Comparative study on dynamics of redundant parallel robot based on two modeling methods
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摘要: 提出一种新型2-UPR/2-RPU冗余并联机器人并以其为研究对象，采用螺旋理论和拉格朗日法两种方法对其进行动力学建模与动力学对比研究。首先，采用封闭矢量法在全局坐标系下建立2-UPR/2-RPU并联机器人的运动学反解方程。其次，采用拉格朗日法求解了并联机器人各构件的速度关系并建立了其动力学模型。然后，采用螺旋理论对并联机器人4个支链中各关节和杆件的速度和加速度进行分析，同时结合虚功原理建立并联机器人的动力学模型。最后，以并联机器人动力学模型为基础，在MATLAB中编程得到并联机构的算法，求解得到了基于螺旋理论和拉格朗日方程建立的动力学模型各支链驱动力数值仿真结果，并通过与ADAMS软件的动力学仿真结果进行仿真验证和误差分析。结果表明：螺旋理论建立的动力学模型精度相对较高、方法方便且计算简单、更适用于少自由度并联机构动力学模型的建立和机构动力学的控制。极大地提高了2-UPR/2-RPU并联机器人响应速度和控制精度，满足磨床打磨曲面的精度要求，为机构的实践应用提供了可靠的理论依据并奠定了重要基础。
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关键词:
- 2-UPR/2-RPU并联机器人 /
- 螺旋理论 /
- 拉格朗日方程 /
- 误差分析
Abstract: A new type of 2-UPR/2-RPU redundant parallel robot is proposed and used as the research object. The dynamic modeling and dynamic comparison research of it is carried out by using the spiral theory and Lagrangian method. First, the closed vector method is used to establish the kinematic inverse equation of the 2-UPR/2-RPU parallel robot in the global coordinate system; Secondly, the Lagrangian method is used to solve the velocity relationship of each component of the parallel robot and its dynamic model is established; Then, the velocities and accelerations of the joints and rods in the four branches of the parallel robot are analyzed using the screw theory, at the same time, the dynamic model of the parallel robot is established based on the principle of virtual work; Finally, based on the dynamic model of the parallel robot, the algorithm of the parallel mechanism is obtained by programming in MATLAB, and the numerical simulation results of the driving force of each branch chain of the dynamic model is established based on the screw theory and Lagrangian equation are obtained. The simulation verification and error analysis are carried out through the dynamic simulation results with ADAMS software.The results show that the dynamic model established by the screw theory has relatively high accuracy, convenient method and simple calculation, and is more suitable for the establishment of the dynamic model of the parallel mechanism with few degrees of freedom and the control of the mechanism dynamics; it greatly improves the 2-UPR/2-RPU,the response speed and control accuracy of the parallel robot meet the precision requirements of the grinding machine for grinding curved surfaces, which provides a reliable theoretical basis and an important foundation for the practical application of the mechanism.-
Key words:
- 2-UPR/2-RPU parallel robot /
- screw theory /
- lagrange equation /
- error analysis
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