Grigore Gogu

Fully-Isotropic Over-Constrained Parallel Wrists with Two Degrees of Freedom

In this paper we present singularity-free fully-isotropic parallel wrists (PWs) with two degrees of freedom. The mobile platform has 2 rotations (2R) driven by two rotary actuators mounted on the base. A method is proposed for structural synthesis of 2R-PWs with uncoupled motions and fully-isotropic based on the theory of linear transformations. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian matrix mapping the two vector spaces of 2R-PWs with uncoupled motions is a diagonal 2×2 matrix. We use the condition number and the manipulability ellipsoids for their performance analysis. The Jacobian matrix of fully-isotropic 2R-PWs presented in this paper is the identity 2×2 matrix throughout their entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. As far as we are aware this paper presents for the first time solutions of singularity-free parallel wrists fully-isotropic throughout their entire workspace.

Kinematic calibration of parallel mechanisms: a novel approach using legs observation

In this paper, a novel approach is proposed for the kinematic calibration of parallel mechanisms with linear actuators at the base. The originality of the approach lies in the observation of the mechanism legs with a camera, without any mechanism modification. The calibration can hence be achieved online, as no calibration device is linked to the end-effector, on any mechanism since no additional proprioceptive sensor installation is necessary. Because of the conditions of leg observability, several camera locations may be needed during the experimentation. The associated calibration method does not however require any accurate knowledge of the successive camera positions. The experimental procedure is therefore easy to perform. The method is developed theoretically in the context of mechanisms with legs linearly actuated at the base, giving the necessary conditions of identifiability. Application to an I4 mechanism is achieved with experimental results.

Branching singularities in kinematotropic parallel mechanisms

The paper addresses the branching singularities in kinematotropic parallel mechanisms. The new formulae of mobility, connectivity, overconstraint and redundancy of parallel robots, recently proposed by the author, are used to characterize the behavior of the kinematotropic parallel mechanisms in the branching singularity and in each distinct branch. Four types of branching singularities are identified starting from the new formulae. The structural parameters associated with the four types of branching singularities and the distinct branches as well can be easily identified by inspection with no need to calculate the Jacobian matrix.

Fully-isotropic over-constrained planar parallel manipulators

In this paper we present singularity-free fully-isotropic planar parallel manipulators (PPMs) with three degrees of mobility. The moving platform has three planar degrees of freedom (DoFs), which are two planar translations and one rotation around the axis perpendicular to the plane of translations. A method is proposed for structural synthesis of four families of fully-isotropic PPMs based on the theory of linear transformations. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian matrix mapping the two vector spaces of fully-isotropic PPMs presented in this paper is the identity 3 /spl times/ 3 matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. As far as we are aware this paper presents for the first time solutions of singularity-free fully-isotropic PPMs.

Singularity-free fully-isotropic parallel manipulators with Schonflies motions

In this paper we present a new family of singularity-free fully-isotropic parallel manipulators with Schonflies motions. The moving platform of a parallel manipulator with Schonflies motions (PMSM) has four degrees of freedom, which are three independent translations and one rotation about an axis of fixed direction. A method is proposed for structural synthesis of fully-isotropic PMSMs based on the theory of linear transformations. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian matrix mapping the two vector spaces of fully-isotropic PMSMs presented in this paper is the identity 4times4 matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. As far as we are aware, the family of 8750 solutions of singularity-free fully-isotropic PMSMs introduced in this paper is presented for the first time in the literature. These solutions are derived from a family of PMSMs with decoupled motions and elementary legs also presented for the first time

Constraint Singularities and the Structural Parameters of Parallel Robots

The paper addresses the constraint singularities in connection with the structural parameters of parallel robots. The new formulae of mobility, connectivity, overconstraint and redundancy of parallel robots, recently proposed by the author, are used to characterize the constraint singularities. By using these formulae, we demonstrate that in a constraint singularity the instantaneous values of the mobility, connectivity of the moving platform and degree of overconstraint increase with no changes in limb connectivity. The constraint singularities are easily identified by inspection without Jacobian calculation.

Performance Criteria to Evaluate a Kinematically Redundant Robotic Cell for Machining Tasks

Machine tools and robots have both evolved fundamentally and we can now question the abilities of new industrial robots concerning accurate task realization under high constraints. Requirements in terms of kinematic and dynamic capabilities in High Speed Machining (HSM) are increasingly demanding. To face the challenge of performance improvement, parallel and hybrid robotic architectures have emerged and a new generation of industrial serial robots with the ability to perform machining tasks has been designed. In this paper, we propose to evaluate the performance criteria of an industrial robot included in a kinematically redundant robotic cell dedicated to a machining task. Firstly, we present the constraints of the machining process (speed, accuracy etc.). We then detail the direct geometrical model and the kinematic model of a robot with closed chain in the arm and we propose a procedure for managing kinematic redundancy whilst integrating various criteria. Finally, we present the evolution of the criteria for a given trajectory in order to define the best location for a rotary table and to analyze the manipulators stiffness.

Fully-isotropic parallel robots with four degrees of freedom T2R2-type

The paper presents singularity-free fully-isotropic parallel manipulators (PMs) with four degrees of freedom T2R2-type. The mobile platform has two independent translations (T2) and two rotations (R2). A method is proposed for structural synthesis of fully-isotropic T2R2-type PMs based on the theory of linear transformations. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian matrix mapping the two vector spaces of fully-isotropic T2R2-type PMs presented in this paper is the identity 4/spl times/4 matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. As far as we are aware, this paper presents for the first time in the literature solutions of singularity-free fully-isotropic PMs with four degrees of freedom T2R2-type.

Optimal pose selection for vision-based kinematic calibration of parallel mechanisms

In this paper, a new pose selection criterion for the kinematic calibration of parallel mechanisms is proposed. It enables one to take into account the measurement noise amplification that may occur for parallel mechanisms, as well as the variation of amplitude and anisotropy of the measuring device accuracy. This new criterion is applied to vision-based calibration of an Orthoglide mechanism, both in simulation, with comparison to existing criteria, and experimentally.

CAD Based Geometric Procedures for Workspace and Singularity Determination of the 3-RPR Parallel Manipulator

This paper presents a set of techniques based on the use of CAD geometric approaches for singularity surfaces and total operational workspace and joint space determination. The main emphasis is given to the use of CAD tools used to characterize and analyze the performance of planar parallel robot manipulators. The CAD environment provides powerful tools for the graphical programming and geometric feature handling. This paper points out the effectiveness of such a method in the robot design process. These developments are illustrated by the 3-RPR planar parallel manipulator case study. All of the proposed geometric algorithms are implemented in the CATIA CAD environment.