Mónica Urízar

Assembly Mode Changing in the Cuspidal Analytic 3-R

In this paper, the analytic 3-RPR platform studied by Wenger and Chablat in 2009 will be analyzed regarding its cuspidality condition. Many investigations have paid great attention to the cuspidality phenomena that arise for some designs of the 3-RPR parallel manipulator. Nevertheless, most of them focus on obtaining the cusp points of direct kinematic singularity curves on a section of the joint space, meaning that one of the input variables must remain constant. The authors, in this paper, obtain the locus of cusp points of the manipulator under study in a complete analytic way and in 3-D joint space. This way, the three inputs can be actuated to perform a nonsingular transition that encircles one of the curves that belong to the locus of cusp points. It will be shown that the duplicity of one of the output variables of this manipulator causes the overlapping of two different cusp points in the joint space. In order to visualize this characteristic, initially, transitions in a section of the joint space will be analyzed using, additionally, the reduced configuration space. Then, transitions in the 3-D joint space will be performed, showing that, in order to ensure a feasible nonsingular transition, it is necessary to represent the direct kinematic singularity surface and assess the evolution of the three output variables along the trajectory.

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It is known that cuspidality phenomenon appears in some parallel manipulators, called cuspidal manipulators, being able to perform non-singular transitions between different assembly modes. In this paper, the authors will present a methodology for obtaining the locus of cusp points in the joint space, which will be applied to generic 3-RPR planar parallel manipulators. This will permit analyzing non-singular transitions in a slice of the joint space and in the 3-dimensional joint space. It will be shown that as well as encircling a cusp point, analyzing the coalescence of solutions in the singular curves will be necessary so as to perform non-singular transitions.

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Proteins play an essential role in biochemical processes. Recently, a new viewpoint has arisen within protein researches, based on the parallelisms between proteins and mechanism. In this paper the authors present a new approach to obtain protein motion paths based in computational kinematic considerations. Finally, simulation results for an specific protein are presented.

Researching into Non-Singular Transitions in the Joint Space

In this paper, the authors present a general methodology for computing the configuration space for three-degree-of-freedom parallel manipulators so that the relation between input and output variables can be easily assessed. Making use of an entity called the reduced configuration space, all solutions of the direct kinematic problem in parallel manipulators are solved. The graphical representation of this entity enables the location of the direct kinematic solutions to be analyzed so as to make use of a wider operational workspace by means of path planning. A descriptive study is presented regarding the diverse possible paths that allow changing between direct kinematic solutions, thus, enlarging the manipulator’s range of motion.

A Kinematic Approach to Calculate Protein Motion Paths

In this article, the authors investigate the spherical 3-RPR parallel manipulator, focusing on the feasibility of performing non-singular transitions between different direct kinematic problem solutions. Making use of the kinematic mapping approach, a geometric interpretation of the constraint equations of the robot will be given. Several designs of the manipulator will be studied, analyzing the direct singularity surface of each case in the kinematic image space. It will be shown that a general design of this robot allows assembly mode change, reaching a larger operational workspace. Also, two specific architectures which do not permit performing non-singular transitions will be analyzed.

Computing the Configuration Space for Tracing Paths Between Assembly Modes

In this paper, the authors will show a methodology for computing the configuration space with one constant input, basing on the principles of the discretization methods. Taking chance of an entity called the reduced configuration space, the Direct Kinematic Problem will be solved. Moreover, this entity allows the transition between different solutions to be performed, with the purpose of enlarging the range of motion of the manipulator.

Assembly Mode Change of Spherical 3-RPR Parallel Manipulator

In this paper, the authors will show a method to visualize the configuration space so that the relation between input and output variables can be easily assessed. Making use of concepts such as the configuration space with constant input, it will be possible to obtain all the Direct Kinematic Problem solutions in parallel manipulators, and analyse how to plan motions between them. Visualizing the entity called reduced configuration space, allows an effective motion planning to reach a wider operational workspace.

Analysis of the Direct Kinematic Problem in 3-DOF Parallel Manipulators

The aim of this work is to approach the difficulties students usually encounter when facing up to kinematic analysis of mechanisms. A deep understanding of the kinematic analysis is necessary to go a step further into design and synthesis of mechanisms. We can conclude from experience that supporting and complementing the theoretical lectures with specific software is really helpful. In this sense, software is used during the practical exercises, serving as an educational complementary tool reinforcing the knowledge acquired by the students. Several questions are outlined to the students, so that they are encouraged to justify the validity of their results. GIM software performs kinematic analysis and motion simulation of planar mechanisms. The main capacities of the software are: solving the position problem, computing velocities and accelerations, singular analysis, and visualization of instantaneous center of rotation, acceleration pole, curvature center and circle, fixed and moving centrodes and main circles. The graphical representation of all results favors the learning of the theoretical concepts explained in the subject and also, stimulates the critical reasoning the students must acquire.

Computing the Configuration Space for Motion Planning between Assembly Modes

The purpose of the present work is to show how the complex theory in subjects related to Mechanism and Machine Theory can be reinforced with some practicals in which the students can perform virtual simulation of the mechanisms under study, and they can even interact with real prototypes to validate by means of experimental analysis the theoretical results. This works deals with Dynamics and Mechanical Vibrations, and presents the capacities of the Dynamics module implemented in GIM software related to the obtaining of free solid diagrams, internal forces maps and diagrams, motion simulation, and so on. In addition to this, interacting with prototypes to carry out experimental measures is also proposed, so that the students can acquire a deeper understanding of some phenomena related to mechanical vibrations.

Kinematic Analysis of Planar Mechanisms by Means of Examples

Modern robotic manipulators play an essential role in industry, developing several tasks in an easy way, enhancing the accuracy of the final product and reducing the executing time. Also they can be found in other fields as aerospace industry, several medical applications, gaming industry, and so on. In particular, the parallel manipulators have acquired a great relevance in the last years. Indeed, many research activities and projects deal with the study and development of this type of robots. Nevertheless, usually, a bilateral communication between industry and research does not exist, even among the different existing research areas. This causes a lack of knowledge regarding works that have been carried out, the ones that are under development and the possible future investigations. Hence, once a specific field of knowledge has acquired a certain level of maturity, it is convenient to reflect its current state of the art. In this sense, the authors of this paper present a review of the different fields in which parallel manipulators have a significant participation, and also the most active research topics in the analysis and design of these robots. Besides, several contributions of the authors to this field are cited.