傳統上常使用於運動與動力傳送系統的螺桿機構，採用等轉速馬達作為動力源；若輸出桿件的運動條件改變，則必須重新設計與製作螺桿的輪廓。若將變轉速輸入的概念用於螺桿機構，則可不改變螺桿輪廓，輸出合適的運動與動力特性。本研究針對螺桿機構，進行變導程螺桿變轉速輸入設計，來達到改善或符合不同從動件運動與動力特性設計需求；另外，亦結合往復運動機構，建立變轉速往復複合螺桿機構，使得輸出運動特性可與利用伺服馬達正反轉控制之螺桿機構有近似的輸出運動特性。
首先推導出變導程螺桿機構與複合螺桿機構的運動與動力分析理論，作為本設計基礎；接著探討輸出運動之連續性，並使用Bezier curve和Fourier series函數作為螺桿與複合螺桿機構之輸入轉速軌跡；然後，透過運動與動力設計來改善螺桿機構之輸出運動與動力特性。再者，透過複合螺桿機構設計，求出螺桿機構運動與動力設計之近似特性效果。最後，本研究設計與製作出一套伺服複合螺桿機構，經由馬達控制輸出所設計之轉速軌跡，透過動態收集與分析相關特性數據，驗證本理論之可行性。
經由設計結果得知，利用Bezier curve與Fourier series進行變轉速設計，可得到比等轉速時更佳的運動與動力特性或更符合設計需求與限制的結果，而這兩曲線中，以Fourier series的改善效果較好；另外，複合螺桿機構的輸出運動特性與螺桿機構相近。透過本研究所建立之實驗設備，實驗結果亦與理論設計相符合，證明了本研究理論之可行性。

A screw mechanism is usually used in the kinematic and dynamic transmission systems. Traditionally, the input power of a screw mechanism is a constant-speed motor. If the output motion changes, the screw contour should be redesigned and rebuilt. Without modifying the screw contour, a variable input speed screw mechanism offers an alternative to achieve kinematic and dynamic characteristics. The purpose of this work is to improve or conform to the various required designs regarding the kinematic and dynamic characteristics of the output follower for a screw mechanism by discussing the variable input speed design of a variable pitch lead screw mechanism. And, this design is developed based on a reciprocating mechanism. Its output kinematic characteristic is similar to the screw mechanism by controlling the input positive and negative directions of the server motor to drive.
Firstly, the kinematic and dynamic analyses for the variable-pitch screw mechanism and the screw-reciprocating compound mechanism are derived as the foundation for the subsequent designs. Bezier curve and Fourier series function are employed to represent the input speed trajectories of the screw mechanism and the compound mechanism, and the motion continuity conditions at trajectories boundary are investigated. Then the kinematic and dynamic design is studied to improve the kinematic and dynamic characteristics of the screw mechanism. Furthermore, the screw-reciprocating compound mechanism is investigated to achieve the near function for kinematic and dynamic designs of the screw mechanism. Finally, a servo compound mechanism is designed and built. The designed speed trajectory is achieved by controlling the servo motor. Data of related characteristics are dynamically measured and then analyzed to verify the design concept as well as to demonstrate the performances of the variable-speed compound mechanism.
Using Bezier curve and Fourier series to design the variable input speed, the kinematic and dynamic characteristics are better than the design with constant input speed or much close to achieve the design requirements and constraints. By comparing these two trajectories, the results are better by using Fourier series. Furthermore, the output motion of the compound screw mechanism is similar to the screw mechanism. In addition, the experimental result is close to the theoretic design. This proves the feasibility of the proposed design theory.

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