In the courier industry, daily labor is required to sort and pack medium-sized pieces, which require more work in parallel mechanisms(PM) space, the workspace of the linear drive PM is larger than the rotary drive; therefore, in response to the above-mentioned problem, a co-directional 3-PUPU PM of the slide rod strut chain. The 3-PUPU PM of the homotropic slide rod strut is investigated according to the geometric relationship and kinematic model of the PM, using the vector method to establish the kinematic solution equations for the PM; secondly, to influence and constrain the 3-PUPU PM of the isotropic slider strut chain, The motion vice and motion branch chain constraints of the workspace are analyzed; finally, the three-dimensional boundary search method is used to pass the parallel. The kinematic equations of the PM are analyzed in terms of the workspace of the 3-PUPU PM of the same directional slider strut, and the workspace of the PM is studied with the objective of volume, and the influence on the workspace of the universal hinged movement angle and the co-rotating sliding rod support chain. The study shows that the workspace of this PM has symmetry, no obvious internal cavity and regular cross-sectional shape. The effect of constraint on workspace volume curve shows that the distance of the coiled rod support chain has the greatest effect on the workspace volume. The 3-PUPU PM of the coiled rod support for medium-sized parts picking, sorting, and packing can be achieved by adding a controlled process to the larger workspace packaging; it provides a reliable basis for subsequent theoretical research and practical application of the institution.