基于线性不等式方程组解的存在性及其通解的工件可达/可离性分析算法

工件的可达/可离性反映了将工件安装到/脱离出夹具装夹布局的可能性，分析可达/可离性有助于在工件上正确选择装夹表面和装夹点。为此依据工件与装夹元件的实际接触或装配情况，利用泰勒定理提出了工件可达/可离性模型。通过将工件安装到/脱离出装夹布局的可能性等价于可达/可离性模型的解的存在性，借助任意数可表达为两个非负数之差这一数学技巧作为桥梁，将工件可达/可离性模型的解的存在性问题转化为线性规划问题，提出了工件可达/可离性的判断方法。尤其是在判断可达/可离性模型有解的情况下，继而考虑了工件安装到/脱离出装夹布局的方向性。在此基础上，进一步将可达/可离的方向性转化为可达/可离性模型的通解，由此构建了求解线性不等式方程组的Γ-算法。这个“先有解-再求解”的算法仅涉及到装夹元件在工件表面处的位置与单位法矢量信息，不仅适用于形状复杂的工件，而且避免了可达/可离性模型无解情况下依旧求解的局限性，同时也拓展和丰富了自动化夹具设计的理论基础。

Analysis Algorithm of Workpiece Attachment/Detachment Based on Solution Existence and General Solution of Inequalities

The workpiece attachment/detachment can reflect the possibility of placing a workpiece in contact with the fixture layout or displacing a workpiece from the fixture layout. The objective of attachment/detachment nanlysis is help the correct selection of fixturing surfaces and fixturing points on workpiece. According to the practical contact/assembly of workpiece with the fixture layout, hence, Taylor theorem is used to formulate the attachment/detachment model. After equalizing the possibility of of placing a workpiece in contact with the fixture layout or displacing a workpiece from the fixture layout to the solution existence of attachment/detachment model, a mathmatics trick is created to express an arbitrary number in the attachment/detachment model as a difference of two nonnegative numbers. Only by doing so can the analysis of solution existence of attachment/detachment model be identified as a linear programming problem and in turn, a judgement method is proposed for the workpiece attachment/detachment. Especially under the condition that the attachment/detachment model has solutions, the direction of attachment/detachment of workpiece to/from the fixturing layout is further considered. By equivalently transforming the directionality of attachment/detachment into the general solution of attachment/detachment model, Γ-algorithm is suggested for solving a set of inear inequalities. The presented "seeking solutions if equations are solvable" algorithm only concerns on the coordinates and unit normal vectors of workpiece at fixturing points. It can not only be carried out for a workpiece with complex surfaces, but also avoid the solving process of the attachment/detachment model without solutions. It is more important, it can develop and enrich the theoretical basis of automated fixture design.