Modelling of a special class of spherical parallel manipulators with Euler parameters

A method of workspace modelling for spherical parallel manipulators (SPMs) of symmetrical architecture is developed by virtue of Euler parameters in the paper. The adoption of Euler parameters in the expression of spatial rotations of SPMs helps not only to eliminate the possible singularity in the rotation matrix, but also to formulate all equations in polynomials, which are more easily manipulated. Moreover, a homogeneous workspace can be obtained with Euler parameters for the SPMs, which facilitates the evaluation of dexterity. In this work, the problem of workspace modelling and analysis is formulated in terms of Euler parameters. An equation dealing with boundary surfaces is derived and branches of boundary surface are identified. Evaluation of dexterity is explored to quantitatively describe the capability of a manipulator to attain orientations. The singularity identification is also addressed. Examples are included to demonstrate the application of the proposed method.