In this paper, the matrix equation AX = XB used for hand to sensor calibration of robotmounted sensors is analyzed using a geometrical approach. The analysis leads to an original way to describe the properties of the equation and to find all of its solutions. It will also be highlighted why, when multiple instances A i X = XB i ͑i =1,2, . . .͒ of the equation are to be solved simultaneously, the system is overconstrained. Finally, singular cases are also discussed.

The assessment of rehabilitation robot safety is a vital aspect of the development process, which is often experienced as difficult. There are gaps in best practices and knowledge to ensure safe usage of rehabilitation robots. Currently, safety is commonly assessed by monitoring adverse events occurrence. The aim of this article is to explore how safety of rehabilitation robots can be assessed early in the development phase, before they are used with patients. We are suggesting a uniform approach for safety validation of robots closely interacting with humans, based on safety skills and validation protocols. Safety skills are an abstract representation of the ability of a robot to reduce a specific risk or deal with a specific hazard. They can be implemented in various ways, depending on the application requirements, which enables the use of a single safety skill across a wide range of applications and domains. Safety validation protocols have been developed that correspond to these skills and consider domain-specific conditions. This gives robot users and developers concise testing procedures to prove the mechanical safety of their robotic system, even when the applications are in domains with a lack of standards and best practices such as the healthcare domain. Based on knowledge about adverse events occurring in rehabilitation robot use, we identified multi-directional excessive forces on the soft tissue level and musculoskeletal level as most relevant hazards for rehabilitation robots and related them to four safety skills, providing a concrete starting point for safety assessment of rehabilitation robots. We further identified a number of gaps which need to be addressed in the future to pave the way for more comprehensive guidelines for rehabilitation robot safety assessments. Predominantly, besides new developments of safety by design features, there is a strong need for reliable measurement methods as well as acceptable limit values for human-robot interaction forces both on skin and joint level.

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In this work, the inverted micro-Stereolithography (SLA) is used to show the potential of such additive manufacturing (AM) technology at prototyping super-shaped dielectric resonator antennas (S-DRAs) rapidly and accurately. The S-DRAs, which exhibit 3D complex geometries, were designed to operate at 3.5 GHz, suitable for the assessment of 5G communications in the mid band. Initially, a cross-starred-shaped S-DRA was designed and manufactured via the inverted micro-SLA by means of a photopolymer resin as material. As no information about the used material was available from literature and supplier, the dielectric properties of the photopolymer resin were characterized. Moreover, in the view of challenging further the SLA capability, several prototypes, based on the cross star shaped geometry but exhibiting a twist of variable angles along the longitudinal axis, were fabricated and tested. In order to compare the antennas performance in relation to the material volume and sizes, rectangular and cylindrical DRAs were also realized using same material and technology. Scattering parameter S 11 , gain, bandwidth (BW), efficiency and co-and cross-polarization of all antennas were measured. The experimental results showed that twisted S-DRAs exhibit same performance of the basic cross-starred-shaped antenna, due to the invariance to symmetry of the basic Gielis geometry. The measured gain is about 2.5 dB over a range of 1 GHz in the frequency range of interest; the BW measured for all S-DRAs is about 10%, whereas the efficiency is about 80% at 3.5 GHz. Finally, better performance in terms of bandwidth is shown by the S-DRAs, considering their dramatic volume reduction (∼85%) compared to classic rectangular and cylindrical DRAs and other DRA examples already reported in the state of the art.

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