluence Part)。重疊桿件之重力位能被分支部分或匯流部分彈簧所平衡之比率定義為分擔系數(Partition Coefficient)。分擔系數利用重疊桿件向量恒定相同，將主幹部分重力位能剛性矩陣之元素按照比率分給分支部分或匯流部分。主幹部分重力位能改變量與分支部分或匯流部分重力位能改變量之和為零，分別平衡兩部分，從而保持機構之靜平衡狀態。由於改變分擔係數會影響各部分重力位能剛性矩陣，主幹部分、分支部分或匯流部分平衡所需彈簧勁度係數與配置將做相應調整。基於此概念，通過調整分擔係數改變各部分彈簧所承擔之載荷， 按照需求設定優化函數，以尋求符合設計需求的最佳分擔係數及設計參數。本文通過例舉一個分支形態機構和一個匯流型態機構證實分擔係數對設計參數的優化效果。本文在最後將該理論應用於下肢復健輔具之設計，下肢復健輔具需外接在人體下肢並保持步態過程中的靜平衡。步態過程中，髖關節會產生相對人體主幹的位移，本設計克服多數外骨骼下肢輔具的缺點，考慮髖關節的位置相對於軀幹在行走時的改變。將髖關節視為平面對，將膝關節視為旋轉對，以致於患者穿戴時，下肢輔具和人體下肢在運動時的運動干涉降至最低，減少運動干涉所產生的不適感。根據下肢運動的需求進行分支形態下肢復健輔具的拓撲合成，並引入分擔係數的進行最佳化設計以尋求最佳的彈簧配置。

The design of branch and confluence type articulated statically balanced planar mechanism is addressed in this thesis. Statically balanced mechanism is capable of self-sustaining the change of gravitational potential energy of the system at any configuration. By installing springs at appointed places of linkages, total potential energy of system remains constant, keeping the system statically balanced. The definition of branch and confluence type mechanism is addressed in this paper. For branch type mechanism, choose the most number of open-loop serial linkages as main part and the other one as branch part. The overlapped linkages of main part and branch part are balanced by main part and branch part together. For confluence type mechanism, the mechanism is divided into main part and confluence part with overlapped linkages in the same way. To definite the ratio of overlapped linkages balanced by springs of branch part or confluence part as partition coefficient. Because the vectors of overlapped linkages are always same, partition the elements of gravitational stiffness block matrix from main part to branch part or confluence part. The summation of variation for main part and variation for branch or confluence part is zero. To keep the system statically balanced, every part is balanced by springs apart. The spring constant of main part, branch part or confluence parts should be adjusted because of the change of gravitational stiffness block matrix. Adjust the springs of every part by changing partition coefficient to set optimize the partition coefficient and design parameters. For proving the impact of partition coefficient, examples of a branch type mechanism and a confluence type mechanism are presented. Finally, this theory is applying to parameter design of lower limb assistive device which is connected with human lower limb and keeps statically balance during gait. Since the hip joint has relation movement to human trunk, unlike most exoskeleton type of lower limb orthosis, considers the hip joint as a plane pair and knee joint as a revolute joint. As a result, the kinematic interference between the orthosis and the human lower limb can be minimized and discomfort can be eliminated. Topological synthesis of the branch type lower limb assistive device according to the kinematic behavior of the human lower limb is first accomplished. And the partition coefficient is applying on optimizing design for spring parameters.