Philippe Serré

The TTRSs : 13 Constraints for Dimensioning and Tolerancing

The dimensioning and the tolerancing model presented in this paper allows the functional tolerancing declaration of a class of mechanical parts independently from the geometric instantiation. That model is based on the use of the TTRS concept and on relative positioning constraints. Moreover, that model is compatible with the exchange standard ISO/CD 10303-47.

Global Consistency of Dimensioning and Tolerancing

The general objective of this paper is to define the problem areas linked to the specification and overall consistency of a dimensioning diagram and to propose a solution principle to solve this problem.

Analysis of functional geometrical specification

“Good” functional tolerancing can only be obtained once the geometrical specification of the mechanism being studied has been analysed from a technological and geometrical standpoint. A geometrical analysis based on a vector approach has been developed. It enables existing tolerancing relations to be written between the design parameters relative to each part and the relative position parameters between two parts of the mechanism in question.

Coordinate Free Approach for the Calculation of Geometrical Requirement Variations

This chapter proposes to investigate the use of a coordinate free approach for the mapping of geometrical requirement along a product life cycle. The geometry of the studied assembly is represented using a Gram matrix that is issued from a parametric model constituted of points and vectors. This parametric model is instanced for all relevant phase of the product life cycle. The calculation of instanced parameters is based on part deformation due to changing operating conditions. This calculation is carried out thanks to existing theoretical techniques. The application presented in this paper is constituted of a simple 3D case composed of 3 articulated bars disposed as a tetrahedron and subjected to some thermal expansion.

Dimensional perturbation of rigidity and mobility

Abstract Mechanisms, defined as assemblies of dimensioned rigid bodies linked by ideal joints, can be partitioned in three mobility states: the rigid state (where bodies can have only one position relative to each other), the mobile state (where bodies can move relatively to each other) and the impossible state (where bodies dimensions and specified joints cannot lead to a feasible assembly). It is also clear that although bodies dimensions can vary in a continuous way, assemblies may experience quite abrupt changes across those states. This paper proposes a new approach to this problem with the goal of being able to predict the mobility class of an assembly of arbitrary complexity, and how it can be affected by a perturbation of the dimensions of its bodies. It does so by proposing a simple and general state transition framework including the three above defined states and seven transitions describing how a dimensional perturbation can affect them. Using this framework, the mobility of a mechanism is easier to capture and predict, using only dimensional ( u ) and positional ( p ) parameters involved in an appropriate equation ( F ( u , p ) = 0 ). This is achieved by focusing on how F ( ) behaves when u and p get perturbed, and the impact of this reaction on the mobility state of the assembly. As a result of this more mathematic approach to the problem, previously used notions of iso-constraint, over-constraint and paradoxical assembly, traditionally used to describe such assemblies, can be rigorously defined and thus clarified.

A Declarative Approach for Geometry and Topology: A New Paradigm for CAD-CAM Systems

The geometric models currently used in CAD-CAM modellers are chiefly based on a procedural approach. Over the past few years, the appearance of parametric and, above all, variational modellers, has opened up the way to a more declarative approach. It is true to say that parametric design is efficient, but it requires knowledge of a design chronology whose flexibility is thus diminished. On the other hand, variational design is very general and flexible but does need the use of solvers to simultaneously solve a large number of non-linear equations.

Clearance vs. tolerance for rigid overconstrained assemblies

Abstract 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 overconstrained assemblies design. An advantage is the small number of input data unlike the tolerance analysis dedicated software.

An Algebraic Method to Compute the Mobility of Closed-Loop Overconstrained Mechanisms

In mechanical engineering, the degree of freedom or mobility is a fundamental property of solid assemblies. To compute it, classical formulas fail when closed-loop overconstrained mechanisms are concerned. Another way to define the mobility is to consider the dimension of the algebraic variety representing the closure of the loop. The approach described here, consists in computing the conditions that ensure that an overconstrained mechanism is mobile.