應用加速度極心理論於曲柄滑塊倒置機構的路徑合成與設計

Abstract

本研究主旨為推導倒置型滑塊四連桿(Turning-block)的加速度極心位置函數式，藉此合成特定路徑的機構幾何參數，同時將加速度極心理論應用於工業自動化的機構設計等用途，並聯式機構在每個瞬間會有一個加速度為零的藕桿點，該點即稱為此瞬間的加速度極心，因為加速度為零，因此具有瞬間等速以及在一定距離內該藕桿點的軌跡為近似直線的特性，這樣的特性可以應用在類似切割移動中的細線型的材料或是網狀材料，以及執行從傳動帶上夾取或放置工件等類型的動作。 推導方法之中，首先推導固定座標系以及設於藕桿的藕桿動座標系之間的座標轉換關係式，建立藕桿點相對於固定座標系以及藕桿動座標系的座標通式；再以各座標通式為基礎進行兩次微分，藉此得到藕桿點的加速度。若是將藕桿點選定，則藕桿點相對於藕桿動座標系的座標為定值，不受運動參數變化影響。接著再使用加速度極心其加速度為零的定義求出該點在藕桿動座標系描述的加速度極心座標。得到藕桿動座標系的座標之後，由最初所訂的座標轉換式求出該點在固定座標系之下的座標。本研究的連桿機構合成(即路徑合成)的部分則是反其道而行，藉由給定特定加速度極心座標採用Matlab撰寫非線性聯立方程組的數值遞迴解析運算程式求解目標機構的幾何參數，解得符合設定路徑的最佳機構幾何尺寸。 本研究應用加速度極心關係式所建立的求解機構幾何參數的數值解析程式，就工業自動化生產線夾-放(Pick and Place)機構設計範例與四足仿生機械獸的節能穩定型足部機構的設計範例分別進行模擬與實作，並利用影像是運動軌跡與速度量測法進行驗證，證實所設計的機構符合原設計的運動特性。 另外，本研究也歸納出藉由研究每個瞬間的加速度極心座標分別在固定座標系以及移動座標系所形成軌跡的交點數量，可確認目標機構是否會出現在兩個不同時刻加速度皆為零的藕桿點，本研究成果將可作為機構應用設計的實用參考。

This study focuses on the kinematic synthesis and its applications of inverted slider-crank mechanism (Turning-block) based on the acceleration pole theorem. In this study, the acceleration pole of the linkage means that a coupler point with zero acceleration is detected at one moment with in a rotation cycle. In other words, at that moment, the velocity of the coupler point is constant. In many cases, constant and smooth velocity profile is usually appearing in the interval near the instant moment. One of the motivations of the study is to develop a mechanism for cutting an object with the shape as rope and transferring the object likes pick-and-place cyclical task in an automation system. The study proposed innovative design and application of inverted slider-crank mechanism based on the characteristic of acceleration pole. First of all, the acceleration functions of the coupler point is devived based on the acceleration pole theorem. The numerical method for solving the nonlinear motion equations is thus developed and applied for constructing the path generator program. As assisted by the developed kinematic synthesis program, several typical design models with the characteristics of acceleration pole are presented. It is also evaluated by using the mechanical simulation software such as Solidworks to verify the motion conditions of each synthesized models. Two typical design example are presented to demonstrate the efficiency of the developed acceleration pole based mechanism design system. One is the mechanism "pick and place" object transfer system. The second example is leg mechanism design for bionic quadraped system. The developed path generator design program and the acceleration pole theorem based mechanism models in the research work deserved to be the demonstrated references for academic and industrial applications.