Higher-order continuation method for the rigid-body kinematic design of compliant mechanisms |
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| Affiliation: | 1. AVR – ICube, CNRS – Université de Strasbourg – INSA Strasbourg, 300 bd Sébastien Brant, F-67412 Illkirch, France;2. Instant-Lab, EPFL-STI-IMT, rue de la Maladière 71b, CH-2000 Neuchâtel, Switzerland;1. Partner State Key Laboratory of Ultra-precision Machining Technology, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong;2. Manufacturing Metrology Team, Faculty of Engineering, University of Nottingham, Nottingham, NG8 1BB, United Kingdom;1. Ningbo Institute of Material Technology and Engineering, Chinese Academy of Science, No.1219 Zhongguan West Road, Ningbo 315201, Zhejiang Province, PR China;2. Key Laboratory of Robotics and Intelligent Manufacturing Equipment Technology of Zhejiang Province, No.1219 Zhongguan West Road, Ningbo 315201, Zhejiang Province, PR China;1. Primary Standards Laboratory (PSL), Sandia National Laboratories, Albuquerque, NM, USA;2. Materials Characterization & Performance, Sandia National Laboratories, Albuquerque, NM, USA;3. Material, Physical, and Chemical Sciences Center, Sandia National Laboratories, Albuquerque, NM, USA;1. Inria Saclay Ile-de-France, M3DISIM Team, Palaiseau, France;2. Université Paris Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME-UMR-CNRS-8208, Bioméca – 61 Avenue du Général de Gaulle, 94010 Créteil, France;3. LMS, CNRS-UMR 7649, Ecole Polytechnique, Route de Saclay, 91128 Palaiseau, France |
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| Abstract: | Compliant mechanisms are of great interest in precision engineering. In this paper, we propose a higher-order continuation method to help their rigid-body kinematic design. The method helps to investigate the choice of a mechanism configuration through the whole exploration of the workspace, and eases the kinematic analysis to avoid, or take advantage of, the vicinity of kinematic singularities. Such approach is relevant for planar and quasi-planar mechanisms that can be obtained with micro-manufacturing processes adapted to precision applications. The higher-order continuation method allows for a direct and accurate plotting of the input–output relationship of any mechanism by considering only its geometrical closed-loop equations, i.e. without the complex derivation of any analytical model. We show that these plots, called bifurcation diagrams, reveal essential information such as the joint velocity profile and the presence of singular configurations. Moreover, the continuous and accurate computation of the mechanism configuration in the vicinity of singularities provides detailed information about the kinematic behavior of the mechanism in its extreme positions. For the design of compliant mechanisms, the designer can advantageously use the bifurcation diagrams to evaluate the relevance of the selected mechanism, then to identify a configuration in order to obtain desired kinematic properties without the derivation of the inverse kinematic model (IKM) or the direct kinematic model (DKM). The method is exemplified with a 3 universal-joint and 3 spherical-joint mechanism (3-US), the IKM and DKM of which cannot be derived analytically. The latter has a large workspace and special kinematic behaviors consisting of a screw-like motion and a platform gyration, which have not been studied before and could lead to novel compliant devices. |
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| Keywords: | Compliant mechanism Mechanical design Higher-order continuation method Bifurcation diagram 3-US mechanism Singularity Workspace analysis |
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