This work is the continuation of a study which is concerned with the kinematics of an universal joint and its use in shaft connections. In the present work, case studies are carried out by numerical implementation of the kinematic formulas illustrated in a previous paper in which two different systems for transmission of rotational motions are kinematically analysed. The first of these systems consists of two shafts (an input and an output shaft) connected via an universal joint, while the other comprises three shafts (an input, an intermediate, and an output shaft) and two universal joints connecting them. Furthermore, it is investigated how the angles between shaft axes, the arm lengths of the cross pieces, the angles between cross arms, and the angle between yoke planes of the intermediate shaft affect the characteristics of output motion. For both systems, the relationships between rotation angles of shafts are derivated by applying the rigidity condition on the cross arms. The case studies show that the arm lengths of cross pieces have no effect on the angular relations, independently of the angles between arms. However, in a coplanar system of the second type, either parallel or crossed assembled, it is concluded that an input rotation cannot be transmitted onto the output shaft without losing its kinematic features as far as the angles between the cross arms in each joint deviate from 90°, and also the angle between the yoke planes from 0°, respectively. The interference of the working planes of the joint is not included in the study.