为提高平面并联机构动力学分析的效率及可靠性,提出了相应的向量键合图法。根据3-PPR型平面并联机构构件间的运动约束关系,将平面运动刚体、旋转铰及移动铰的向量键合图模型组合起来,建立了3PPR型平面并联机构向量键合图模型。针对该类机构构件间非线性几何约束所导致的微分因果环问题,提出了有效的解决方法,克服了其给机构自动建模与动力学分析所带来的代数困难。应用相应的算法,实现了3-PPR型平面并联机构计算机辅助动力学建模与分析。通过实际算例说明了所述方法的可靠性及有效性。
For improving the reliability and efficiency of the dynamic analysis for planar parallel mechanism, the corresponding vector bond graph procedure is proposed. From the moving constraint relations between components of 3-PPR planar parallel mechanism, the corresponding vector bond graph model of the mechanism is made by assembling the vector bond graph models of planar rigid body, revolute joint and translational joint. For the problem of differential causality loop brought by nonlinear geometric constraints between components of the mechanism, the corresponding effective method is proposed. As a result, the algebraic difficulty in the mechanism automatic modeling and analysis is overcome. By the corresponding algorithm, the computer aided dynamic modeling and analysis of 3-PPR parallel mechanism is realized. By a practical example system, the reliability and validity of the procedure proposed are illustrated.
3-PPR型平面并联机构,动力学建模与分析,向量键合图,因果关系,铰约束, 3-PPR Planar Parallel Mechanism Dynamic Modeling and Analysis Vector Bond Graph Causality Joint Constraint基于向量键合图法的3-PPR型平面并联机构动力学分析
动。机构运动到任意位置时,杆件AiBi长为ai,质量为,杆件BiCi长为bi,杆件质量为。动平台C 1 C 2 C 3为正三角形,其边长为c,中心P与其三个顶点的距离为e,其质量为,转动惯量为。机构位于初始位置时,杆件AiBi长为a,BiCi长为b,固定坐标系XOY的原点O与动平台中心P重合,构件A1B1与OY轴重合,构件A2B2、A3B3依次逆时针转过120˚、240˚。设动坐标系xoy固结于动平台上,其坐标原点o位于动平台中心P处,在固定坐标系XOY中的坐标为,x轴相对于X轴的夹角即动平台的姿态角为Qp。
该机构是由三条支链AiBiCi及动平台C 1 C 2 C 3所构成,每条支链包含两个刚体、两个移动副及一个转动副。
王中双,吕航. 基于向量键合图法的3-PPR型平面并联机构动力学分析The Dynamic Analysis for 3-PPR Planar Parallel Mechanism Based on Vector Bond Graph Method[J]. 机械工程与技术, 2016, 05(03): 238-246. http://dx.doi.org/10.12677/MET.2016.53028
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