A geometrical approach for configuration and singularity analysis of a new non-symmetric 2DOF 5R Spherical Parallel Manipulator

Abstract

A new non-symmetric 5R-SPM is introduced and a geometrical approach is developed to analyze its configurations and singularities. The proposed methodology determines the type of configuration of a 5R-SPM, i.e. regular, singular, or out-of-workspace and also the type of singularity, i.e. instantaneous or finite, only based on geometric parameters and without solving verbose kinematic equations. It also provides insights into the workspace and singularities of 5R-SPMs, in the preliminary stage of design. The mechanism was analyzed by both the new geometrical approach and conventional methods for comparison. The geometrical approach could intuitively detect all the singularities observed by the Jacobian matrix and the kinematic analysis, with more details on the type and characteristics of each singularity. The dimensional synthesis for the designed mechanism was also performed based on the type and existence of singularities. The proposed methodology might be further developed to specify the configurations and singularities of general SPMs and also to introduce a geometrical measure for singularity closeness.