The kinematics and design for isotropy of six-dof 3-CCC parallel mechanisms of general geometry and arbitrary actuation schemes

Parallel mechanisms (PMs) of the 3-CCC class exhibit many attractive features, such as decoupled motion, degenerated singularity, simple forward-kinematics relations and high dexterity, making them promising in many applications. However, in order to simplify the analysis, existing research mainly focuses on its several subclasses, leading to drawbacks such as limited choices of the architecture parameters, excessive link interference and limited orientation workspace. In this paper, a uniform formulation is proposed for the kinematics analysis of the whole class of 3-CCC PMs of general geometry and arbitrary actuation schemes; the geometric meanings of the relevant quantities are revealed, significantly simplifying the analysis of 3-CCC PMs. Next, the design for isotropy of the whole class of 3-CCC PMs is investigated, yielding a large set of isotropic designs, including a subset admitting a continuous isotropy locus; several typical layouts with attractive features are proposed thereafter, including designs admitting unlimited rotation about a fixed or an adjustable direction. The results above can also be applied to six-dof PMs with more sophisticated topologies, as long as they are kinematically equivalent to 3-CCC PMs.