二自由度球型機構設計

Abstract

本研究致力於二自由度球型機構開發，其中二自由度為可驅動之旋轉自由度，且旋轉軸相互正交。機構設計分為兩個方向，分別是串聯式機構與並聯式機構。針對串聯式機構的設計，旨在降低兩個連接的桿件，對另一方旋轉範圍的限制，進而擴增工作範圍。另一方面，針對並聯式機構的設計，旨在引進遠端運動中心(Remote Center of Motion, RCM)的運動方式，來移除萬向關節與球關節作為連接點的使用，以此增加末端平台工作空間。 本篇內容講述針對這兩種型式的機構設計流程，並推導對應機構的順、逆向運動學，再經由實作來驗證機構的表現。其中，串聯式機構有進行額外的動力學分析與模擬。最後，鑒於兩種型式的機構皆呈現球型的工作空間，本篇使用物體雅可比(Body Jacobian)與其可操作性(Manipulability)這項指標，來呈現末端點移動的不同之處，更進一步揭露出機構在球面上是否存在奇異點位置(Singular Point)，造成末端無法移動的狀況。機構實作後其實驗結果證明本篇所提出之設計的可行性。而操作性指標顯示出，串聯式球型機構具有較大的工作空間，但末端點會在特定位置無法移動;反之，並聯式球型機構的工作空間較小，但末端點在球面任何位置都可以移動。

This dissertation focuses on developing a spherical mechanism with two active rotations (2-DOF) whose rotation axes are placed orthogonally. The mechanism design is divided into two aspects: serial and parallel types. The design for the serial type of mechanism aims to reduce the structural limitations caused by the connection method of two linkages, thereby increasing the range of motion of two DOFs. On the other hand, the design for the parallel type of mechanism aims to incorporate the concept of the Remote Center of Motion (RCM) to eliminate universal joints or ball joints as connection components, expanding the workspace of the end effector plate. This dissertation describes the process of designing mechanisms, deriving both forward and inverse kinematics, and implementing prototypes to assess performance. Additionally, the dynamics is derived and simulated for the serial type mechanism. Eventually, because both mechanisms have a spherical workspace, the Body Jacobian and Manipulability are displayed to show the differences in their movement capabilities. The results illustrate that the serial type mechanism provides a larger workspace with singular positions; conversely, the parallel type mechanism offers a smaller workspace without a singular position, meaning that the parallel type mechanism is better at moving the end effector across the workspace.