Jacobian-based methods of singularity analysis are known to be unreliable when applied to kinematically redundant parallel robot manipulators, due to their potential to miss certain singularities and incorrectly identify others in the manipulator’s workspace. In this paper, a geometric method of singularity avoidance for kinematically redundant planar parallel robot manipulators is presented, which firstly determines the manipulator’s proximity to a singularity and then computes how the kinematically redundant degree(s) of freedom should be optimised for the given pose of the end-effector. The singularity analysis is conducted by examining the mechanism in terms of the instantaneous centres of rotation of its corresponding mobility one sub-mechanisms when all but one of the actuators are locked, where the manipulator is in a type-II singularity when these points either are indeterminable or coincide with one another, and an index, rmin, is introduced which describes the minimum normalised distance from such conditions being met. A predictor-corrector method is employed to compute the configuration for which rmin is optimised, and is reachable without crossing a singularity. Finally, the advantages of the geometric method of singularity analysis are shown in comparison to traditional Jacobian-based methods when applied to kinematically redundant parallel robot manipulators.