Abstract
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.
Highlights
Industrial tasks like welding, gluing, milling or drilling represent a major part of the applications of industrial robots, which generally have full mobility, i.e., the operational space of their end-effector has three translational and three rotational (“3T3R”) degrees of freedom (“DoF”)
To be able to perform the dimensional synthesis for all structures, the inverse kinematics has to be implemented in a general form to calculate the performance criteria over a given trajectory for further optimization of the structures and their comparison
For the generation of task redundant parallel robots, the inverse kinematics has to include an optimization of the performance criteria and the restrictions such as joint limits to ensure a comparability of the results
Summary
Industrial tasks like welding, gluing, milling or drilling represent a major part of the applications of industrial robots, which generally have full mobility, i.e., the operational space of their end-effector has three translational and three rotational (“3T3R”) degrees of freedom (“DoF”). Parallel robots like the Stewart platform have especially been proposed for milling tasks regarding their high structural stiffness. The task space of the named applications can be defined by three translational DoF and only two rotations due to a symmetry around the tool axis (“3T2R”). This results in a functional or task redundancy, which is not exploited to full extend yet for parallel robots
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