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首页> 外文会议>4th International Conference on Integrated Design and Manufacturing in Mechanical Engineering - IDMME 2002 May 14-16, 2002 Clermont-Ferrand, France >A UNIFIED JACOBIAN-TORSOR MODEL FOR ANALYSIS IN COMPUTER AIDED TOLERANCING
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A UNIFIED JACOBIAN-TORSOR MODEL FOR ANALYSIS IN COMPUTER AIDED TOLERANCING

机译：计算机辅助四边形分析的统一雅可比-TOROROR模型

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摘要

This paper presents a unified model for computer-aided tolerancing. It combines the benefits of the Jacobian matrix model and the torsor (or screw) model. The former is based on small displacements modeling of points using 6x6 transformation matrices of open kinematic chains in robotics. The latter models the boundaries of 3-D tolerance zones resulting from a feature's small displacements using a torsor representation with constraints. The proposed unified model expands the functionalities of the Jacobian model under two important aspects. First, the punctual small displacement variables of the former Jacobian formulation are now considered as intervals formulated and solved using interval-based arithmetic. The equations describing the bounds within which the feature is permitted to move, which are the constraint equations of the torsor formulation, are applied on the unified model. Second, some of the small displacement variables used in the model are eliminated due to the invariant nature of the movements they generate with respect to the toleranced feature. This standard result of the torsor formulation is applied to the unified model. The effect of this is to significantly reduce the unified model size. A example application is also presented.
机译：本文提出了计算机辅助公差的统一模型。它结合了Jacobian矩阵模型和Toror（或螺钉）模型的优点。前者基于使用机器人中开放运动链的6x6变换矩阵的点的小位移建模。后者使用带有约束的扭转表示来模拟由特征的小位移导致的3-D公差带的边界。所提出的统一模型在两个重要方面扩展了雅可比模型的功能。首先，现在将以前的雅可比公式的守时小位移变量视为使用基于区间的算法制定和求解的区间。在统一模型上应用了描述允许特征移动的边界的方程式，即扭矩公式的约束方程式。其次，由于它们相对于公差特征产生的运动具有不变性，因此消除了模型中使用的一些小位移变量。将该标准公式的结果应用于统一模型。这样的效果是大大减小了统一模型的大小。还提供了示例应用程序。

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