Parallel kinematic machines (PKMs) whose moving platforms realises one-translational and two-axes rotation (1T2R) motion pattern, find a wide variety of applications. However, a majority of the 1T2R PKMs suffer from singularities and parasitic motions. Higher dexterity requirements further constrict its already limited workspace volume. This paper introduces a novel 1T2R parallel mechanism to address typical issues in dexterity, singularities, and parasitic motions. The mathematical modelling covers a comprehensive analytical inverse kinematics modelling. The analyses performed evaluate mobility, singularities, and dexterity of the mechanism. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.