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Open AccessArticle

Modeling Parallel Robot Kinematics for 3T2R and 3T3R Tasks Using Reciprocal Sets of Euler Angles

Institute of Mechatronic Systems, Leibniz University Hannover, 30167 Hannover, Germany
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Robotics 2019, 8(3), 68; https://doi.org/10.3390/robotics8030068
Received: 27 June 2019 / Revised: 31 July 2019 / Accepted: 1 August 2019 / Published: 6 August 2019
(This article belongs to the Special Issue Kinematics and Robot Design II, KaRD2019)
Industrial manipulators and parallel robots are often used for tasks, such as drilling or milling, that require three translational, but only two rotational degrees of freedom (“3T2R”). While kinematic models for specific mechanisms for these tasks exist, a general kinematic model for parallel robots is still missing. This paper presents the definition of the rotational component of kinematic constraints equations for parallel robots based on two reciprocal sets of Euler angles for the end-effector orientation and the orientation residual. The method allows completely removing the redundant coordinate in 3T2R tasks and to solve the inverse kinematics for general serial and parallel robots with the gradient descent algorithm. The functional redundancy of robots with full mobility is exploited using nullspace projection. View Full-Text
Keywords: parallel robot; five-DoF task; 3T2R task; functional redundancy; task redundancy; redundancy resolution; reciprocal Euler angles; inverse kinematics parallel robot; five-DoF task; 3T2R task; functional redundancy; task redundancy; redundancy resolution; reciprocal Euler angles; inverse kinematics
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Schappler, M.; Tappe, S.; Ortmaier, T. Modeling Parallel Robot Kinematics for 3T2R and 3T3R Tasks Using Reciprocal Sets of Euler Angles. Robotics 2019, 8, 68.

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