Aim: The aim of this review paper is to summarize recent developments and research in robotics, relevant to the field of ankle rehabilitation, to overview new findings and determine the actual state of the art. Method: The literature search was performed using scientific and medical databases (Scopus, PubMed and Web of Science) and other websites related to robots used in the area of ankle rehabilitation, analysing studies from 1950s to present. Information about the mechanical and kinematic specifications, actuation and stage of development was extracted from the selected literature. Results: Several types of rehabilitation robots have been considered, and they were classified depending on their architecture and design features. We we found that, regardless of the differences in architectures, only a few of them have been commercialized. The majority of rehabilitation robots designs allows plantarflexion-dorsiflexion movements. Unless some exceptions, most of the wearable robots do not allow the adduction-abduction movement. Neither the physical appearance of the robot nor the user’s perception towards it has not regularly been taken into account in the design stage. This limits the possibility of successful commercialization. Conclusions: Up to the present moment, the main challenges in the field of robot rehabilitation are the lack of unique rehabilitation protocols capable to fulfil the needs of all types of patients and the additional resources to measure the effectiveness of proposals that have not yet been commercialized. Nonetheless, we have mentioned above three areas were the challenges in design are more pressing. The first one is the robot architecture, which still presents some incommodities nowadays to emulate the ankle joint movement in a natural way. Thus, the displacements experienced by the axes in the joint must be adaptable to each patient and a wide range of pathologies. Moreover, many proposals are not been conceived to the purpose of commercialization, and even less to become an object of personal use.

In this work the kinematic and dynamic analyses of a robot manipulator whose topology consists of parallel kinematic structures with linear actuators are approached by means of the theory of screws and the principle of virtual work. The input/output equations of velocity and acceleration are obtained by applying screw theory. Then the generalized forces of the manipulator are determined combining screw theory and the principle of virtual work. Finally, a case study, whose numerical results are compared with simulations generated with the aid of specialized software, is included.

In this contribution, the Jacobian analysis of a four-legged six-degrees-of-freedom decoupled parallel manipulator is carried out through the screw theory. As an intermediate step, for the sake of completeness the inverse/forward displacement analysis as well as the computation of the workspace of the robot are achieved by taking advantage of the decoupled orientation and position of the moving platform. Afterward, the input/output equation of velocity of the parallel robot is obtained by harnessing of the properties of reciprocal screw systems. Once the Jacobian matrices are identified and investigated, the analysis of singularities for the robot manipulator emerges as a natural application of the Jacobian analysis. Numerical examples are included with the purpose to show the practicality and versatility of the method of kinematic analysis. Furthermore, the numerical results obtained by means of the theory of screws are successfully verified with the aid of commercially available software like ADAMS.

SUMMARY This study addresses the kinematics of a six-degrees-of-freedom parallel manipulator whose moving platform is a regular triangular prism. The moving and fixed platforms are connected to each other by means of two identical parallel manipulators. Simple forward kinematics and reduced singular regions are the main benefits offered by the proposed parallel manipulator. The Input–Output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. A case study, which is verified with the aid of commercially available software, is included with the purpose to exemplify the application of the method of kinematic analysis.