臺灣博碩士論文加值系統

本論文係探討數項與六自由度全並聯式線性驅動平台之運動學與動力特性相關問題。依驅動機構類型之不同，本研究將線性驅動平台區分為Stewart型（S type）與Hexaglide型（H type）兩種類型。
首先，提出一種兩階段式之數值方法，以求解此兩類平台機構之正運動學問題。第一階段先將正運動學問題轉化為等效之非線性規劃問題，藉此可迅速調整活動平台之任意初始值到正確解附近，進而於第二階段中利用牛頓-雷佛遜數值法以疊代方式收斂至精確解。此兩階段運算法則不僅數值穩定性佳、計算效率高，且適用於求解正運動學問題之多重解。
其次，針對此兩類平台機構系統之運動特性，規劃出三項區域操控問題分別深入探討。第一項問題為分析活動平台於任意指定位置時，沿刀具主軸方向旋轉之最大容許範圍。第二項問題為分析刀具主軸相對於任意指定之活動平台位置與方位，刀具平台可傾斜活動之最大容許範圍。第三項問題為探討活動平台於任意指定位置之三自由度方位工作空間的建立方法。此三項操控問題所受到之運動拘束為支撐桿間之干涉現象、被動接頭之活動範圍限制、以及驅動接頭之行程限制。本文將此三類運動拘束皆納入考量，並提出了一種泛用且具高度運算效率之區域操控特性的分析方法。
最後，當六自由度平台機構應用於五軸加工時，活動平台繞裝置其上之刀具軸旋轉的自由度即為多餘，此多餘自由度可用來調整驅動機構之構形以改善其動力特性。因此，本文即針對此直角座標空間多餘自由度提出兩類最佳化動力軌跡規劃問題及其求解方法。第一類問題係指在最佳切削力分佈條件下，沿指定切削路徑合成出平台之點到點自轉軌跡。第二類問題則在最佳驅動力分佈條件下，沿指定加工路徑決定出最大固定切削力值，以避免線性驅動器之控制驅動扭力發生不連續或突跳現象。本文中對此兩類最佳化問題所提出之數值求解方法係源於近似規劃法，此方法之基本觀念相當直接簡易，且可將系統所受之所有非線性動力與運動限制條件皆納入考量。

This dissertation investigates several problems in associated with the kinematics and dynamics properties of six degree-of-freedom (DOF) fully parallel linearly actuated platform (LAP) manipulators. Based on the characteristics of the kinematic structure of the driving mechanisms, the LAPs studied in this work are classified into two types, namely the Stewart type (S-type) and the Hexaglide type (H-type).
A two stage numerical approach is first presented for solving the direct kinematics problem of these manipulators. The first stage of this approach transforms the direct kinematics problem into an equivalent nonlinear programming program, and a robust search algorithm which would bring the mobile platform from virtually any initial approximation to the neighborhood of the true solution is developed. The second stage uses the Newton-Raphson method to iteratively converge the solution to the desired degree of accuracy. This approach not only is numerically stable and computationally efficient, but also is useful for finding multiple solutions to the direct kinematics problem.
Secondly, an in depth investigation of three problems in associated with the local manipulation properties of the two types LAPs is presented. The first problem is to find the physically allowable region that the mobile platform can be freely rolled about any given direction at any specified position. The second problem is to examine the maximum angle that the mobile platform can be tilted about any given position and orientation. The third problem is to analyze the orientation workspace of the mobile platform with respect to any specified position of one of its points. The kinematic constraints involved in these problems are the stroke limitation of the linear actuators, the motion constraints of the passive spherical and universal joints, and the interference condition between the supporting limbs. A unified and computationally efficient approach for solving these problems which takes into account all of the kinematic constraints is developed.
Thirdly, it is found that when using a six-DOF LAP to perform five-axis machining process, the rotation of the mobile platform about the spindle axis of the tool bit mounted on it is in fact a redundant DOF, and which can be used for adjusting the configuration of the driving mechanism to improve the dynamic performance of the robot. Consequently, two optimal dynamic trajectory planning problems in associated with this task space redundant DOF are investigated. The first problem involves of synthesizing the point-to-point rotational trajectory of the mobile platform about the spindle axis such that the distribution of the cutting force along the given machining contour is optimized. The second problem is to determine the maximum constant cutting force along the given machining contour while maintaining the optimal distribution of the control forces of the linear actuators to avoid discontinuities and sudden jumps. The numerical algorithms developed for solving these problems are based on the method of approximate programming, which is not only conceptually straightforward but also taking into account all of the nonlinear dynamic and kinematic constraints imposed on the system.

中文摘要 ………………………………………………………….. …….…. I
英文摘要 ..………………………………………………………………... III
誌 謝 ………………………………………………………………….. V
符號索引 ………………………………………………………….……….XI
圖表索引 ……………………………………………………………….. XIII
第一章 緒論 ……………………………………………………..………… 1
第二章 運動學分析 …………………………………………….……….. 13
2.1座標系統之定義與反運動學 ……………………….…………... 13
2.2合理構形搜尋法則 ………………………………….…………... 16
2.3閉迴路微分方程式 ……………………………….……………... 22
2.4數值演算法則 ……………………………………………….………... 23
2.5數值範例 …………………………………………………….………... 25
第三章 區域操控特性分析 ………………………………..…………….. 31
3.1 定義區域操控特性 ……………………………….…………….. 31
3.2 運動拘束分析 …………………………………….…………….. 34
3.2.1支撐桿間干涉 …………………………….……………… 34
3.2.2線性驅動接頭之行程拘束限制 …………….…………… 41
3.2.3從動接頭之拘束限制 ……………………….…………… 43
3.3支撐桿干涉分析 ………………………………………………..…….. 43
3.4線性驅動接頭之行程限制分析 ………………………..……….. 50
3.5從動接頭限制分析 …………………………………….………... 51
3.6電腦計算流程 ……….…………………………………………... 52
3.7數值範例 ……………..………………………………...………... 54
第四章 動力學分析 ………...…………………………..………………... 63
4.1 變分運動拘束式 ………………………………..………………. 63
4.2 動力方程式 ………………………………………..……………. 72
4.2.1外作用力所作之虛功 ……………………….…………… 73
4.2.2慣性力所作之虛功 ……………………….……………… 74
4.3 參數式動力方程式 ………………………………..……………. 78
第五章 動力軌跡規劃 ………………………………………..………….. 81
5.1 運動拘束條件之離散化與線性化 ……………….…………….. 81
5.2 最佳化切削力分佈 ………………………………….………….. 89
5.3 最佳驅動力分佈與固定切削力之最大化 …………………… 100
第六章 結論與建議 ……………………………………………………. 107
參考文獻 ………………………………………………………….……... 109
附錄A運動學分析中方程式之係數展開式……………………………. 117
附錄B運動學分析中(2-17)式之推導過程……………………..………. 119
附錄C區域操控分析中(3-13)式之推導過程………………………..…. 121
附錄D區域操控分析中方程式之係數展開式…………………………. 123
附錄E區域操控分析中(3-30)式之推導過程…………………………... 127
附錄F驅動連桿組之速度與加速度分析………………………..….… 131
附錄G 動力方程式之參數向量 ……………………………….………. 135
附錄H 四階多項式仿線 ………………………………….……………. 141
作者簡介 …………………………………………………….…………... 143

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