Motivations and general objectives
This master thesis deals with the assembly conditions of parallel manipulators considering Joint Clearances, Geometric Errors and Link Flexibilities.
Proposed work plan
First, the candidate will have to understand an error prediction model applicable to both serial and parallel manipulators that we have just developed [1, 2]. Then, he/she (they) will have to think of a clearance model associated with axisymmetrical joints, which are widely used in robotic manipulators. As a result, two nonconvex quadratically constrained quadratic programs (QCQPs) will be formulated in order to find the maximum reference-point position error and the maximum orientation error of the moving-platform for given joint clearances. In order to solve the optimization problems, the candidate(s) will write a piece of code on Matlab and use the Hoffmann’s algorithm , which is dedicated to global minimization of concave functions over convex sets. The candidate will analyze the sensitivity of Orthoglide 5-axes (see Fig. 1), a five-degree-of-freedom translational parallel manipulator developed in IRCCyN, to joint clearances. Then the candidate will analyze the assembly conditions of a five –bar linkage  and the Orthoglide 5-axes considering joint clearances and geometric errors assuming that the links are rigid. Finally, the candidate will consider the link flexibilities by using a Virtual Joint Model  in order to evaluate the energy required for the assembly of those manipulators subject to joint clearances and geometric errors.
List of bibliographic references
1. Caro, S., Binaud, N., and Wenger, P., 2009. “Sensitivity analysis of 3-RPR planar parallel manipulators”. ASME Journal of Mechanical Design, 131 , pp. 121005–1–121005–13
2. Berger, N., Soto, R., Goldsztejn, A., Caro, S., and Cardou,P., 2010. “Finding the maximal pose error in robotic mechanical systems using constraint programming”. In The Twenty Third International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems – IEA-AIE.
3. Hoffman, K. L., 1981. “A method for globally minimizing concave functions over convex sets”. Mathematical Programming, 20 (1) , pp. 22–32.
4. Binaud, N., Caro, S., and Wenger, P., “Étude des Conditions d’Assemblage de Manipulateurs Hyperstatiques : Application à un Manipulateur 5 barres”, 20èmeCongrès Français de Mécanique, Besan¸ con, 29 août au 2 septembre 2011.
5. Pashkevich, A., Klimchik, A., Caro, S., and Chablat, D., “Cartesian stiffness matrix of manipulators with passive joints : analytical approach”, The 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2011), San Francisco, California, USA, September 25-30, 2011.
S. Caro and A. Pashkevich
Stephane.Caro@irccyn.ec-nantes.fr – Phone : 02 40 37 69 68 Anatol.Paskevich@irccyn.ec-nantes.fr – Phone 02 40 37 69 68