向量式有限元素法應用於繩驅動連續型機械臂之運動分析

Motion Analysis of Cable-driven Continuum Robot Using Vector Form Intrinsic Finite Element Method

何欣容(Hsin-Jung Ho)

指導教授 ： 李志中

國立臺灣大學/工學院/機械工程學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201901504

摘要

連續型機械臂是一種可連續彎曲、且具有多自由度的機構，由柔體與剛體桿件所組成，沒有運動接頭。連續型機械臂依照其形態可分為無支柱、單一支柱和多支柱三種型態。由於支柱變形屬於非線性大變形，因此本研究將應用向量式有限元素法於連續型機械臂之運動分析。向量式有限元素法以牛頓第二運動定律為基礎，使用點值描述及途徑單元處理空間與時間的關係，並透過時間積分來處理結構大變形求解。此法為模擬結構動力的分析分法，加入阻尼的效應即可模擬靜力問題，在計算效率上有很大的優勢。本文模擬單一支柱繩驅動連續機械臂，首先建立機構的模型，描述驅動繩與繩孔間接觸力，再透過等效力的方式施於支柱，應用向量式有限元素法求解流程來進行機械臂的力量及位移分析；接著進行數值模擬，並探討楊氏係數、繩孔摩擦係數和圓盤數目對變形的影響，最後架設實驗平台進行力量、位移量測並和數值模擬比較。

關鍵字

繩驅動連續型機械臂 ； 向量式有限元素法 ； 運動阻尼 ； 力量分析 ； 位移分析

並列摘要

A continuum arm is a mechanism, which is capable of continuously curving and has infinite number of degree of freedom. It is composed of soft body and rigid body without the connection of joints. The continuum arm can be classified into three types according to the number of backbones, namely, the type without backbone, the type of single-backbone and the type of multi-backbone. Due to the nonlinear large deformation of backbone, this research applied the Vector Form Intrinsic Finite Element method to solve the relationship between force and deformation of continuum arm. The aim of this research is to analyze the motion of the cable-driven continuum arm with single backbone by using the Vector Form Intrinsic Finite Element method (VFIFE). First, a model of mechanism was established. Then, the contact force between driven-cables and cable holes on the disk was formulated to be equivalent to the forces applied to backbone. Next, the Vector Form Intrinsic Finite Element method was applied to analyze the force and displacement of the continuum arm. Finally, an experiment was conducted to validate the results of simulation.

並列關鍵字

Continuum Arm with Single Backbone ； Cable-driven Continuum Arm ； Vector Form Intrinsic Finite Element Method ； Dynamic-Relaxation Method ； Force and Displacement Analysis

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