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This paper presents a screw theory approach for the computation of the instantaneous rotation axes of indeterminate spherical linkages. Since the last part of the XIX century, the determination of the instantaneous rotation, or velocity, centers of planar mechanisms has been studied using the Aronhold-Kennedy theorem, extended to the spatial case until the second part of last century. In the beginning of the XX century, it was found that there were planar mechanisms for which the application of the Aronhold-Kennedy theorem was unable to find all the instantaneous rotation centers; these mechanisms where denominated complex or indeterminate. The beginning of this century saw a renewed interest on the complex or indeterminate mechanisms, both planar and spherical; and very soon, taken advantage of the results obtained for planar mechanisms, there were several methods for the determination of the indeterminate instantaneous rotation axes. The new screw theory approach, presented here, provides a more straightforward method for setting up the equations; furthermore, the algebraic equations to be solved are simpler than the ones published up to date. In addition, the method is part of a comprehensive method for the determination of the instantaneous screw axes of spatial mechanisms or their many special cases. The method is based on a systematic application of screw theory, which is isomorphic to the Lie algebra, se(3), of the Euclidean group, SE(3), and the invariant symmetric bilinear forms defined on se(3). [ABSTRACT FROM AUTHOR]

One of the main challenges on the use of planar mechanisms is to verify and monitor that the trajectories described by the mechanism correspond to those originally required. However, very few research studies have focused on tracking and monitoring the motion of target points located on the mechanisms during operation conditions. In this paper, a comparative study to evaluate the performance of several computer vision methods (CVMs) when used in motion tracking of planar mechanisms is presented. The aim is to compare and identify the best CVM, in terms of precision, speed, low cost, and computational performance, to track the movement of planar mechanisms. For this purpose, a case study corresponding to a planar four-bar mechanism is selected and analysed. The results show that the vision methods based on the homogeneous and non-homogeneous solution of the camera calibration matrix are a technological alternative for monitoring motion trajectories of planar mechanisms. [ABSTRACT FROM AUTHOR]

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. This review states that the use of robotic devices for ankle rehabilitation is a consolidated paradigm in the ankle's rehabilitation. Platform-based robots allow to do complex and specialized spatial movements and these architectures endow the device with high stiffness, a balanced force distribution and better adaptability to the mechanical properties of human ankle joints. Unless some exceptions, most of the wearable robots do not allow the adduction-abduction movement. For a full integration of these technologies in the ankle's rehabilitation field, more clinical evaluations are needed. Regardless of the potential of robotic devices in rehabilitation, only a few of them have been commercialized. [ABSTRACT FROM AUTHOR]

This paper presents a systematic approach to compute the angularity and the axiality indices for a Schönflies parallel manipulator. Angularity index may be considered as a measure of the sensitivity of the mobile platform to changes in rotation, while axiality index can be used to measure the sensitivity of the OP of the mobile platform to changes in translation. Since both indices were inspired by very fundamental concepts of classical kinematics (angular velocity vector and helicoidal velocity field), they offer a clear and simple physical meaning, which may be useful to the designer of parallel manipulators. Moreover, both dexterity indices do not require obtaining a dimensionally homogeneous Jacobian matrix, nor do they depend on having similar types of actuators in each manipulator's leg. Detailed numerical examples are given in order to illustrate the computation of the dexterity indices. [ABSTRACT FROM PUBLISHER]

This paper presents a screw theory approach for the computation of the instantaneous rotation centers of indeterminate planar linkages. Since the end of the 19th century, the determination of the instantaneous rotation, or velocity centers of planar mechanisms has been an important topic in kinematics that has led to the well-known Aronhold–Kennedy theorem. At the beginning of the 20th century, it was found that there were planar mechanisms for which the application of the Aronhold–Kennedy theorem was unable to find all the instantaneous rotation centers (IRCs). These mechanisms were denominated complex or indeterminate. The beginning of this century saw a renewed interest in complex or indeterminate planar mechanisms. In this contribution, a new and simpler screw theory approach for the determination of indeterminate rotation centers of planar linkages is presented. The new approach provides a simpler method for setting up the equations. Furthermore, the algebraic equations to be solved are simpler than the ones published to date. The method is based on the systematic application of screw theory, isomorphic to the Lie algebra, s e (3) , of the Euclidean group, S E (3) , and the invariant symmetric bilinear forms defined on s e (3) . [ABSTRACT FROM AUTHOR]

A letter to the editor is presented in response to an article about optimization of industrial, vision-related, intuitively generated robot point-allocating tasks using genetic algorithms.

The Lie product involves two screws, namely, a driver screw (so-called screwer in this paper) and a driven screw (termed screwen in this paper). Thus, in a spatial motion, the screwer performs a displacement of the screwen. Under this context, the Lie product represents the change of the screwen due to the infinitesimal motion performed by the screwer. To this end, this paper sets forth an integrated formulation that brings together a general geometric interpretation of the Lie product and a novel and simple derivation of the Lie product in terms of the involved screws. Moreover, since the formulation is purely geometric, a great deal of physical insight into the description of the motion problem is gained. As a result, the screw partial derivatives, in terms of the involved Lie products, are obtained for three frequently encountered types of kinematic joints, namely, helical, revolute and prismatic. Since the derivation of the Lie product is completely general, this derivation should provide a sound foundation for further applications of the Lie product. [Copyright &y& Elsevier]

This article presents an integrated methodology for the determination of the workspace and the singularity distribution for the 5R spherical, symmetric manipulator. In the first instance, the branching problem of the manipulator was considered and its solution was used to locate positions on a sphere that can be attained by the end effector. Moreover, it was found that the bounds on the workspace depend on the relative position existing between two major circles and two minor circles, which were geometrically determined in terms of the manipulator’s link lengths. Second, singular configurations were defined and singularity curves were generated. Thus, it was possible to obtain an integrated characterization scheme for the workspace and singularity distribution, by analyzing the relative position of the major and minor circles. As a result, 14 different characteristic shapes of the manipulator’s workspace and their related singularity curves were obtained. This should be a key issue in the context of manipulator’s design and trajectory design. [Copyright &y& Elsevier]

Introduced in this paper is a robust classification scheme for the 4R spherical linkage. The robustness is acquired by means of a systematic and detailed analysis of the relative motions existing between adjacent links. Thus, one can avoid the usual ambiguities encountered in type-identification procedures which have become somewhat standard. Moreover, it is shown that there are only 33 distinct types of 4R spherical linkages instead of 81, as it was reported elsewhere. Finally, an unambiguous terminology is proposed and several examples with numerical values of link lengths for each linkage type are also provided. [Copyright &y& Elsevier]