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RESEARCH PAPER

Performance Evaluation and Calibration of Gantry‑Tau Parallel Mechanism Mohammad Reza Chalak Qazani1 · Siamak Pedrammehr1 · Hamid Abdi1 · Saeid Nahavandi1 Received: 21 March 2018 / Accepted: 26 September 2019 © Shiraz University 2019

Abstract The Gantry-Tau is a family of parallel manipulators with three linear actuators. This mechanism is of interest for various applications because of the large workspace and its performance in terms of high acceleration, precision, and stiffness characteristics. This paper presents workspace analysis and calibration for a Gantry-Tau mechanism using its forward kinematics. The mathematical model of the systematic errors in the kinematics model of the manipulator is obtained. Analysis of the error is then performed to identify the parameters that have a dominant effect on the kinematics error and the regions of the workspace with a high error due to the calibration. Minimization of the mean square and mean absolute errors is employed for calibration through kinematics parameters. For demonstration purposes, a SimMechanics kinematic model of the mechanism is used and its calibration is performed over many sampled positions within the workspace borders of the robot. The result demonstrates that the kinematic error is significantly reduced after the calibration. Keywords  Parallel mechanism · Kinematics · Workspace · Dexterity · Calibration

1 Introduction Industrial robots are an important part of the current and future automation systems, especially for manufacturing and assembly. Currently, many of these robots are based on serial mechanisms, which suffer from limited flexibility, low stiffness, and inadequate precision for some applications (Dressler et al. 2007a). For some industrial applications, such as grinding or machining where high stiffness is required, parallel robots are of special interest (Patel and George 2012; Pedrammehr et al. 2011a, 2013, 2014; Kong and Gosselin 2007; Qazani et al. 2014, 2018; Pedrammehr 2012). Among parallel robots, there is a high level of focus on the Stewart platform manipulator (Li et al. 2017; Pedrammehr et al. 2011b, 2012; Harib and Srinivasan 2003; Rahmani et al. 2014); however, this platform has limited application due to its small workspace. The SCARA Delta robot was introduced to reduce some of the limitations in common parallel robots. Kinematic and dynamic analyses of * Mohammad Reza Chalak Qazani [email protected] 1



Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds Campus, Waurn Ponds, VIC 3217, Australia

this robot have been studied in Zhu et al. (2005) and Crothers et al. (2009). This mechanism also has some limitations in its workspace and relatively small payload. Therefore, the SCARA-Tau concept has been extended to six degree-offreedom (DOF) octahedral hexarot mechanisms in Pedrammehr et al. (2016, 2017, 2018a, b, c, d, 2019a, b, c). Since the introduction of the Gantry-Tau mechanism by Johannesson et al. (2003), several researchers have performed different s