Geometrical conditions for the design of partial or full isotropic hexapods

This paper presents a methodology for the design of PKMs (parallel kinematic machines) with defined isotropy and stiffness. Partial isotropy or full isotropy can be achieved by suitable design choices. The former is useful for five axis applications, while the latter for six axis manipulators. The paper summarizes the concept of full and partial isotropy, and for a wide class of hexapods defines in analytical form the conditions to achieve it exactly. These conditions can be used to design isotropic parallel manipulators. The methodology requires that the six legs have to be divided into two groups (terns). The legs belonging to one tern are mutually identical and are positioned with radial symmetry with respect to the TCP (tool center point). The paper shows that the manipulator structure can be defined in term of 13 design parameters, the value of six of them are chosen in order to achieve the required isotropy and stiffness properties, while the remaining seven parameters can be used to optimize the structure. The design criterion here presented assures that stiffness isotropy, force, and velocity isotropy are all achieved contemporarily. This methodology can be practically applied to a large family of hexapods.