In contrast to the case of serial manipulators, the analysis and design of parallel manipulators is much less intuitive. For example the boundaries of the workspace are relatively easy to determine for a serial robot — one simply extends the arm of the robot — whereas they are much more complex for a parallel robot.

    Thus, algorithms must be developed for the analysis of the different properties of parallel robots, such as:


    These problems have been addressed in numerous research studies in the Robotics laboratory and algorithms have been developed for various types of parallel manipulators: planar, spherical and spatial. Three graphical examples of solutions developed are shown below.

    Fig. 1: Representation of the dexterity and the singularity locus for the Gough-Stewart platform. The singularity locus, represented by dark black lines, has been plotted using an analytical expression while the dexterity, represented by the grey scale, was obtained through the analysis of the Jacobian matrix.
    Fig. 2: Representation of the workspace for the Gough-Stewart platform. The boundary of the workspace was determined analytically using a geometric analysis. The calculation takes but a few milliseconds.
    Fig. 3: Superposition of the workspace (blue curves) on the singularity locus (red curves) for a 6-DOF spatial manipulator. This superposition indicates that singularities are unfortunately present within the workspace. Tools have been developed in the laboratory to analytically detect the presence of singularities within the workspace.