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雅克比矩阵近似更新的三维装配约束求解研究

摘 要：提出了三维装配约束求解中雅克比矩阵近似更新的方法。该方法通过对#br# 迭代过程中满秩以及行秩秩亏雅克比矩阵进行近似更新，提高了约束求解的效率。首先在非#br# 线性迭代求解过程中添加雅克比矩阵及其逆矩阵近似更新的公式；然后给出使用近似更新公#br# 式需要满足的限制条件；最后通过对奇异点扰动算法的描述介绍迭代求解过程中雅克比矩阵#br# 发生行秩秩亏的处理办法。文中提出的策略与算法已在三维装配约束求解引擎CBABench#br# 中实现，给出的实例表明本文提出的方法效果显著。#br# 关 键 词：约束求解；雅克比更新；几何约束；三维装配；非线性方程   

  • 出版日期:2015-06-30 发布日期:2015-05-05

Research on 3D Assembly Constraint Solving with Approximate Update Formula of Jacobian Matrix

Abstract: A new method of approximately updating Jacobian matrix during 3D assembly#br# constraint solving is proposed in this paper. This method principally improves the efficiency of#br# constraints solving based on the approximate update of Jacobian matrix. First, an approximate#br# update formula of Jacobian matrix and its inverse matrix are inserted to the non-linear iterative#br# solution process. After that, the indispensable constraint is put forward, which must be satisfied#br# when using the formulas above. At last, a solution handling row rank defect of Jacobian matrix is#br# introduced via disturbance algorithm description. The methodology presented is implemented in a#br# 3D assembly constraint solving engine, named CBABench. An example given at the end of this#br# paper shows that the method has achieved a considerable effect.#br# Key words: constraint solving; Jacobian update; geometric constrains; 3D assembly;#br# non-linear equations   

  • Online:2015-06-30 Published:2015-05-05

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被引次数

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摘要： 提出了三维装配约束求解中雅克比矩阵近似更新的方法。该方法通过对
迭代过程中满秩以及行秩秩亏雅克比矩阵进行近似更新，提高了约束求解的效率。首先在非
线性迭代求解过程中添加雅克比矩阵及其逆矩阵近似更新的公式；然后给出使用近似更新公
式需要满足的限制条件；最后通过对奇异点扰动算法的描述介绍迭代求解过程中雅克比矩阵
发生行秩秩亏的处理办法。文中提出的策略与算法已在三维装配约束求解引擎CBABench
中实现，给出的实例表明本文提出的方法效果显著。

关键词: 约束求解, 雅克比更新, 几何约束, 三维装配, 非线性方程

Abstract: A new method of approximately updating Jacobian matrix during 3D assembly
constraint solving is proposed in this paper. This method principally improves the efficiency of
constraints solving based on the approximate update of Jacobian matrix. First, an approximate
update formula of Jacobian matrix and its inverse matrix are inserted to the non-linear iterative
solution process. After that, the indispensable constraint is put forward, which must be satisfied
when using the formulas above. At last, a solution handling row rank defect of Jacobian matrix is
introduced via disturbance algorithm description. The methodology presented is implemented in a
3D assembly constraint solving engine, named CBABench. An example given at the end of this
paper shows that the method has achieved a considerable effect.

Key words: constraint solving, Jacobian update, geometric constrains, 3D assembly;
non-linear equations