@InProceedings{Erdogan2011d,
	booktitle = {ECCOMAS Thematic Conference on Multibody Dynamics},
	author = {Ahmetcan Erdogan and Volkan Patoglu},
	title = {Kinematics and Control of a 3RPS-R Mechanism using Euler Parameters},
	year = {2011},
	abstract = {In this study, a forearm-wrist rehabilitation robot is designed and controlled. In particular, to comply with the rotational workspace of the human forearm-wrist, a 3RPS-R mechanism is proposed as the underlying kinematic structure of the device. The equations governing kinematics of the 3RPS-R mechanism are derived using Euler parameters (unit quaternions) to avoid representation singularities and the device is controlled using quaternion feedback to ensure the
geometrical consistency of resulting interactions. To this end, first the reference trajectories for the human forearm-wrist rotations are calculated as geodesics using spherical linear interpolation. Next, an impedance controller is implemented with proper orientation error in SO(3) for assistance and dynamic interaction. In order to
motivate the active participation of the patient, a contour tracking algorithm is used with properly defining a potential field in the same manifold of the end-effector space and a passive velocity field controller is synthesized. The controllers are implemented on the forearm-wrist rehabilitation robot and experimental results are
presented.}
}

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