Robotics and Computer–Integrated Manufacturing 51 (2018) 63–72 Contents lists available at ScienceDirect Robotics and Computer–Integrated Manufacturing journal homepage: www.elsevier.com/locate/rcim Analysis of the 2P RU-1P RS 3DOF parallel manipulator: kinematics, singularities and dynamics Saioa Herrero ∗ , Charles Pinto , Oscar Altuzarra , Mikel Diez Department of Mechanical Engineering University of Basque Country, Spain a r t i c l e i n f o Keywords: Parallel manipulator Kinematics Singularities Dynamics a b s t r a c t Parallel manipulators, especially those with outputs as a translation and two rotations (1T2R), are being increas- ingly studied. The 3PRS mechanism is a very typical example of this category, but it has peculiar kinematic characteristics caused by parasitic motions and by low orientation capability. To overcome these problems, new mechanisms are being studied, such as the 2PRU-1PRS manipulator. As in the case of the 3PRS manipulator, the degrees of freedom of the 2PRU-1PRS are one translation along the Z-axis and two rotations about the X- and Y-axes. The advantages are that the parasitic motion appears only in one direction instead of in three and that the orientation capability is higher. In this paper we solve the kinematics, singularities and dynamics of a 2PRU-1PRS mechanism. We first analyse a general 2PRU-1PRS mechanism and then present the results for the particular case of the 2PRU-1PRS used for automobile pieces testing purposes. © 2017 Elsevier Ltd. All rights reserved. 1. Introduction Parallel manipulators, compared to serial manipulators, have some interesting properties, such as high stiffness, low inertia, high velocity, good accuracy and large payload capacity. Thus, parallel manipulators are attracting more attention nowadays. Nevertheless, they also present important disadvantages like smaller useful workspace (WS), higher de- gree of design complexity and higher complexity in forward kinematics as Tsai [1] and Merlet [2] explained. According to these characteristics, the most important applications of parallel manipulators are vehicle driving simulator as Zhang [3] pro- posed, pick-and-place applications as Clavel [4] suggested, pilot training simulators and high speed machine tool. The advantage of using a par- allel manipulator as a simulation platform is the high load/weight ratio, as Merlet [5] showed. Lower-mobility parallel manipulators are manipulators with less than 6 degree-of-freedom (DOF) and, especially the 3DOF manipula- tors, have become a very important research topic in the last few years. Since Hunt [6] presented the 3RPS in 1983, different 3 DOF manipula- tors have been developed and studied. Liu et al. [7,8] presented a manip- ulator with high tilting capabilities called HALF, Clavel [4] developed the famous 3 DOF DELTA robot, Tsai et al. [9] presented a manipulator similar to DELTA and Wahl [10] patented an articulated tool head with 3DOF. ∗ Corresponding author. E-mail addresses: saioa.herrero@ehu.es (S. Herrero), charles.pinto@ehu.es (C. Pinto), oscar.altuzarra@ehu.es (O. Altuzarra), mikel.diez@ehu.es (M. Diez). However, the 3PRS parallel manipulator is one of the most typ- ical and representative lower-manipulators. In 2000, Carretero et al. [11] presented the 3P RS PM. For this manipulator, each kinematic leg is always contained in a plane defined as limb plane (LP). The three LPs of the 3P RS PM studied by Carretero et al. [11] has the three limb planes intersecting at a common line with non-collinear spherical cen- tres and arranged symmetrically, as seen in Fig. 1. They studied the kinematics of the manipulator and saw that small movements appeared also in the DOF where there was supposed to be no motion. They called those unexpected and undesired motions parasitic motions. They noted that they were no due to errors, but inherent to the geometry of the manipulator. Tsai et al. [12] presented a 3PRS parallel manipulator variant with vertical linear guides. In this case, the theoretical vertical displacement is infinite, but the length of the linear guides limits it. There are two possible configurations – one with the legs pointing inwards, as seen in Fig. 2b, and the other with the legs pointing outwards, as shown in Fig. 2c. They studied and compared both options and concluded that the solution with the legs pointing inwards had a lower possibility of suffer- ing collisions between the legs. Merlet [13] presented the 3PRS parallel manipulator as an endoscopy tool. In this case, the linear guides are also perpendicular to the fixed base but the legs are pointing outwards, so the diameter of the endoscopy tool is smaller. Pond and Carretero [14] com- pared the 3PRS configurations presented by Carretero, Tsai and Merlet– https://doi.org/10.1016/j.rcim.2017.11.018 Received 27 July 2016; Received in revised form 20 November 2017; Accepted 20 November 2017 0736-5845/© 2017 Elsevier Ltd. All rights reserved.