The Mobility Analysis of a 3-CCR Parallel Manipulator with Three Screw-Type Terminal Constraints

In the traditional three DOFs (degrees of freedom) PMs (parallel manipulators), the terminal constraints are constraint forces and torques. A recent study showed that the terminal constraints of some three DOFs PMs are screw-type constraints. However, determining the mobility of this class of PMs remains challenging. In order to solve the above problems, this paper discusses the mobility of PMs having independent screw-type terminal constraints by introducing the principal screws. Firstly, taking a 3-CCR (C: cylindrical joint, R: revolute joint) PM as an example, the problem of identifying the mobility of PMs having screw-type constraints is proposed. Secondly, combined with the analytical expression of the terminal constraint and theory of quadratic curve decomposition, the mobility determination approach is given. Finally, a numerical example for solving the principal screws and determining the mobility of the 3-CCR PM is provided. Furthermore, the axodes of four poses with three helical DOFs and four poses with three rotational DOFs were plotted. The results show that there is a special phenomenon in which three rotational DOFs and three helical DOFs exist alternately in the workspace of this PM. This paper provides a method for directly identifying the independent helical DOFs in parallel manipulators and for studying the distribution of helical DOFs within the workspace.