並聯式機械手臂於現今已是工業上非常重要以及經常被廣泛使用的一種機械手臂。本文研究了並聯式機械手臂的歷史以及發展過程，同時也點出九個並聯式機械手臂與串聯式機械手臂最大的差異性以及並聯式機械手臂在特定工業上的廣泛應用。藉由已發展成熟的Delta 並聯式機械手臂理論本論文清楚的推導出Delta 並聯式機械手臂的正向運動學、逆向運動學、奇異點分析以及工作空間上的分析。
以下我們會針對Delta 並聯式機械手臂進行各種的路徑規劃，其中曲線包含：直線、圓、拋物線、螺旋線、貝茲曲線、Cubic-spline、B-spline。由上敘述中所提及的路徑皆為現今工業上使用頻繁的路徑，而當我們規劃好路徑後，將會利用辛普森積分法以及二分法結合兩種不同的速度控制以達到平滑的效果；其中速度包含了：梯形速度控制以及S-curve 速度控制，以上這兩種速度控制方式同時也是現今工業上經常運用的方式。
針對Delta並聯式機械手臂，本文於文末會進行不同的路徑，分別套用於S-curve 速度控制進行討論以及分析。

A parallel robot is one kind of robot that plays an important role, and also the Delta robot is widely used in industry nowadays. It not only presents the background of the Delta robot including its history and development in this thesis but also explains the industrial applications, the current design and the future trend of Delta robot. Then it proposes nine differences between the parallel robot and the series robot. Ultimately, the kinematics of the Delta robot, including the direct and inverse kinematics, the workspace, and the singularity analysis, are systematically presented in detailed.
This study mainly focuses on the trajectory planning for the Delta robot, which includes the path planning in the three-dimensional space and the motion profile design of the end-effector. The path planning provides straight lines, circles, parabolic curves, Bézier curves, Cubic-spline curves, and B-spline curves. The motion profile design provides the trapezoid speed control and the S-curve speed control. These paths and the speed control methods are usually applied to the industry. When the path is specified, the Simpson's rule and the bisection method are applied to determine the coordinate of the end-effector at any specific time, and then the angles of the active joints can be evaluated based on the inverse kinematics.

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