# Modélisation géométrico-statique des mécanismes parallèles compliants

 Authors: Quennouelle, Cyril Advisor: Gosselin, Clément Abstract: The use of compliant joints reduces the mechanical clearance in robotic manipulators. However, the particularities of their behaviour, which differs from that of conventional joints, cannot be taken into account in existing models, which mitigates the expected gain in accuracy. In this thesis, a model satisfying both the kinematic constraints and the static constraints between the joint variables is proposed. It enables to precisely describe the behaviour of a compliant mechanism, notably by allowing the consideration of several degrees of freedom for a single compliant joint. The generalized coordinates, which correspond to a minimal set of joint variables required to completely describe the configuration of the mechanism, are used to calculate the pose of the end-effector in the geometric model. These coordinates are not directly set by the user but adjust themselves such that the static equilibrium of the mechanism is satisfied. Therefore, they are function of some external parameters taken into account in the proposed kinemato-static model: the position of the actuators, the external efforts applied on the mechanism and the weight of its rigid links. Because of the complexity of some equations of this kinemato-static model, a quasi-static model was also developed. The latter gives linear relationships between the variations of the external parameters and the variations of the configuration of the mechanism. To obtain these relationships, the stiffness matrix of compliant parallel mechanisms was derived in a general form. The formulation of this quasi-static model is very simple and uses two new matrices: the Cartesian compliance matrix and the quasi-static Jacobian matrix. The latter matrix integrates the effects of the deformations of the mechanisms in its kinematic behaviour using a matrix of the transmission ratios of the motion of the actuators. Finally, three examples of applications are given in order to illustrate the contributions of these models, not only regarding the gain in precision, but also the novel possibilities they offer. From then on, compliant parallel mechanisms, but also bistable mechanisms, under-actuated compliant mechanisms and even conventional mechanisms can be modeled with the same equations. Document Type: Thèse de doctorat Issue Date: 2009 Open Access Date: 16 April 2018 Permalink: http://hdl.handle.net/20.500.11794/21022 Grantor: Université Laval Collection: Thèses et mémoires

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