This article presents a new three-degree-of-freedom (3-DOF) parallel mechanism (PM) with two translations and one rotation (2T1R), designed based on the topological design theory of the parallel mechanism using position and orientation characteristics (POC). The PM is primarily intended for use in package sorting and delivery. The mobile platform of the PM moves along a translation axis, picks up objects from a conveyor belt, and tilts them to either side of the axis. We first calculate the PM's topological characteristics, such as the degree of freedom (DOF) and the degree of coupling, and provide its topological analytical formula to represent the topological information of the PM. Next, we solve the direct and inverse kinematic models based on the kinematic modelling principle using the topological features. The models are purely analytic and are broken down into a series of quadratic equations, making them suitable for use in an industrial robot. We also study the singular configurations to identify the serial and parallel singularities. Using the decoupling properties, we size the mechanism to address the package sorting and depositing problem using an algebraic approach. To determine the smallest segment lengths, we use a cylindrical algebraic decomposition to solve a system with inequalities.