Parallel manipulators have a rigid structure and can pick up the heavy objects. Therefore, a parallel manipulator has been developed based on the cooperative of three arms of a robotic system to make the whole system suitable for solving many problems such as materials handling and industrial automation. The three revolute joints are used to achieve the mechanism operation of the parallel planar robot. Those revolute joints are geometrically designed using an open-loop spatial robotic platform. In this paper, the geometric structure with three revolute joints is used to drive and analyze the inverse kinematic model for the 3RRR parallel planar robot. In the proposed design, three main variables are considered: the length of links of the 3RRR parallel planar robot, base positions of the platform, and joint angles’ geometry. Cayley-Menger determinants and bilateration are proposed to calculate these three variables to determine the final position of the platform and to move specific objects according to given desired trajectories. The proposed structure of the 3RRR parallel planar robot is simulated and different desired trajectories are tested to study the performance of the proposed stricter. Furthermore, the hardware implementation of the proposed structure is accomplished to validate the design in practical terms.