To cite this version:Moinet Mireille, Guillaume Mandil, Philippe Serré. Defining tools to address over-constrained geometric problems. Computer-Aided Design, Elsevier, 2014, 48, pp. AbstractThis paper proposes a new tool for decision support to address geometric over-constrained problems in Computer Aided Design (CAD). It concerns the declarative modelling of geometrical problems. The core of the coordinate free solver used to solve the Geometric Constraint Satisfaction Problem (GCSP) was developed previously by the authors. This research proposes a methodology based on Michelucci's witness method to determine whether the structure of the problem is over-constrained. In this case, the authors propose a tool for assisting the designer in solving the over-constrained problem by ensuring the consistency of the specifications. An application of the methodology and tool is presented in an academic example.

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In order to manage quality, companies need to predict performance variations of products due to the manufacturing components deviations. Usually, to enable the assembly of overconstrained mechanical structure, engineers introduce clearance inside joints. We call mechanical assembly, a set of undeformable components connected together by mechanical joints. This paper presents a solution: firstly, to compute the minimum value of clearance for any given components sizes, and, secondly, to simulate variation of the minimum clearance value when the components dimensions vary between two limits. To achieve this goal, a regularized closure function G is defined. It depends on dimensional parameters, u, representing components dimensions, on positional parameters, p, representing components positions and on clearance parameters, j, representing mechanical joints clearance. A constrained optimization problem is solved to determine the minimum clearance value. An imaginative solution based on numerical integration of an ordinary differential equation is proposed to show the clearance variation. The method is designed to be used during the preliminary phase of overcontrained assemblies design. An advantage is the small number of input data unlike the tolerance analysis dedicated software.

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