Configuration and singularity analysis of a parallel hip joint simulator based on the forward kinematics

• The closed-form solution for forward position of the manipulator was presented.
• A new method to identify a singularity for the parallel manipulators was proposed.
• The configurations are divided into two types of spaces according to distributions.
• Singular loci degenerate into a single surface in the basic configuration spaces.

The singularities of parallel manipulators are usually identified by geometrical methods or by the kinematic principles based on the pose parameters. The methods have limitations in applications that involve singularity avoidance, such as motion planning from input parameters. To identify a singularity from an input parameter point of view, which would make the singularity avoidance strategy more direct and more effective in practical applications, this paper focuses on the relationship between the singularities, the configuration spaces and the input parameters with a 3SPS+1PS parallel hip joint simulator selected to implement this approach. A univariate-form polynomial equation of the forward kinematics is obtained with the aid of the Sylvester dialytic method of elimination, therefore proving that the manipulator has at most eight configurations for a single input. The configurations are then divided into two types of spaces according to their distributions. It is discovered that in practice, we only need concern ourselves with the basic configuration spaces, where the singular loci degenerate into a single surface. Finally, the singular condition is proved to be equivalent to that when the univariate-form input–output equation has a repeated root in the real number field. Therefore, the singular condition equation of the input parameters and the singular loci of the input parameters in the basic configuration spaces are obtained. This study provides new insight into the singularity avoidance of a parallel manipulator, especially for the singularity-free design in the motion planning from input parameters.