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

doi:10.3901/JME.2017.21.136

Abstract

Abstract: 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.

Key words: attachment/detachment, convex cone, directionality of attachment/detachment, dual cone, inequalities, linear programming

CLC Number:

TG702

QIN Guohua, WANG Zhe, WU Zhuxi, WANG Huamin, WU Tiejun, LI Ling. Analysis Algorithm of Workpiece Attachment/Detachment Based on Solution Existence and General Solution of Inequalities[J]. Journal of Mechanical Engineering, 2017, 53(21): 136-148.

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