Despite their well-known advantages in terms of higher intrinsic rigidity, larger payload-to-weight ratio, and higher velocity and acceleration capacities, parallel robots have drawbacks. Among them, the most important one is surely the presence of singularities in the workspace, which divide the workspace into different aspects (each aspect corresponding to one or more assembly modes) and near which the performance is considerably reduced. In order to increase the reachable workspace of parallel robots, a promising solution consists in the definition of optimal trajectories passing through the singularities to change either the leg working modes or the robot assembly modes. Previous works on the field have shown that it is possible to define optimal trajectories that allow the passing through the robot type 2 singularities. Such trajectories must respect a physical criterion that can be obtained through the analysis of the degeneracy conditions of the parallel robot inverse dynamic model. However, the mentioned works were not complete: they lacked a degeneracy condition of the parallel robot inverse dynamic model, which is not due to type 2 singularity anymore, but to a serial singularity. Crossing a serial singularity is appealing as in that case we can change the robot leg working mode and then potentially access to other workspace zones. This absence is due to the fact that the authors used a reduced dynamic model, which was not taking into account all link dynamic parameters. The present paper aims to fill this gap by providing a complete study of the degeneracy conditions of the parallel robot dynamic model and by demonstrating that it is possible to cross the type 2, but also serial singularity, by defining trajectories that respect some given criteria obtained from the analysis of the degeneracy of the robot dynamic model. It also aims to demonstrate that the serial singularities have impacts on the robot effort transmission, which is a point that is usually bypassed in the literature. All theoretical developments are validated through simulations and experiments.

https://hal.archives-ouvertes.fr/hal-01203185/document

Degeneracy conditions of the dynamic model of parallel robots

Parallel Kinematic Machines (PKMs) are being widely used for precise applications to achieve complex motions and variable poses for the end effector tool. PKMs are found in medical, assembly and manufacturing industries where accuracy is necessary. It is often desired to have a compact and simple architecture for the robotic mechanism. In this paper, the kinematic and dynamic analysis of a novel 3-PRUS (P: prismatic joint, R: revolute joint, U: universal joint, S: spherical joint) parallel manipulator with a mobile platform having 6 Degree of Freedom (DoF) is explained. The kinematic equations for the proposed spatial parallel mechanism are formulated using the Modified Denavit-Hartenberg (DH) technique considering both active and passive joints. The kinematic equations are used to derive the Jacobian matrix of the mechanism to identify the singular points within the workspace. A Jacobian based stiffness analysis is done to understand the variations in stiffness for different poses of the mobile platform and further, it is used to decide trajectories for the end effector within the singularity free region. The analytical model of the robot dynamics is presented using the Euler-Lagrangian approach with Lagrangian multipliers to include the system constraints. The gravity and inertial forces of all links are considered in the mathematical model. The analytical results of the dynamic model are compared with ADAMS simulation results for a pre-defined trajectory of the end effector.

/pdf/kinematic-and-dynamic-analysis-of-a-3-prus-spatial-parallel-iwm8u460mr.pdf

Kinematic and Dynamic Analysis of a 3-PRUS Spatial Parallel Manipulator

This paper deals with the design of a new robust adaptive controller for parallel manipulators based on sliding mode and modelbased adaptive control. More precisely, the proposed controller relies on continuous finite-time terminal sliding mode (TSM) control and the linear-in-the-parameters property of the inverse dynamics of the manipulator. The main motivation behind the proposed scheme is to improve the tracking performance of fast and accurate parallel manipulators while guaranteeing the closed-loop system's robustness. Based on the linear-in-the-parameters property of the inverse dynamics of the manipulator, an adaptive law is proposed in order to estimate in real-time the dynamic parameters of the manipulator. The proposed controller has the advantage of relying on the desired reference trajectories instead of measured ones which can improve its robustness and efficiency. To demonstrate the effectiveness of the proposed controller, real-time experiments are conducted on a four-degree-of-freedom parallel manipulator called Veloce.

/pdf/a-novel-adaptive-terminal-sliding-mode-control-for-parallel-1d6key6wu8.pdf

A novel adaptive terminal sliding mode control for parallel manipulators: Design and real-time experiments

This article presents the variability of Fused deposition modelling (FDM) technology and the possibilities of its use in the design and implementation of a prototype atypical device. The assumptions of the behaviour of individual components and subsystems of the design result from an extensive application of the finite element method and motion analysis of subsystems and various parts of the structure. The use of this method to such an extent accelerated the design process and its implementation. The proposal itself reflects the current state of this technology and its focus is on improving sustainable development. As is generally known, great efforts are currently being made to reduce plastic waste volume and its environmental burden. The proposed concept is modified to replace the final treatment of the top layers of the models, called “ironing” by non-planar layering of material. At the same time, it points out the advantages of this method in reducing energy requirements and the time required to produce models. The conclusion is a conceptual design of a printhead for a proposed prototype, designed to use recycled FDM, intending to streamline the possibility of recycling with little serial and piece production. This process thus closes the circle of opportunities published by us, which in the future can contribute to the optimisation of this technology towards increasing the efficiency of resource use, reduction of energy demands and environmental burden.

Design of an Atypical Construction of Equipment for Additive Manufacturing with a Conceptual Solution of a Printhead Intended for the Use of Recycled Plastic Materials

Пространственный механизм манипулятора с шестью степенями свободы, содержащий основание, выходное звено, соединяющие основание и выходное звено кинематические цепи, включающие в себя промежуточные звенья и приводы вращательного и поступательного движения, отличающийся тем, что выходное звено с установленным на хвостовике приводом вращательного движения установлено на платформе, соединенной с основанием посредством кинематической цепи, включающей в себя семь поступательных приводов, четыре из которых с вертикальным расположением осей сопряжены с одной стороны с основанием, а с другой стороны - с тремя приводами с горизонтальным расположением осей, соединенных между собой по ортогональной схеме, один из которых сопряжен с закрепленным на платформе вращательным приводом, имеющим в свою очередь кинематическую связь с установленным на хвостовике выходного звена вращательным приводом посредством кинематической цепи, состоящей из трех пар последовательно соединенных вращательных приводов с параллельно расположенными осями, при этом установленный на хвостовике вращательный привод подвижно связан с платформой посредством направляющей, выполненной в виде дуги с прорезью, концы которой присоединены к подвижным частям двух вращательных приводов, соосно закрепленных на платформе

Пространственный механизм с шестью степенями свободы

This paper presents a novel six-legged parallel robot, the kinematic model of which is simpler than that of the simplest six-axis serial robot. The new robot is the 6-DOF extension of the Cartesian parallel robot. It consists of three pairs of base-mounted prismatic actuators, the directions in each pair parallel to one of the axes of a Cartesian coordinate system. In each of the six legs, there are also two passive revolute joints, the axes of which are parallel to the direction of the prismatic joint. Finally, each leg is attached to the mobile platform via a spherical joint. The direct kinematics of the novel parallel robot can be solved easily by partitioning the orientation and the position of the mobile platform. There are eight distinct solutions, which can be found directly by solving a linear system and alternating the signs of three radicals. This parallel robot has a large workspace and is suitable for machining or rapid prototyping, as detailed in this paper.

Nicholas Seward

Papers

A new 6-DOF parallel robot with simple kinematic model