Sébastien Briot

Optimal Force Generation in Parallel Manipulators for Passing through the Singular Positions

It is known that a parallel manipulator at a singular configuration can gain one or more degrees of freedom and become uncontrollable, that is, it might not reproduce a stable motion along a prescribed trajectory. However, it is proved experimentally that there is possible passing through the singular zones. This was simulated and shown through numerical examples and illustrated on several parallel structures. In this paper, we determine the optimal dynamic conditions generating a stable motion inside the singular zones. The obtained results show that the general condition for passing through a singularity can be defined as follows: the end-effector of the parallel manipulator can pass through the singular positions without perturbation of motion if the wrench applied on the end-effector by the legs and external efforts of the manipulator are orthogonal to the twist along the direction of the uncontrollable motion. This condition is obtained from the tion of the uncontrollable motion. This condition is obtained from the inverse dynamics and analytically demonstrated by the study of the Lagrangian of a general parallel manipulator. Numerical simulations are carried out using the software ADAMS and validated through experimental tests.

Pantopteron: A New Fully Decoupled 3DOF Translational Parallel Robot for Pick-and-Place Applications

In this paper, a novel 3-DOF fully decoupled translational parallel robot, called the Pan-topteron, is presented. This manipulator is similar to the Tripteron Cartesian parallel manipulator, but due to the use of three pantograph linkages, an amplification of the ac-tuators displacements is achieved. Therefore, equipped with the same actuators, the mobile platform of the Pantopteron moves many-times faster than that of the Tripteron. This amplification is defined by the magnification factor of the pantograph linkages. The kinematics, workspace and constraint singularities of the proposed parallel robot are studied in detail. Design considerations are also discussed and a possible prototype is illustrated. .

Self-Motions of General 3-RPR Planar Parallel Robots

We study 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 behavior 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.

Singularity analysis of zero-torsion parallel mechanisms

This paper presents the singularity analysis of four 3-DOF symmetric zero-torsion parallel mechanisms. These mechanisms are composed of three identical legs ending with a spherical joint that is constrained to move in one of three equally spaced planes intersecting at one line. The computation of the singularity loci is based on the degeneracy of the system of screws applied on the platform by the legs. The whole study is based on the use of a special orientation representation, previously introduced under the name of Tilt-and-Torsion angles. This representation is briefly introduced. Then the interdependence between the Cartesian coordinates of the general class of parallel mechanisms is derived. Finally, the singularity loci are derived and the size of the workspace taking into account all singular configurations is shown.

ON THE OPTIMAL DESIGN OF PARALLEL ROBOTS TAKING INTO ACCOUNT THEIR DEFORMATIONS AND NATURAL FREQUENCIES

This paper discusses the utility of using simple stiffness and vibrations models, based on the Jacobian matrix of a manipulator and only the rigidity of the actuators, whenever its geometry is optimised. In many works, these simplified models are used to propose optimal design of robots. However, the elasticity of the drive system is often negligible in comparison with the elasticity of the elements, especially in applications where high dynamic performances are needed. Therefore, the use of such a simplified model may lead to the creation of robots with long legs, which will be submitted to large bending and twisting deformations. This paper presents an example of manipulator for which it is preferable to use a complete stiffness or vibration model to obtain the most suitable design and shows that the use of simplified models can lead to mechanisms with poorer rigidity.

Kinematic characterisation of hexapods for industry

Purpose – The purpose of this paper is to propose two simple tools for the kinematic characterization of hexapods. The paper also aims to share the experience of converting a popular commercial motion base (Stewart‐Gough platform, hexapod) to an industrial robot for use in heavy duty aerospace manufacturing processes.Design/methodology/approach – The complete workspace of a hexapod is a six‐dimensional entity that is impossible to visualize. Thus, nearly all hexapod manufacturers simply state the extrema of each of the six dimensions, which is very misleading. As a compromise, a special 3D subset of the complete workspace is proposed, an approximation of which can be readily obtained using a computer‐aided design (CAD)/computer‐aided manufacturing (CAM) software suite, such as computer‐aided 3D interactive application (CATIA). While calibration techniques for serial robots are readily available, there is still no generally agreed procedure for calibrating hexapods. The paper proposes a simple calibration ...

A Pair of Measures of Rotational Error for Axisymmetric Robot End-Effectors

This paper deals with the problem of representing the rotational error of spatial robots with three orientational degrees of freedom (DOF). Typically, the errors on each of three Euler angles defining the orientation of an end-effector are analyzed separately. However, this is wrong since an accuracy measure should depend only on the “distance” between the nominal pose and the actual one, and not on the choice of reference frame in which these are represented. Several bi-invariant metrics for rotational error exist but are single-parameter and, by definition, disregard the shape of the robot end-effector. Yet, robot end-effectors are typically axisymmetric. Therefore, we propose a two-parameter measure of rotational errors that is better suited for such robot endeffectors.

Shaking Forces Minimization of High-Speed Robots via an Optimal Motion Planning

This paper deals with the problem of shaking force balancing of high-speed robots based on a new optimal trajectory planning approach. The aim of the new approach is the optimal path planning of the robot links centre of masses, which allows a considerable reduction of the variable inertia forces transmitted to the robot frame. The efficiency of the suggested method is illustrated by a numerical simulation of a planar two links 2R serial robot, in which reductions in the shaking force of 63 % and in input torque of 84 % are achieved.

Technology-Oriented Optimization of the Secondary Design Parameters of Robots for High-Speed Machining Applications

In this paper, a new methodology for the optimal design of the secondary geometric parameters (shape of links, size of the platform, etc.) of parallel kinematic machine tools is proposed. This approach aims at minimizing the total mass of the robot under position accuracy constraints. This methodology is applied to two translational parallel robots with three degrees-of-freedom (DOF): the Y-STAR and the UraneSX. The proposed approach is able to speed up the design process and to help the designer to find more quickly a set of design parameters.Copyright

ON THE DYNAMIC PROPERTIES OF FLEXIBLE PARALLEL MANIPULATORS IN THE PRESENCE OF PAYLOAD AND TYPE 2 SINGULARITIES

It is known that a parallel manipulator at a singular configuration can gain one or more degrees of freedom and become uncontrollable. In our recent work [1], the dynamic properties of rigid-link parallel manipulators, in the presence of Type 2 singularities, have been studied. It was shown that any parallel manipulator can pass through the singular positions without perturbation of motion if the wrench applied on the end-effector by the legs and external efforts is orthogonal to the twist along the direction of the uncontrollable motion. This condition was obtained using symbolic approach based on the inverse dynamics and the study of the Lagrangian of a general rigid-link parallel manipulator. It was validated by experimental tests carried out on the prototype of a four-degrees-of-freedom parallel manipulator. However, it is known that the flexibility of the mechanism may not always been neglected. Indeed, for robots, joint flexibility can be the main source contributing to overall manipulator flexibility and can lead to trajectory distortion. Therefore, in our second paper [2], the condition of passing through a Type 2 singularity for parallel manipulators with flexible joints has been studied. In the present paper, we expand information about the dynamic properties of parallel manipulators in the presence of Type 2 singularity by including in the studied problem the link flexibility and the payload. The suggested technique is illustrated by a 5R parallel manipulator with flexible elements (actuated joints and moving links) and a payload. The obtained results are validated by numerical simulations carried out using the software ADAMS.