Kinematic synthesis of a novel rapid spherical CRS/PU parallel manipulator

• A novel spherical parallel manipulator has been proposed with the rapidness characteristic during positioning and orienting tasks.
• The kinematic equations have been solved with a simple geometric interpretation of the mechanism.
• A comparison study has been done between three well-known mechanisms with the same degrees of freedom.
• Performance indices have been investigated between candidates with normal structures.

In this research work, a novel parallel manipulator with complex degrees of freedom (DoF) has been represented. Each active kinematic chain consisted of cylindrical-revolute-spherical joints located on a curved guide and passive middle link contains prismatic-universal joint. Each of curved guides mounted as a sector of a circle with specified radius and center point. Cylindrical joints are activated by a crank mechanism and motors which are located at the center of the curved guide, provide two rotational displacements around x and y axes and one translational displacement along z direction. The mobility analysis has been analyzed by Grübler-Kutzbach criterion, and kinematic equations are provided. Then, using a search algorithm, the boundary of workspace has been determined for a case study structure. Two different methods are used to make Jacobian matrix homogeneous. The performance indices such as Local Condition Index (LCI), Maximum Singular Value, and Minimum Singular Value have been investigated throughout the workspace. Two types of well-known parallel kinematic mechanisms have been optimized with regard to the workspace volume and compared base on some global indices. All results have demonstrated the well condition of the manipulator in positioning and orienting tasks with desired precision and speed.