Proceedings of the ASME 2014 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2014 August 17-20, 2014, Buffalo, USA DETC2014/MR-34593 WORKSPACE AND JOINT SPACE ANALYSIS OF THE 3-RPS PARALLEL ROBOT D. Chablat, R. Jha Institut de Recherche en Communications et Cybern´ etique de Nantes (UMR CNRS 6597) France Email addresses: Damien.Chablat@irccyn.ec-nantes.fr Ranjan.Jha@irccyn.ec-nantes.fr F. Rouillier INRIA Paris-Rocquencourt Institut de Math ´ ematiques de Jussieu (UMR CNRS 7586), France Email addresses: Fabrice.Rouillier@inria.fr G. Moroz INRIA Nancy-Grand Est, France Email addresses: Guillaume.Moroz@inria.fr ABSTRACT The Accurate calculation of the workspace and joint space for 3 RP S parallel robotic manipulator is a highly addressed re- search work across the world. Researchers have proposed a va- riety of methods to calculate these parameters. In the present context a cylindrical algebraic decomposition based method is proposed to model the workspace and joint space. It is a well know feature that this robot admits two operation modes. We are able to find out the set in the joint space with a constant num- ber of solutions for the direct kinematic problem and the locus of the cusp points for the both operation mode. The characteristic surfaces are also computed to define the uniqueness domains in the workspace. A simple 3-RPS parallel with similar base and mobile platform is used to illustrate this method. INTRODUCTION The workspace of parallel robots mainly depends upon the actuated joint variables, the range of motion of the joints and the mechanical interferences between the bodies of mechanism. There are different techniques based on geometric, discretiza- tion, numerical and algebraic methods which are used to calcu- late the workspace of parallel robot. The main advantage of the geometric approach is that, it establish the nature of the bound- ary of the workspace [1]. Also it allows the computation of the surface and volume of the workspace while being very efficient in terms of storage space, but if the rotational motion is included, it becomes more complex. The interval analysis based method can be used to compute the workspace but the computation time depends on the complexity of the robot and the accuracy re- quested. The ALIAS library is a good implementation for the parallel robots [2]. Discretization methods are usually less com- plex and take into account all kinematic constraints, but require more space and computation time for higher resolutions. The majority of numerical methods which is used to determine the workspace of parallel manipulators includes the discretization of the pose parameters for the determination of workspace bound- aries [3]. Algebraic methods are used in [4–6] to study planar or spatial parallel robots. Two main teps are necessary to per- form the workspace and jointspace analysis. First, the discrim- inant variety is computed to characterize the boundaries of the workspace and jointspace as well as the singularities. Second, the Cylindrical Algebraic Decomposition (CAD) is used to de- fine the connected regions where there exists a constant number of real solutions to the inverse and direct kinematic problem and no parallel or serial singularities [5–7]. For the design or the trajectory planning, the workspace of the parallel manipulator is divided into singularity-free regions [8]. The singularities divide the workspace into aspects and the characteristic surfaces induce a partition of each aspect into a set of regions (the basic regions) [9]. For the parallel robots with several inverse and direct kinematic solutions, the aspects are de- 1 Copyright c  2014 by ASME hal-01006614, version 1 - 16 Jun 2014 Author manuscript, published in "ASME 2013 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Buffalo : United States (2014)"