Uniqueness domains and non singular assembly mode changing trajectories

Parallel robots admit generally several solutions to the direct kinematics problem. The aspects are associated with the maximal singularity free domains without any singular configurations. Inside these regions, some trajectories are possible between two solutions of the direct kinematic problem without meeting any type of singularity: non-singular assembly mode trajectories. An established condition for such trajectories is to have cusp points inside the joint space that must be encircled. This paper presents an approach based on the notion of uniqueness domains to explain this behaviour

Non-singular assembly mode changing trajectories in the workspace for the 3-RPS parallel robot

Having non-singular assembly modes changing trajectories for the 3-RPS parallel robot is a well-known feature. The only known solution for defining such trajectory is to encircle a cusp point in the joint space. In this paper, the aspects and the characteristic surfaces are computed for each operation mode to define the uniqueness of the domains. Thus, we can easily see in the workspace that at least three assembly modes can be reached for each operation mode. To validate this property, the mathematical analysis of the determinant of the Jacobian is done. The image of these trajectories in the joint space is depicted with the curves associated with the cusp points

Workspace and Assembly modes in Fully-Parallel Manipulators : A Descriptive Study

International audienceThe goal of this paper is to explain, using a typical example, the distribution of the different assembly modes in the workspace and their effective role in the execution of trajectories. The singular and non-singular changes of assembly mode are described and compared to each other. The non-singular change of assembly mode is more deeply analysed and discussed in the context of trajectory planning. In particular, it is shown that, according to the location of the initial and final configurations with respect to the uniqueness domains in the workspace, there are three different cases to consider before planning a linking trajectory

A study of the singularity locus in the joint space of planar parallel manipulators: special focus on cusps and nodes

Cusps and nodes on plane sections of the singularity locus in the joint space of parallel manipulators play an important role in nonsingular assembly-mode changing motions. This paper analyses in detail such points, both in the joint space and in the workspace. It is shown that a cusp (resp. a node) defines a point of tangency (resp. a crossing point) in the workspace between the singular curves and the curves associated with the so-called characteristics surfaces. The study is conducted on a planar 3-RPR manipulator for illustrative purposes.Comment: 4th International Congress Design and Modeling of Mechanical Systems, Sousse : Tunisia (2011

Non-Singular Assembly Mode Changing Trajectories of a 6-DOF Parallel Robot

International audienceThis paper deals with the non-singular assembly mode changing of a six degrees of freedom parallel manipulator. The manipulator is composed of three identical limbs and one moving platform. Each limb is composed of three prismatic joints of directions orthogonal to each other and one spherical joint. The first two prismatic joints of each limb are actuated. The planes normal to the directions of the first two prismatic joints of each limb are orthogonal to each other. It appears that the parallel singularities of the manipulator depend only on the orientation of its moving platform. Moreover, the manipulator turns to have two aspects, namely, two maximal singularity free domains without any singular configuration, in its orientation workspace. As the manipulator can get up to eight solutions to its direct kinematic model, several assembly modes can be connected by non-singular trajectories. It is noteworthy that the images of those trajectories in the joint space of the manipulator encircle one or several cusp point(s). This property can be depicted in a three dimensional space because the singularities depend only on the orientation of the moving-platform and the mapping between the orientation parameters of the manipulator and three joint variables can be obtained with a simple change of variables. Finally, to the best of the authors' knowledge, this is the first spatial parallel manipulator for which non-singular assembly mode changing trajectories have been found and shown

An algebraic method to check the singularity-free paths for parallel robots

Trajectory planning is a critical step while programming the parallel manipulators in a robotic cell. The main problem arises when there exists a singular configuration between the two poses of the end-effectors while discretizing the path with a classical approach. This paper presents an algebraic method to check the feasibility of any given trajectories in the workspace. The solutions of the polynomial equations associated with the tra-jectories are projected in the joint space using Gr{\"o}bner based elimination methods and the remaining equations are expressed in a parametric form where the articular variables are functions of time t unlike any numerical or discretization method. These formal computations allow to write the Jacobian of the manip-ulator as a function of time and to check if its determinant can vanish between two poses. Another benefit of this approach is to use a largest workspace with a more complex shape than a cube, cylinder or sphere. For the Orthoglide, a three degrees of freedom parallel robot, three different trajectories are used to illustrate this method.Comment: Appears in International Design Engineering Technical Conferences & Computers and Information in Engineering Conference , Aug 2015, Boston, United States. 201

Nonsingular change of assembly mode without any cusp

International audienceThis paper shows for the first time a parallel manipulator that can execute nonsingular changes of assembly modes while its joint space is free of cusp points and cuspidal edges. The manipulator at hand has two degrees of freedom and is derived from a 3-RPR manipulator; the shape of its joint space is a thickening of a figure-eight curve. A few explanations concerning the relationship between cusps and alpha curves are given

Hidden cusps

International audienceThis paper investigates a situation pointed out in a recent paper, in which a non-singular change of assembly mode of a planar 2-RPR-PR parallel manipulator was realized by encircling a point of multiplicity 4. It is shown that this situation is, in fact, a non-generic one and gives rise to cusps under a small perturbation. Furthermore , we show that, for a large class of singularities of multiplicity 4, there are only two types of stable singularities occurring in a small perturbation: these two types are given by the complex square mapping and the quarto mapping. Incidentally , this paper confirms the fact that, generically, a local non-singular change of solution must be accomplished by encircling a cusp point