目前工業上所使用的機器人，可大致分為串聯式與並聯式兩類。相較於串聯式機構，並聯式機構有著高剛性、高負載、高精度、高速度、低移動慣性等優點，雖然運動學及動力學的分析較為困難，且工作空間較為窄小，但在精密加工的領域，由於加工的物體通常不大，故可忽略工作空間狹小的缺點。
從最早期的並聯式機構-史都華平台的發明開始，一直以來都有人研究多個自由度與不同結構的並聯式機器人。近年來，隨著自己動手做的風潮蔚為流行，各式各樣的機器人架構被提出來討論並被加以應用，三角洲型(delta)機構是被廣泛運用的其中之一，隨著移動端所裝設的工具不同而有著各式各樣的運用，如:機械手臂、3D列印、噴射塗裝、表面檢測等。
由於設計結構上的限制，目前常見的三角洲型機器人，其工作端(移動平台)與固定端(基座)往往只能做平行的相對運動(X-Y-Z 三自由度)，若想擁有更多的移動自由度(α-β-γ)，或是想要做弧面運動，就必須加裝更多的驅動馬達與更複雜的關節設計，如此一來不僅機構成本提高了，運動控制的複雜度也跟著提升，如何能在不大量增加額外成本與設計困難度的條件下，使三角洲平台能適用於不同的運動自由度，是相當值得討論的議題。本篇論文是基於三角洲型3D印表機的架構，重新設計移動平台與連桿的結構，以彈簧的拉力取代原先結構的限制力，並根據逆運動學重新設計移動演算法，進而達成在保持三個驅動馬達的情況下，工作端(移動平台)能做到球面運動，將來可以應用在球形物體的檢測與加工方面，最後結果以Matlab做模擬檢驗，並以雷射光點配合影像處理做誤差的分析與實測。

The robot arms which are used in industry can generally be separated into two kinds: serial robot and parallel robot. Compared with serial robots, parallel robots have advantages in high precision, high stiffness, high load, high speed and low inertia. Although the workspace of parallel robots has more limitation, it is not a big problem in precision processing due to the small size of processing goods.
Researchers try different kinds of structure for proper applications after the invention of earliest parallel robot - Stewart platform. DIY or Being a Maker has become more and more popular in recent year. Due to that, many types of robots emerge to our sight. Delta robot is one of the common types and has been widely used in many places. Users can choose different DOF (degree of freedom) and different end-effector they need to fit their requirement such as robot arms, 3D printing, painting, surface inspection, etc.
Due to the restriction on it structure, most of the common used delta robots’ end-effector (moving platform) can only move parallel to the fix platform (base). If we want end-effector to do more DOF movement or spherical motion, we need to combine more motors and joints. This will lead to higher manufacture cost and complex kinematics analysis. How to design a new structure which can do spherical motion with the same or only a little higher cost is the question we wondering about.
This thesis is based on delta 3D printer and we redesign the moving platform, link sticks and new inverse kinematics analysis to make the end-effector side can do spherical motion with the same number of motors. It can be used on ball-like surface inspection or machining. In the final, we use Matlab to do the virtual test, and use laser point with image processing to analysis the error.

References
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http://reprap.org/wiki/Ultimaker's_v1.5.7_PCB
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http://reprap.org/wiki/Rostock