球面連桿機構之模組化運動學與機械誤差分析方法

A Modular Method for Kinematics and Mechanical Error Analysis of Spherical Linkage Mechanisms

賴柏妤(Pa-Yu Lai)

指導教授 ： 徐冠倫

國立臺灣大學/工學院/機械工程學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202102440

摘要

球面連桿機構雖已廣泛使用在醫療和工業的領域，但是球面連桿機構的分析仍然缺乏簡易與系統化的方法。因此，本文提出一套模組化方法以分析球面連桿機構的運動學和誤差。首先，本研究採用旋轉矩陣推導球面串聯式機器人之順向與逆向運動學方程式並以副函式呈現，接著再對應地套用這些副函式到拆解後的球面連桿機構，就能得到輸入角相對於輸出角的關係和端接點的位置、速度和加速度。此外，本研究也發展出球面串聯式機器人之順向與逆向機械誤差的方程式，用以探討各連桿尺寸誤差和接頭運動誤差對輸出運動造成的影響。分析的結果可用於確認尺寸和接頭誤差對輸出運動的影響程度是否在可接受的範圍。目前，本研究成果適用於大部分的球面連桿構，而未來將持續探討本方法於高階的模組的可行性。

關鍵字

模組化方法 ； 球面連桿機構 ； 運動學分析 ； 機械誤差分析 ； 速度誤差分析 ； 加速度誤差分析

並列摘要

Although spherical mechanisms have been widely implemented in the medical and industrial fields, there still lacks a simple and systematic approach for analyzing their kinematics and mechanical errors. Therefore, the purpose of this paper is to provide a modular approach for kinematics and mechanical errors analysis of spherical mechanisms. Firstly, the forward and inverse kinematics, described by rotation matrices, of the spherical serial manipulator is derived and embedded in the form of subroutines. By applying the subroutines correspondingly to the decomposed topologies of the spherical mechanisms, the relationship between the input angle and the output angle and the position, velocity and acceleration of the end-effector point can be obtained. In addition, the error propagations of the spherical serial manipulator are formulated and programed into subroutines, which can be applied to analyze the influence of dimensional and joint motion errors on the output motion. The results of the analysis can be used to confirm whether the dimensional and joint motion errors affect the output motion in an acceptable range. Up to now, the concept of the modular approach is applicable to most spherical mechanisms, and the feasibility of this method adopting high-class modules will be explored in the future.

並列關鍵字

modular method ； spherical linkage mechanisms ； kinematics analysis ； mechanical error analysis ； velocity error ； acceleration error

參考文獻

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