Analytical determination of the workspace of symmetrical spherical parallel mechanisms

This paper presents a methodology for the analytical determination and representation of the workspace boundaries of symmetrical spherical parallel mechanisms (SPMs). The methodology is based on an intuitive orientation representation which, while not well known, has proven to be very useful for the analysis of symmetrical parallel mechanisms. The latter, previously introduced as "tilt-and-torsion angles," are briefly described. Then, relatively simple analytical expressions are found for the workspace boundaries of general symmetrical SPMs. Next, using these expressions and a simple numerical procedure, a fast algorithm is proposed for representing the so-called constant-torsion workspace. Finally, several examples are provided