Geometric analysis of parallel mechanisms

The primary objective of this dissertation is to demonstrate the incontestable effectiveness of geometric methods to the design and analysis of parallel mechanisms. To this end, it is shown how geometry brings deep insight into the principles of motion, much better than algebraic or numerical methods. Furthermore, this thesis is expected to prove that geometry develops creativity and intuition, abilities much needed for the proper synthesis and study of complex mechanisms.

Firstly, the singularities of all 3-DOF planar parallel mechanisms are fully analysed. The velocity equations are derived by using both screw theory and differentiation with respect to time. For this purpose, a considerable attention is paid to explaining the not-so-well-known use of screw theory in the plane. Once these velocity equations are set up, an exhaustive study on the various types of singularities of these mechanisms is performed. Several new designs are identified, having few or no singularities at all. Finally, a new research path emerges through an in-depth discussion on the problem of workspace segmentation, working modes, and assembly modes.

Next, the investigation leaves the plane and starts with a comprehensive discourse on the complex issue of orientation representation via the relatively unknown Tilt & Torsion angles. Numerous advantages of these angles are shown. Then, using the Tilt & Torsion angles, several 3-DOF spatial parallel mechanisms with one translational and two rotational degrees of freedom are analysed. The relationships between the three constrained and three feasible degrees of freedom are derived and it is shown clearly that the mechanisms belong to a special class of constrained mechanisms that have zero torsion of the platform.

Finally, the focus is shifted to the kinematic analysis of 6-DOF six-legged spatial parallel mechanisms with base-mounted revolute actuators and fixed-length struts. In the first section, a geometric method for the computation of the edges of the constant orientation workspace is elaborated. In the second section, another geometric algorithm is described for the computation of the constant-orientation workspace. This new algorithm computes not only the edges of the workspace but its cross-sections as well. (Abstract shortened by UMI.)