Analysis of constraint forces in multibody systems based on the null space matrix method of differential equation type
Analysis of constraint forces in multibody systems based on the null space matrix method of differential equation type
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DOI：
10.1299/transjsme.19-00419
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
K. Kamiya
中科院分区：
文献类型：
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作者：
K. Kamiya
在以前的论文中，作者提出了多体系统的运动分析方法。该方法首先通过求解微分方程得到约束雅可比矩阵的零空间矩阵，然后利用零空间矩阵消去运动方程中的拉格朗日乘子，从而提高了计算效率。然而，消除拉格朗日乘子可能会成为约束力/力矩分析的缺点，因为拉格朗日乘子对应于所考虑约束的约束力/力矩。本文提出了一种新的分析约束力/力矩的方法，该方法既能有效地分析约束力/力矩，又能保持前人方法的优点。首先，通过引入违反约束的相对位移（称为反约束相对位移）推导出包含约束力/力矩的控制方程。然后提出了一种通过消除拉格朗日乘子来确定约束力/力矩的方法。此外，所提出的方法扩展到系统的冗余约束。最后通过数值算例艾德了所提方法的有效性。
In previous papers, the author presented motion analysis methods of multibody systems. In the presented methods, the null space matrix for the constraint Jacobian is obtained by solving a di ff erential equation, then the Lagrange multipliers are eliminated from the equation of motion with the obtained null space matrix.This enables us to perform e ffi cient computation. The elimination of the Lagrange multipliers, however, may become drawback for analysis of constraint forces / moments since the Lagrange multipliers correspond to the constraint forces / moments for the considered constraints. In this report, a new method which can analyze constraint forces / moments e ffi ciently with keeping advantage of the methods presented in the previous papers is developed. First, governing equations which involve the constraint forces / moments explicitly are derived by introducing relative displacements that violate the constraints, called anti-constraint relative displacements. Then a procedure to determine the constraint forces / moments with eliminating the Lagrange multipliers is presented. In addition, extension of the presented method to systems with redundant constraints is given. Finally, validity of the presented method is verified by some numerical examples.