A fast branch-and-prune algorithm for the position analysis of spherical mechanisms

The final publication is available at link.springer.comDifferent branch-and-prune schemes can be found in the literature for numerically solving the position analysis of spherical mechanisms. For the prune operation, they all rely on the propagation of motion intervals. They differ in the way the problem is algebraically formulated. This paper exploits the fact that spherical kinematic loop equations can be formulated as sets of 3 multi-affine polynomials. Multi-affinity has an important impact on how the propagation of motion intervals can be performed because a multi-affine polynomial is uniquely determined by its values at the vertices of a closed hyperbox defined in its domain.Peer ReviewedPostprint (author's final draft

Self-Motions of General 3-RPR Planar Parallel Robots

This paper studies the kinematic geometry of general 3-RPR planar parallel robots with actuated base joints. These robots, while largely overlooked, have simple direct kinematics and large singularity-free workspace. Furthermore, their kinematic geometry is the same as that of a newly developed parallel robot with SCARA-type motions. Starting from the direct and inverse kinematic model, the expressions for the singularity loci of 3-RPR planar parallel robots are determined. Then, the global behaviour at all singularities is geometrically described by studying the degeneracy of the direct kinematic model. Special cases of self-motions are then examined and the degree of freedom gained in such special configurations is kinematically interpreted. Finally, a practical example is discussed and experimental validations performed on an actual robot prototype are presented

Asymptotic singularities of planar parallel 3-RPR manipulators

We study the limits of singularities of planar parallel 3-RPR manipulators as the lengths of their legs tend to infinity, paying special attention to the presence of cusps. These asymptotic singularities govern the kinematic behavior of the manipulator in a rather large portion of its workspace

On the kinematic constraint surfaces of general three-legged planar robot platforms

The variants of general three-legged planar robot platforms are enumerated and classified. Constraint surfaces corresponding to individual platform legs in the kinematic mapping image space are classified and parametrized. The parametric equations are free from representational singularities. The entire set consists of hyperboloids of one sheet and hyperbolic paraboloids. This result corrects an oversight in the body of literature. These surfaces have important applications to the kinematic analysis of planar three-legged robot platforms, hence appropriate attention should be given to their classification

Solving the forward kinematics of a planar three-legged platform with holonomic higher pairs

A practical solution procedure for the forward kinematics problem of a fully-parallel planar three-legged platform with holonomic higher pairs is presented. Kinematic mapping is used to represent distinct planar displacements of the end-effector as discrete points in a three dimensional image space. Separate motions of each leg trace skew hyperholoids of one sheet in this space. Therefore, points of intersection of the three hyperholoids represent solutions to the forward kinematics problem. This reduces the problem to solving three simultaneous quadratics. Applications of the platform are discussed and an illustrative numerical example is given

Extreme distance to a spatial circle

Determination of shortest distances in the three dimensional task space of robots is pertinent to pick-and-place operations, collision avoidance, and for impact prediction in dynamic simulation. The conventional approach is to find perpendicular distances between planar patches approximating body surfaces. In contrast, this paper treats four variants of shortest distance computations wherein one or both elements are circular edges. These three dimensional cases include circle and point, circle and plane, circle and line and two non coplanar circles. Solutions to these four fundamental problems are developed with elementary geometry. Examples are presented, and the closed form algebraic solutions are verified with descriptive geometric constructions

Singular configurations of wrist-partitioned 6R serial robots: A geometric perspective for users

In this paper the singular configurations of wrist-partitioned 6R serial robots in general, and the KUKA KR-15/2 industrial robot in particular, are analytically described and classified. While the results are not new, the insight provided by the geometric analysis for users of such robots is. Examining the problem in the joint axis parameter space, it is shown that when the end-effector reference point is taken to be the wrist centre the determinant of the associated Jacobian matrix splits into four factors, three of which can vanish. Two of the three potentially vanishing factors give a complete description of the positioning singularities and the remaining one a complete description of the orientation singularities, in turn providing a classification scheme

A One-Motor Full-Mobility 6-PUS Manipulator

8 páginas, 2 figuras.-- Trabajo presentado al 18th CISM-IFToMM Symposium on Robot Design, Dynamics and Control (ROMANSY) celebrado en Udine (Italia) del 5 al 8 de Julio de 2010.This paper presents the feasibility study of an under-actuated parallel manipulator with 6-PUS topology, destined to handle work-tables in CNC machine tools. The proposed device exploits the fact that, in such an application, the path between the initial and final poses of the mobile platform is not assigned to reduce the number of actuators to only one.This work was supported by the Spanish Ministry of Science and Innovation, by the contribution of Regione Emilia Romagna (District Councillorship for Productive Assets, Economic Development, Telematic Plan), PRRIITT misura 3.4 azione A, to InterMech (Division Acoustics and Vibrations - LAV), and by UNIFE funds.Peer reviewe

Self-Motions of Planar Projective Stewart Gough Platforms

It has been previously shown that non-architecturally singular parallel manipulators of Stewart Gough type, where the planar platform and the planar base are related by a projectivity, have either so-called elliptic self-motions or pure translational self-motions. As the geometry of all manipulators with translational self-motions is already known, we focus on elliptic self-motions. We show that these necessarily one-parameter self-motions have a second, instantaneously local, degree of freedom in each pose of the self-motion. More-over, we introduce a geometrically motivated classification of elliptic self-motions and study the so-called orthogonal ones in detail