The planar 3-RRR parallel manipulator is known to have six assembly modes. However, analysing it in the framework of spatial kinematics reveals that it has a total of twelve assembly modes, six in each of the two possible operation modes. The modes are derived using a Study parameter formulation first, and later confirmed in another formulation in the joint-space, and finally visualised in terms of the planar constraint curves generated by the sub-chains of the manipulator. Numerical results show that all the twelve modes can be real for certain inputs. © Springer International Publishing AG 2018.