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Dynamic modeling of parallel manipulators based on Lagrange–D’Alembert formulation and Jacobian/Hessian matrices
Multibody System Dynamics ( IF 3.4 ) Pub Date : 2019-10-02 , DOI: 10.1007/s11044-019-09705-0
Roshdy Foaad Abo-Shanab

This paper describes the development of a dynamic model for parallel manipulators based on the Lagrange–D’Alembert equation, the Hessian matrix of the kinetic energy of the manipulator, and the Jacobian/Hessian matrices of the constraint equations. The model generates the forward and inverse dynamics formulations of parallel manipulators. First, the kinematic relations between the input actuated variables and the output variables are defined in terms of the Jacobian and Hessian matrices of the constraint equations. Then, a new form of Lagrange–D’Alembert equation is introduced and used to derive the dynamic model of parallel manipulators. In the present model, the inertia, centrifugal, and Coriolis generalized forces/torques are obtained directly from Hessian matrix of the kinetic energy of the manipulator. The developed model is simple, straightforward, and appropriate for parallel processing techniques as the elements of the Jacobian and Hessian matrices can be calculated simultaneously. The developed model is validated using the conservation of work and energy principle. A trajectory tracking control of a simple 3RRR planar parallel manipulator is used to illustrate the developed model.

中文翻译:

基于Lagrange-D'Alembert公式和Jacobian / Hessian矩阵的并联机械手的动力学建模

本文描述了基于Lagrange-D'Alembert方程,机械手动能的Hessian矩阵以及约束方程的Jacobian / Hessian矩阵的并联机械手动力学模型的开发。该模型生成并联机械手的正向和反向动力学公式。首先,根据约束方程的雅可比矩阵和黑森矩阵,定义了输入驱动变量和输出变量之间的运动关系。然后,引入了一种新形式的Lagrange–D'Alembert方程,并将其用于导出并联机械手的动力学模型。在本模型中,惯性力,离心力和科里奥利广义力/扭矩直接从机械手动能的黑森州矩阵获得。开发的模型很简单,简单易用,适合并行处理技术,因为可以同时计算Jacobian和Hessian矩阵的元素。使用工作量和能量守恒原理验证了开发的模型。简单3的轨迹跟踪控制R RR平面并联机械手用于说明开发的模型。
更新日期:2019-10-02
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