The development of exoskeletons and wearable robots has caught the attention of the academic community in recent years due to its high potential in Neurorehabilitation. In addition to this, exoskeletons have found commercial use in motion assistance, military, labour and industrial applications. Most of the exoskeletons that have been proposed in the literature are designed for the lower-limbs due to the motivation of providing mobility to stroke and SCI patients, however there are few developments for upper-limbs. This paper presents a novel upper-limb exoskeleton that provides four degrees-of-freedom (henceforth denoted as DoF) per each arm, where 4 DoF and 1 DoF are given to the shoulder and elbow, respectively. Closed-form solutions for the inverse and forward kinematics of the exoskeleton are determined, and by using accelerometers, this work obtains the pose and orientation of the exoskeleton in real-time. The experimental work includes healthy subjects that wear the exoskeleton for daily use activity, while the device monitors their motion and reachable workspace, which are compared to statistical parameters found in the literature. Simulations and numerical examples are performed in order to compare the results obtained in the experiments in order to verify their plausibility.