本文探討一種由兩條皆可推拉之超彈性纜線與雙平板組成的平面線驅動連續型機器人，在已知兩條纜線推拉長度之條件下，我們將兩條纜線視為兩個大變形之歐拉-伯努力樑(Euler-Bernoulli beam)，探討末端效應器在此輸入條件下的位置與方位。研究首先比較橢圓積分(Elliptic integral)、偽剛體模型(Pseudo rigid body model)與非線性樣條理論(Nonlinear spline theory)等三種計算歐拉-伯努力樑變形之準確性與計算時間。然後，根據上述比較結果，運用其中最適用於即時(real-time)控制的偽剛體模型法，計算平面雙線驅動之連續型機器之順向位移分析，即當兩條纜線之長度為已知，求得末端效應器的位置及方位。接著建立實驗平台，以NDI Aurora電磁式追跡系統量測末端效應器之位置與方位，比較理論模型與實際量測的誤差，同時以荷重元量測纜線在驅動端的推力及拉力，並對誤差造成原因進行討論。研究結果顯示，偽剛體模型法所推導得到的位移解與實驗量測值相去不遠，應可適用於平面連續型機器人的運動學求解。本文之產出，可為線驅動連續型機器人之運動分析選用提供一個良好的依據。

This thesis studies the displacement and error analyses of a planar wire-driven continuum robot made up of two superelastic wires, one moveable disk fixed to the wires, and one grounded disk. The wires here are formulated by using the Euler-Bernoulli beam theory. First, a comparative study on the three analytical methods for formulating the deformation of Euler-Bernoulli beam, i.e., the elliptic integral, pseudo rigid body model, and nonlinear spline theory, is carried out. The computational effort and accuracy via these three methods are compared. Accordingly, owing to its potential excellence for real-time control, the pseudo rigid body model is employed to analyze the forward kinematics of the planar wire driven continuum robot. That is, the lengths of the two wires are known, and the position and orientation of the end-effector are to be determined. An experimental platform is established for validating the accuracy of the developed analytical model. In this platform, the NDI Aurora electromagnetic tracking system is used for measuring the location of the end-effector, while the load cells are attached in the distal ends of the wires for sensing the pushing and pulling forces of the wires. The results show that the pseudo rigid body model can provide a satisfied accuracy for the forward kinematics analysis of the robot. In conclusion, the output of this work provides a good basis for the analysis of planar continuum wire driven robots.

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