Non-singular transitions based design methodology for parallel manipulators

• Design methodology intended for planar or spatial 3 DoF cuspidal parallel manipulators.
• Non-singular transitioning ability based on cuspidality property is incorporated at the design stage.
• The dimensional synthesis is based on the design parameter space approach.
• The multiobjective optimization process evaluates the locus of cusps, the workspace and the Jacobian conditioning.

In this paper, a design methodology intended for the so-called cuspidal parallel manipulators is presented. The methodology is valid for three-degree-of-freedom planar or spatial parallel manipulators. The paper explains step-by-step a process to take advantage of a parallel manipulator that owns the cuspidality property, and thus, it can perform non-singular transitions. The latter ability enables the robot to move among different solutions of the direct kinematic problem, resulting in a wider workspace in comparison to a design that does not have this transitioning capacity. Therefore, it makes sense to incorporate the cuspidality property as one design criteria which is exactly the main purpose of the present research. The proposed design methodology exploits the cuspidality property to find a set of optimum designs that widen the workspace of the manipulator and, in addition to this, maintain a regular shape of the singularity locus existing in the workspace. Moreover, the design procedure includes the evaluation of the condition number of the Jacobian matrix, providing the set of designs that yield a well conditioned matrix.