Working Paper Article Version 1 This version is not peer-reviewed

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

Version 1 : Received: 27 June 2019 / Approved: 1 July 2019 / Online: 1 July 2019 (12:17:56 CEST)

How to cite: Schappler, M.; Tappe, S.; Ortmaier, T. Modeling Parallel Robot Kinematics for 3T2R and 3T3R Tasks Using Reciprocal Sets of Euler Angles. Preprints 2019, 2019070015 Schappler, M.; Tappe, S.; Ortmaier, T. Modeling Parallel Robot Kinematics for 3T2R and 3T3R Tasks Using Reciprocal Sets of Euler Angles. Preprints 2019, 2019070015

Abstract

Industrial manipulators and parallel robots are often used for tasks like 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 to completely remove 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.

Subject Areas

parallel robot; five-DoF task; 3T2R task; functional redundancy; task redundancy; redundancy resolution; reciprocal Euler angles; inverse kinematics

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