A parallelogram allows the output link to remain at a fixed orientation with respect to an input link, for which it acts as a unique role in the design of parallel mechanisms. In this paper, the unique role of a parallelogram is used completely to design some new parallel mechanisms with two to six degrees of freedom (DoFs). In these mechanisms, some with three DoFs possess the advantage of very high rotational capability and some with two DoFs have the translational output of a rigid body. More than that, the design concept is also applied first to some parallel mechanisms to improve the systems' rotational capability. The parallel mechanisms proposed in this paper have wide applications in industrial robots, simulators, micromanipulators, parallel kinematics machines, and any other manipulation devices in which high rotational capability and stiffness are needed. Especially, the paper provides new concepts of the design of novel parallel mechanisms and the improvement of rotational capability for such systems.