The terminal constraint and coupling kinematics of a novel 3-UPU parallel mechanism with screw type terminal constraints

The previous researches on 3-UPU parallel mechanisms (PMs) mainly focused on mechanisms with force and torque type terminal constraints. However, the 3-UPU PMs with screw type constraints have not been investigated. This paper proposes a novel 3-UPU PM with screw type terminal constraints, and systematically studies its analytical terminal constraints and closed form coupled kinematics. Based on the geometric characteristics of the terminal constraint of the particular UPU leg and the geometric property of the second-order screw system, the analytical form terminal constraints of the 3-UPU PM are derived. This type of PMs has high motion coupling at its moving platform, which is different from the traditional lower mobility PMs. By revealing the multiple coupling principle of the kinematic parameters through the kinematics constraint equations, a pose decoupling model of this mechanism is established and the analytical solution of the inverse position problem is derived. Meanwhile, the closed form forward displacement is derived using the Sylvester dialytic elimination method. The work presented in this article provides new insights into the 3-UPU type PMs.