Computational approaches to biological motor control are used to discover the building blocks of human motor behaviour. Models explaining features of human hand movements have been studied thoroughly, yet only a few studies attempted to explain the control of the orientation of the hand; instead, they mainly focus on the control of hand translation, predominantly in a single plane. In this study, we present a new methodology to study the way humans control the orientation of their hands in three dimensions and demonstrate it in two sequential experiments. We developed a quaternion-based score that quantifies the geodicity of rotational hand movements and evaluated it experimentally. In the first experiment, participants performed a simple orientation-matching task with a robotic manipulator. We found that rotations are generally performed by following a geodesic in the quaternion hypersphere, which suggests that, similarly to translation, the orientation of the hand is centrally controlled, possibly by optimizing geometrical properties of the hand’s rotation. This result established a baseline for the study of human response to perturbed visual feedback of the orientation of the hand. In the second experiment, we developed a novel visuomotor rotation task in which the rotation is applied on the hand’s rotation, and studied the adaptation of participants to this rotation, and the transfer of the adaptation to a different initial orientation. We observed partial adaptation to the rotation. The patterns of the transfer of the adaptation to a different initial orientation were consistent with the representation of the orientation in extrinsic coordinates. The methodology that we developed allows for studying the control of a rigid body without reducing the dimensionality of the task. The results of the two experiments open questions for future studies regarding the mechanisms underlying the central control of hand orientation. These results can be of benefit for many applications that involve fine manipulation of rigid bodies, such as teleoperation and neurorehabilitation.