膝關節輔具的最佳化設計與分析

Abstract

本研究為了幫助腿部肌肉力量較不夠，但是還有能力坐立的人們，在大腿和小腿之間的膝關節處，設計一輔助機構，幫助使用者能夠達到自行坐立且省力的效果。 本研究分為兩部份，第一部份是人體模型與簡易連桿彈簧式輔具，由於人體的三個肢段大腿、小腿、軀幹的重心位置不在中心點，且有一定的轉動慣量，為非均質的細長連桿，利用控制兩個小質量塊的方法，去合成新的連桿，使新連桿的質量中心和轉動慣量和原來的連桿相同，克服軟體不能建立非均質桿的缺點，使能夠在ADAMS 中模擬。接著，考慮簡易連桿彈簧式輔具機構，運用Lagrange 動力學理論，去推導拉伸彈簧，零長彈簧，壓縮彈簧，扭簧，複合彈簧等不同類型彈簧裝設方式的彈力位能對膝關節扭矩影響的關係式。接著選用最佳化理論進行參數設計，首先將坐立過程中輔具的彈簧所形成的扭矩與原來未加輔具時膝關節扭矩的差值的平方和做為目標函數，再使用MATLAB的兩個最佳化方法，fmincon和patternsearch指令，採用數值分析法搜尋最佳的輔具設計參數，使膝關節在加裝輔具後所需扭矩降到最小，找出最佳的彈簧的彈性係數以及最佳的彈簧的連接位置。第二部份是利用托板、彈簧、拐杖，來設計輔助坐立的輔具，以大腿和軀幹的質心在同一垂直線上的模式坐立，利用重力平衡的公式，算出彈簧的k值，來達到重力平衡，並比較在同樣的k值下，以重力平衡和人體工學的模式坐立，對於膝關節扭矩造成的影響。本研究的第一部份發現用fmincon的指令進行最佳化分析所設計得的扭簧和拉伸彈簧所組合裝置的效果最好，可以達到平均省力指標81.161%，第二部份發現以本研究所設計的拐杖型輔具的建議參數與採取質心同線方式由坐姿到站立的模式，平均省力指標約100%。本研究的設計成果可提供膝關節輔具設計的參考。

The purpose of this research is to design an orthosis mounted at knee which is between thigh and shank. The proposed knee orthosis is aimed to help people whose legs muscle power are not sufficiently to raise them to stand from sit posture. This research has two parts. In the first part, the study focuses on the linkage-spring optimal design aspect applying the multiple variables optimization algorithm. Two kinds of MATLAB’s commands such as "fmincon" and "patternsearch" were adopted to search the optimal parameters of the object funtion. The variables are specified as link length and spring constant. The object was to find the most feasible combination of the link length and spring combination. The requested torques of knee joint at each moment were derived using Lagrange dynamic method and the simulated data of knee torque were also generated as an analytical function of time. Several optional model of the springs are considered, such as general tensional/compression spring, zero length spring, torsion spring, tensional-torsion composed spring system, and so on. The study presents a model of human body and knee orthosis using the kinematic model of linkages and springs. Human body are simplified and modeled as three links, such as shank, thigh and hat. For approaching the realistic model of human body with the simple uniform links, the study proposes a two masses synthesis method. Two additional counter-weight mass blocks were stuck on each link with synthesized mass distribution to form a proper mass distribution and moment inertia same as each simulated original limb segment. Then the synthesized models can thus be simulated in dynamic analysis simulation system like ADAMS. Stick-spring orthosis design is the second part of the research. The study proposes a new knee orthosis mechanism composes with stick, pallet and spring components etc. to solve the problem of S-T-S (Sit to Stand). Except the standard S-T-S processes suggested from ergonomic engineering, the study proposes new concept of keeping the two centers of weight of the limb segment of hat and thigh in a vertical straight line. The spring constant and the location position of the spring were derived by using gravity balance method. The proposed concept in the model was verified as the best choice of the design from the proposed design process. In the first part, the design group which adopts the "fmincon" optimization command and tensional-torsion composed spring system is the best. Average saving force index is 81.161%. In the second part, find that Average saving force index is approaching 100% when applying the Stick-spring orthosis model and the proposed S-T-S function . This result of the research demonstrated itself as a reference of related S-T-S knee orthosis design and study.