  Workspace and joint space analysis are essential steps in describing the task
and designing the control loop of the robot, respectively. This paper presents
the descriptive analysis of a family of delta-like parallel robots by using
algebraic tools to induce an estimation about the complexity in representing
the singularities in the workspace and the joint space. A Gr{\"o}bner based
elimination is used to compute the singularities of the manipulator and a
Cylindrical Algebraic Decomposition algorithm is used to study the workspace
and the joint space. From these algebraic objects, we propose some certified
three dimensional plotting describing the the shape of workspace and of the
joint space which will help the engineers or researchers to decide the most
suited configuration of the manipulator they should use for a given task. Also,
the different parameters associated with the complexity of the serial and
parallel singularities are tabulated, which further enhance the selection of
the different configuration of the manipulator by comparing the complexity of
the singularity equations.
