In performing tasks requiring less than 6 degrees-of-freedom (DOF), lower mobility robots having a parallel structure are effective. This work investigates an asymmetric type 4 degrees-of-freedom parallel mechanism having Schönflies motions. This mechanism would be useful for multi-purpose tasks because it incorporates a transmission linkage with appropriate output modules. The mobility analysis, kinematic modelling, and singularity analysis for the mechanism are performed. Optimal design parameters with respect to both the workspace size and kinematic isotropy are identified by employing composite global design index. In addition, to cope with the singularity problem, a new design involving redundant actuation is suggested. And dynamic simulations are conducted to reaffirm its high potential in real manufacturing applications.