Anatoly Pashkevich

Stiffness analysis of overconstrained parallel manipulators

The paper presents a new stiffness modeling method for overconstrained parallel manipulators with flexible links and compliant actuating joints. It is based on a multidimensional lumped-parameter model that replaces the link flexibility by localized 6-dof virtual springs that describe both translational/rotational compliance and the coupling between them. In contrast to other works, the method involves a FEA-based link stiffness evaluation and employs a new solution strategy of the kinetostatic equations for the unloaded manipulator configuration, which allows computing the stiffness matrix for the overconstrained architectures, including singular manipulator postures. The advantages of the developed technique are confirmed by application examples, which deal with comparative stiffness analysis of two translational parallel manipulators of 3-PUU and 3-PRPaR architectures. Accuracy of the proposed approach was evaluated for a case study, which focuses on stiffness analysis of Orthoglide parallel manipulator.

Kinematics and workspace analysis of a three-axis parallel manipulator: the Orthoglide

The paper addresses kinematic and geometrical aspects of the Orthoglide, a three-DOF parallel mechanism. This machine consists of three fixed linear joints, which are mounted orthogonally, three identical legs and a mobile platform, which moves in the Cartesian x-y-z space with fixed orientation. New solutions to solve inverse/direct kinematics are proposed, and we perform a detailed workspace and singularity analysis, taking into account specific joint limit constraints.

Kinematic aspects of a robot-positioner system in an arc welding application

This paper focuses on the kinematic control of a redundant robotic system taking into account particularities of the arc welding technology. The considered system consists of a 6-axis industrial robot (welding tool manipulator) and a 2-axis welding positioner (workpiece manipulator) that is intended to optimise a weld joint orientation during the technological process. The particular contribution of the paper lies in the area of the positioner inverse kinematics, which is a key issue of such system off-line programming and control. It has been proposed a novel formulation and a closed-form solution of the inverse kinematic problem that deals with the explicit definition of the weld joint orientation relative to the gravity. Similar results have also been obtained for the known problem statement that is based on a unit vector transformation. For both the cases, a detailed investigation of the singularities and uniqueness-existence topics have been carried out. The presented results are implemented in a commercial software package and verified for real-life applications in the automotive industry.

Stiffness Matrix of Manipulators With Passive Joints: Computational Aspects

This paper focuses on stiffness matrix computation for manipulators with passive joints, compliant actuators, and flexible links. It proposes both explicit analytical expressions and an efficient recursive procedure that are applicable in the general case and allow us to obtain the desired matrix either in analytical or numerical form. Advantages of the developed technique and its ability to produce both singular and nonsingular stiffness matrices are illustrated by application examples that deal with stiffness modeling of two Stewart-Gough platforms.

Optimal technology-oriented design of parallel robots for high-speed machining applications

In this paper, a new methodology for the optimal design of parallel kinematic machine tools is proposed. This approach is based on the concept of the maximal inscribed parallelepiped and uses technology-oriented constraints that are motivated by particular applications. This methodology is applied on two translational parallel robots with three degrees-of-freedom (DOF): the Y-STAR and the UraneSX. An analysis of the size of their workspace as a function of the design constraints is made. It is shown that, for identical workspaces with similar properties, the size of the legs of the UraneSX are greater than for the Y-STAR, thus leading to larger deformations. However, the footprint surface needed in order to install the Y-STAR is about two times bigger than for the UraneSX. Therefore, it may be interested to use the UraneSX in order to save some place on ground in manufacturing centres.

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.

Manipulator motion planning for high-speed robotic laser cutting

Recent advances in laser technology, especially the increase of the cutting speed, has motivated the amendment of the existing robot path methods, which do not allow the complete utilisation of the actuator capabilities and neglect certain particularities in the mechanical design of the wrist of the manipulator arm. This research addresses the optimisation of the six-axis robot motion for continuous contour tracking while considering the redundancy caused by the tool axial symmetry. The particular contribution of the paper is in the area of multi-objective path planning using the graph-based search space representation. In contrast to previous work, the developed optimisation technique is based on dynamic programming and explicitly incorporates verification of the velocity/acceleration constraints. This allows the designer to define interactively their importance with respect to the path-smoothness objectives. In addition, this optimisation technique takes into account the capacity of certain manipulator wrist axes for unlimited rotation in order to produce more economical motion. The efficiency of the developed algorithms has been carefully investigated via computer simulation. The presented results are implemented in a commercial software package and verified for real-life applications in the automotive industry.

Stiffness analysis of 3-d.o.f. overconstrained translational parallel manipulators

The paper presents a new stiffness modelling method for overconstrained parallel manipulators, which is applied to 3-d.o.f. translational mechanisms. It is based on a multidimensional lumped-parameter model that replaces the link flexibility by localized 6-d.o.f. virtual springs. In contrast to other works, the method includes a FEA-based link stiffness evaluation and employs a new solution strategy of the kinetostatic equations, which allows computing the stiffness matrix for the overconstrained architectures and for the singular manipulator postures. The advantages of the developed technique are confirmed by application examples, which deal with comparative stiffness analysis of two translational parallel manipulators.

Cluster-level operations planning for the out-of-position robotic arc-welding

Recent advances in computer vision and arc-welding technology have motivated a rethinking of several postulates and conventions incorporated in the existing robot off-line programming methods. This paper addresses relaxing of the downhand-position assumption, which became a de facto standard in robotic welding and requires the weldline to be horizontal and the weld normal vector to be opposite to gravity. In contrast to the standard techniques, the developed method explicitly assumes that a weld may be processed in the out-of-position location, which differs from the downhand location within given tolerances. However, to ensure the prescribed quality, the downhand deviation is charged by a reduction in the welding speed. For such settings, a novel method is proposed for the cluster-level welding operations planning for a robotic cell with a positioning table. The objective is to minimize the overall manufacturing time by finding a reasonable trade-off between the positioner motion times and the cluster processing times. It is shown that the associated optimization problem may be presented as a specific case of the generalized travelling salesman problem, for which an efficient heuristic algorithm has been developed that produces both the optimal welding cluster sequence and corresponding optimal motions of the positioner. The algorithm effectiveness was verified for a number of randomly generated test problems, for which the results are reported and analysed in detail. An industrial case study is also presented, confirming the validity of the developed technique.

Modeling Demand For Inventory Management Of Slow-Moving Items in Case of Reporting Errors

Abstract The paper is devoted to the problem of modeling demand for inventory management of slow-moving items in the case of reporting errors. It is proposed a generalization of the beta-binomial demand model that takes into account possible reporting errors in the learning sample. For the new model, there are developed identification and forecasting algorithms that provide consistent estimators of the model parameters and mean square optimal forecasts. The efficiency of the proposed approach is illustrated by an application example for slow-moving car parts.