In this study we discuss a method of solving the inverse kinematics of the planar kinematic chains containing one actuated prismatic joint and two passive revolute joints. The mathematical model of the chain allows an arbitrary selection of the reference frame, therefore making it easy to integrate into more complex models of the mechanisms (planar or spatial) containing chains or subchains of the discussed type. The constraint equations for the chain are obtained in the form of a quadratic equation. We also provide a numerical example of the planar mechanism with four such chains that can serve as the top module of the robotic system with relative motion of its modules. This example shows that the discussed approach can be easily and conveniently used for calculating the Jacobian matrix of the mechanism, which can be used for velocity and singularity analysis of the mechanism.