Analysis of the inverse kinematics problem for 3-DOF axis-symmetric parallel manipulators with parasitic motion

Determining an analytical solution to the inverse kinematics problem for a parallel manipulator is typically a straightforward problem. However, lower mobility parallel manipulators with 2-5 degrees of freedom (DOFs) often suffer from an unwanted parasitic motion in one or more DOFs. For such manipulators, the inverse kinematics problem can be significantly more difficult. This paper contains an analysis of the inverse kinematics problem for a class of 3-DOF parallel manipulators with axis-symmetric arm systems. All manipulators in the studied class exhibit parasitic motion in one DOF. For manipulators in the studied class, the general solution to the inverse kinematics problem is reduced to solving a univariate equation, while analytical solutions are presented for several important special cases.