Variable geometry trusses are composed, in general, of unit cells which can be modeled as bars connected by spherical joints. Under mild conditions, it has been shown that the only feasible cells are topologically equivalent to bipyramids. Unfortunately, using standard formulations, the closed-form position analysis of bipyramids is not a trivial task. Actually, it has only been achieved for bipyramids with up to 7 vertices, whose closure polynomial has been shown to be of order 24. In this paper, using a distance-based formulation and a kinematic inversion for fans of tetrahedra, the problem is solved for bipyramids with up to 11 vertices, whose closure polynomial is of degree 896. No other position analysis problem leading to such a high-order closure polynomial has been previously solved.
Pàmies-Vilà, R.; Pätkau, O.; Doria-Cerezo, A.; Font-Llagunes, J.M. Mechanism and machine theory Vol. 107, p. 123-138 DOI: 10.1016/j.mechmachtheory.2016.09.002 Data de publicació: 2017-01 Article en revista
The analysis of a captured motion can be addressed by means of forward or inverse dynamics approaches. For this purpose, a 12 segment 2D model with 14 degrees of freedom is developed and both methods are implemented using multibody dynamics techniques. The inverse dynamic analysis uses the experimentally captured motion to calculate the joint torques produced by the musculoskeletal system during the movement. This information is then used as input data for a forward dynamic analysis without any control design. This approach is able to reach the desired pattern within half cycle. In order to achieve the simulation of the complete gait cycle two different control strategies are implemented to stabilize all degrees of freedom: a proportional derivative (PD) control and a computed torque control (CTC). The selection of the control parameters is presented in this work: a kinematic perturbation is used for tuning PD gains, and pole placement techniques are used in order to determine the CTC parameters. A performance evaluation of the two controllers is done in order to quantify the accuracy of the simulated motion and the control torques needed when using one or the other control approach to track a known human walking pattern.
Peña-Pitarch, E.; Ticó, N.; Lopez, J.A.; A. Al Omar; Alcelay, J. I. Mechanism and machine theory Vol. 105, p. 388-396 DOI: 10.1016/j.mechmachtheory.2016.07.014 Data de publicació: 2016-11-01 Article en revista
People with disabilities have limitations in activities of daily life such as grasping a glass of water or moving an object. Orthotic products that improve or restore the functionality of the musculoskeletal system of a patient contribute to some extent to overcome the limitations described. So does the hand brace, used to treat musculoskeletal disorders caused by various diseases (rheumatic disorders, neurological, orthopedic and others). The paper simulates a novel exoskeleton helping to grasp any object. The novelty of this mechanism is that works without external energy, it works with a wrist movement that generates a kinetic movement and helps to grasp objects with an extra force. The orthosis facilitates the functionality, being comfortable and easy to be used by the patient. It is adaptable to hand size and finger length of the patient.
This paper shows how, using elementary Distance Geometry, a closure polynomial of degree 8 for the Dixon linkage can be derived without any trigonometric substitution, variable elimination, or artifice to collapse mirror configurations. The formulation permits the derivation of the geometric conditions required in order for each factor of the leading coefficient of this polynomial to vanish. These conditions either correspond to the case in which the quadrilateral defined by four joints is orthodiagonal, or to the case in which the center of the circle defined by three joints is on the line defined by two other joints. This latter condition remained concealed in previous formulations. Then, particular cases satisfying some of the mentioned geometric conditions are analyzed. Finally, the obtained polynomial is applied to derive the coupler curve of the generalized Peaucellier linkage, a linkage with the same topology as that of the celebrated Peaucellier straight-line linkage but with arbitrary link lengths. It is shown that this curve is 11-circular of degree 22 from which the bicircular quartic curve of the Cayley's scalene cell is derived as a particular case.
Gholami, F.; Pàmies-Vilà, R.; Koevecses, J.; Font-Llagunes, J.M. Mechanism and machine theory Vol. 93, p. 175-184 DOI: 10.1016/j.mechmachtheory.2015.07.003 Data de publicació: 2015-11-01 Article en revista
In this study, effects of some of the foot modelling assumptions on the ankle kinematics and dynamics are investigated based on the experimental data. For the kinematics analysis, the appropriateness of the stationary axis of rotation of the human ankle flexion is examined. Moreover, an interpolated function which is capable of predicting the directional changes of this axis is proposed. For the dynamics analysis, two main modelling assumptions of the number of the foot segments and the dimension of the foot model are the subject of the study. To this end, the ankle joint torque and power are selected as the comparison indicators and inverse dynamics analyses are carried out. The analyses show that the number of segments of the foot model does not have a considerable effect on the calculated ankle joint torque. On the other hand, the calculated ankle power is highly affected by both of the segmentation and the dimension of the foot model.
In constant-breadth cam mechanisms closure of the higher kinematic pairs formed by the bilateral cam-follower contact is guaranteed by the geometry of both cam and follower. A study of the cam profile by means of its radius of curvature and the sliding velocities in the upper pair enables us to predict the correct functioning of the mechanism. This work presents the equations for calculating cam breadth when the translating follower is eccentric with an inclination, the radius of curvature of its profile and the sliding velocities of constant-breadth cam mechanisms with translating and oscillating followers. This study also analyses the influence of the angle of inclination and the offset of the flat-faced translating followers on the size of the cam and the kinematics of the mechanism. Numerical examples are given of constant-breadth cams obtained for distinct values of the mentioned parameters. Additionally, this paper describes the redesign of a cam of a conventional sewing machine and the new cam prototype, with a continuity of an order higher than the original profile, is included. (C) 2014 Elsevier Ltd. All rights reserved.
Pàmies-Vilà, R.; Font-Llagunes, J.M.; Lugrís, U.; Cuadrado, J. Mechanism and machine theory Vol. 75, p. 107-116 DOI: 10.1016/j.mechmachtheory.2014.01.010 Data de publicació: 2014-05-01 Article en revista
A new parameter identification method for a three-dimensional foot-ground contact model is presented. The model is used to reproduce the relationship between the contact forces and the relative foot-ground displacements and velocities. The parameters of the contact model are estimated using the optimization method known as covariance matrix adaptation evolution strategy. An extended Kalman filter is implemented as a controller to compute a forward dynamic analysis of the foot motion using body segment parameters and the ankle joint wrench as input data. The aim of this work is to adjust the position and size of the contact elements (spheres) and the model parameters in order to obtain both, a predicted motion provided by forward dynamics as faithful as possible to the captured motion and a resultant foot-ground wrench (obtained through the foot-ground contact model) as close as possible to the measured foot-ground reactions. The results show that the obtained motion is really similar to the captured one and, moreover, the vertical force and the moments in the horizontal plane are in agreement with the experimental mesurments. However, the bristle friction model used for tangential forces provides lower level of agreement with the experimental data. (C) 2014 Elsevier Ltd. All rights reserved.
The constant-breadth cam mechanisms, which drive a parallel flat-faced double follower, are desmodromic, and guarantee global bilaterality. In the said mechanisms, the law of displacement of the follower can only be freely designed for an interval of the rotation angle of the cam – the designed segment – close or equal to 180°, and the remaining interval – the calculated segment – is obtained through calculation from the first. Guaranteeing the continuity between segments is not a trivial task. This work shows a design procedure which guarantees automatically the global continuity of the law of displacement. This procedure provides the expressions of calculation for both parallel flat-faced double translating follower and parallel flat-faced double oscillating follower. Non-parametric Bézier curves are used for the definition of the displacement functions. For both types of followers, two numerical examples of the design of the displacement functions are given. Furthermore, the corresponding cam profiles are provided.
The study of the singularity set is of utmost utility in understanding the local and global behavior of a manipulator. After reviewing the mathematical conditions that characterize this set, and their kinematic and geometric interpretation, this paper shows how these conditions can be formulated in an amenable manner in planar manipulators, allowing the definition of a conceptually-simple method for isolating the set exhaustively, even in higher-dimensional cases. As a result, the method delivers a collection of boxes bounding the location of all points of the set, whose accuracy can be adjusted through a threshold parameter. Such boxes can then be projected to the input or output coordinate spaces, obtaining informative diagrams, or portraits, on the global motion capabilities of the manipulator. Examples are included that show the application of the method to simple manipulators, and to a complex mechanism that would be difficult to analyze using common-practice procedures.
Pàmies-Vilà, R.; Font-Llagunes, J.M.; Cuadrado, J.; Alonso, F.J. Mechanism and machine theory Vol. 58, p. 153-164 DOI: 10.1016/j.mechmachtheory.2012.07.010 Data de publicació: 2012-12-01 Article en revista
Goma, J.; Diego, U.; Minguella-Canela, J.; Fenollosa, F.; Joan Vivancos-Calvet Mechanism and machine theory Vol. 51, p. 217-229 DOI: 10.1016/j.mechmachtheory.2011.07.011 Data de publicació: 2012-05 Article en revista
This paper presents an interval propagation algorithm for variables in planar single-loop linkages. Given intervals of allowed values for all variables, the algorithm provides, for every variable, the whole set of values, with out over-estimation, for which the linkage can actually be assembled. We show further how this algorithm can be integrated in a branch-and-prune search scheme, in order to solve the position analysis of general planar multi-loop linkages. Experimental results are included, comparing the method’s perfor mance with that of previous techniques given for the same task.
The exact position analysis of a planar mechanism reduces to compute the roots of its
characteristic polynomial. Obtaining this polynomial usually involves, as a first step, obtaining a system of equations derived from the independent kinematic loops of the mechanism. Although conceptually simple, the use of kinematic loops for deriving characteristic polynomials leads to complex variable eliminations and, in most cases, trigonometric substitutions. As an alternative, a method based on bilateration has recently been shown to permit obtaining the characteristic polynomials of the three-loop Baranov trusses without relying on variable eliminations or trigonometric substitutions. This paper shows how this technique can be applied to solve the position analysis of all catalogued Baranov
trusses. The characteristic polynomials of them all have been derived and, as a result, the maximum number of their assembly modes has been obtained. A comprehensive literature
survey is also included.
Goma, J.; Joan Vivancos-Calvet; Minguella-Canela, J.; Diego, U.; Fenollosa, F. Mechanism and machine theory Vol. 46, num. 11, p. 1744-1754 DOI: 10.1016/j.mechmachtheory.2011.06.005 Data de publicació: 2011-07-13 Article en revista
Es presenta una revisió històrica del telègraf d'Agustin de Betancourt i se n'analitzen les seves característiques tècniques. Es presenten de manera analítica, numèrica i gràfica algunes de les declaracions fetes sobre el telègraf i se'n corregeixen d'altres. Finalment, se'n fa una reconstrucció detallada utilitzant diferents tècniques avançades de CAD, les quals permeten una visió estàtica i dinàmica precisa de cada una de les seves parts.
The position analysis of planar linkages has been dominated by resultant elimination and
tangent-half-angle substitution techniques applied to sets of kinematic loop equations.
This analysis is thus reduced to finding the roots of a polynomial in one variable, the
characteristic polynomial of the linkage. In this paper, by using a new distance-based
technique, it is shown that this standard approach becomes unnecessarily involved when
applied to the position analysis of the three seven-link Assur kinematic chains. Indeed, it is shown that the characteristic polynomials of these linkages can be straightforwardly derived without relying on variable eliminations nor trigonometric substitutions, and using no others tools than elementary algebra.
A pentapod is usually defined as a 5-degrees-of-freedom fully-parallel manipulator with
an axial spindle as moving platform. This kind of manipulators has revealed as an
interesting alternative to serial robots handling axisymmetric tools. Their particular
geometry permits that, in one tool axis, high inclination angles could be attained, thus
overcoming the orientation limits of the classical Stewart-Gough platform. This paper
deals with pentapods with coplanar base attachments.
In previous works changes in the location of the leg attachments that do not modify
the singularity locus of the pentapod were studied. Such leg rearrangements reveal here
as a powerful tool to shed light on the geometric structure of the singularity locus and,
in particular, on architectural singularities.
Indeed, a complete analysis of such singularities is carried out, providing both algebraic
conditions, which complete previous results found in literature, and a geometrical
interpretation that permits defining a measure of distance to architectural singularities.
Such measure can be used as a index in the design process to obtain manipulators as far
as possible from architectural singularities, leading to a better global behavior.
The main objective of this paper is twofold. First, to conclude the overview about
tensegrity frameworks, started by the same authors in a previous work, covering the most important dynamic aspects of such structures. Here, the most common approaches to tensegrity dynamic modeling used so far are presented, giving the most important results about their dynamic behavior under external action. Also, the main underlying problems are identified which allow the authors to give a clear picture of the main research lines currently open, as well as the most relevant contributions in each of them, which is in fact the second main objective of this paper. From the extensive literature available on the subject, four main areas have been identified: design and form-finding methods which deal with the problem of finding stable configurations, shape changing algorithms which deal with the
problem of finding stable trajectories between them and, also control algorithms
which take into account the dynamic model of the tensegrity structure and possible
external perturbations to achieve the desired goal and performance.
Finally, some applications of such structures are presented emphasizing the increasing interest of the scientific community on tensegrity structures.
At the end of the 19th century, several analog machines had been proposed for solving algebraic equations. These machines – based not only on kinematics principles but also on dynamic or hydrostatic balances, electric or electromagnetic devices, etc. – had one important drawback: lack of accuracy.
Leonardo Torres was the first to beat the challenge of designing and implementing a machine able to compute the roots of algebraic equations that, in the case of polynomials of degree eight, attained a precision down to 1/1000. The key element of Torres’ machine was the endless spindle, an analog mechanical device designed to compute log(a + b) from log(a) and log(b). This short account gives a detailed description of this mechanism.
This paper hands in a review of the basic issues about the statics of tensegrity structures. Definitions and notation for the most important concepts, borrowed from the vast existing literature, are summarized. All of these concepts and definitions provide a complete mathematical framework to analyze the rigidity and stability properties of tensegrity structures from three different, but related, points of view: motions, forces and energy approaches. Several rigidity and stability definitions are presented in this paper and hierarchically ordered, from the strongest condition of infinitesimal rigidity to the more wide concept of simple rigidity, so extending some previous classifications already available. Important theorems regarding the relationship between these definitions are also put together to complete the static overview of tensegrity structures. Examples of different tensegrity structures belonging to each of the rigidity and stability ca\-tegories presented are described and analyzed. Concluding the static analysis of tensegrity structures, a review of existing form-finding methods is presented.