四連桿組運動方程式推導與模擬之研究

本文的目的在推導四連桿組的運動方程式並探討其動態反應。對一個自由度的剛體機構系統輸入作用力時，其連桿機構作動的運動方程式可以利用一條二階非線性微分方程式，或是一組二階非線性微分方程式來表示，由此方程式可求出連桿機構各桿件位置、速度以及加速度與時間關係的動態變化數據。本文利用機器動力學中的向量迴路法，來推導四連桿組各桿件和質心的運動係數，以了解各桿件之間的速度比與質心在X和Y方向的運動係數，並且在已知的輸入作用力矩作用下，利用數值方法求解運動方程式，以分析在不同阻尼或桿件尺寸下的動態反應。最後，推導出一組二階非線性微分的Lagrange方程式，並與一條二階非線性微分一般化運動方程式相比較，利於往後此類機構工程分析研究，以故為選擇運動方程式分析機構動態反應的基礎。

關鍵字

四連桿組；運動方程式；動態反應； Lagrange運動方程式

並列摘要

The objective of this paper is to derive of the equation of motion four-bar linkage and investigate the dynamic response. For a rigid body system with one degree of freedom represented by its equation of motion can be a second order nonlinear differential equations, or a set of second order nonlinear differential equations. From the equation, link position, velocity and acceleration of each link with respect to time can be obtained. In this paper, the vector loop method in machine dynamics is used to derive the position analysis of four-bar linkage. Then, the kinematic coefficients of each link and the mass center of gravity is derived, when the input force is known, the equations of motion can be solved using numerical method in order to study to dynamic response with different damping ratio and dimension. Finally, a set of second-order nonlinear differential of the Lagrange equations are derived and compared with the equation of motion. The result of this paper can be a basis for the beneficial to the subsequent dynamic analysis of mechanism.

並列關鍵字

Four-bar linkage ； equation of motion ； dynamic response ； Lagrange equation

參考文獻

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國際替代計量

四連桿組運動方程式推導與模擬之研究

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