! " #$%&’( ’()’&% %# $% *)$’ $ (’%’$ +%& *&), Ballu Alex 1 , Jay Antoine 1 , Darnis Philippe 2 (1) : Université Bordeaux 1 LMP – UMR 5469 CNRS 351 Cours de la Libération 33 405 TALENCE Cedex - France + 33 5 4000 66 13 E-mail : alex.ballu@u-bordeaux1.fr (2) : Université Bordeaux 1 LGM 2 B – EA 496 15 rue Naudet 33175 Gradignan Cedex +33 556 847 976 E-mail : philippe.darnis@iut.u-bordeaux1.fr ’!- In tolerancing, numerous works deal with the theory of tolerance analysis and synthesis of mechanism, other ones deal with verification of isolated part, but none about metrology of mechanism. Now, metrology of mechanism is important for validation of theoretical model of joint. At first, a measuring system is presented; it allows to determine experimentally joint behaviour. The device is based on a set of displacement sensors, located outside the pair, to capture every spatial displacement. From the measures, the three rotation and three translations of displacement are computed. The particularity of the system is to permit the visualization of the gap hull of the joint. More, the distribution of the local form defects of the surfaces in contact inside the joint may be determined. In parallel, the surfaces in contact are measured with a texture surface measurement instrument and the different results are compared. ./ 0 Gap hull, difference surface, joint behaviour, form defect, tolerancing. %&$)&% On one hand, coordinate metrology was developed for isolated parts or assemblies without mobilities, but, what about the metrology of the assemblies with mobilities? What about gap metrology? There exist applications to particular case, but there is no general work on the subject. On the other hand, several papers focus on models and methods for tolerance simulation. The more pertinent models are based on perfect form surfaces and constraints of non- interference of the surfaces. For tolerances, these constraints define the bound of feasibility spaces [T1]. Giordano et al. have greatly developed this concept, they introduce gaps, but they do not consider form defaults. They have adopted the term of clearance and deviation spaces [GD1, GP1]. This approach is more and more used with variants and various terms according to the authors: variation zones [RL1], polytopes [TD1], interface and specification hulls [TB1, DM1] and, more recently, Tolerance-Map [JA1, BA1]. However, there are no confrontation between theoretical models and experimental data. This paper focuses on planar joint. The aim is to determine experimentally the relative positions of the parts and to compare the experimental data to the theoretical models already developed. The joint used for experiments is made of a rectangular bar in a groove. A measuring device has been developed. It is composed of linear displacement sensors with contact, fixed with respect to one part. The sensors tips are in contact with the second part and measure the relative displacements due to the gap in the joint [section 2]. Numerical processing allows to treat the measures to determine the displacements between the two parts [section 3]. Thanks to the great number of data, the gap hull of the displacements and the envelope of the positions may be represented with a good accuracy. A 2D study [section 4] and a 3D study [section 5] are presented. A comparison between theory and experiment is conducted all along these sections. #$%&’( The basic principle is to measure small relative displacements due to the gaps between the parts. Considering linear displacement sensors, the default number of sensors is six to measure displacements according to the six degrees of possible displacements, three translations and three rotations. For a particular joint, the necessary number of sensors is equal to the number of degrees of kinematic constraints. The sensors used in this work are DP5 probes of Solartron Metrology. They are based on LVDT technology, they have a measurement range of 5mm and an accuracy lower than 0.5μm. The location of the sensors obviously depends on the components of the displacements to measure. For a bilateral planar pair, the number of degrees of kinematic constraints, and, thus, the number of sensors, is of three. Figure 1 represents the measurement device designed to measure the HOME