Dynamics of the Orthoglide parallel robot

Recursive matrix relations for kinematics and dynamics of the Orthoglide parallel robot having three concurrent prismatic actuators are established in this paper. These are arranged according to the Cartesian coordinate system with fixed orientation, which means that the actuating directions are normal to each other. Three identical legs connecting to the moving platform are located on three planes being perpendicular to each other too. Knowing the position and the translation motion of the platform, we develop the inverse kinematics problem and determine the position, velocity and acceleration of each element of the robot. Further, the principle of virtual work is used in the inverse dynamic problem. Some matrix equations offer iterative expressions and graphs for the input forces and the powers of the three actuators

Mechatronic modeling of a parallel kinematics multi-axial simulation table based on decoupling the actuators and manipulator dynamics

In this work a mechatronic model was developed for a parallel Multi-Axial Simulation Table (MAST) mechanism. The dynamics of the mechanism was obtained using the principle of energy equivalence and Boltzmann–Hamel equations. In this way, the procedure to obtain the explicit dynamic equations is simplified and has the advantage of being systematic. Also, the actuators and the control were modeled and integrated to simulate and study the system’s positioning and torque. A remarkable contribution of this work is that the mechatronic model developed considers the mechanism as a disturbance to the actuators in a decoupled manner, allowing to easily evaluate alternative designs of whether the actuators, the mechanism or both. Additionally, the procedure taken has been validated with experimental data from an actual MAST prototype.The authors of this paper wish to acknowledge the funding received from the Spanish Government via the Ministerio de Economía y Competitividad (BES-2012-053723 under Project DPI2011-22955 and DPI2015-64450-R), the ERDF of the European Union, the Government of the Basque Country (SAIOTEK 2013 SAI13/245), and the financial support from the University of the Basque Country(UPV/EHU) under the program UFI 11/29

Modeling and simulation of a Stewart platform type parallel structure robot

The kinematics and dynamics of a Stewart Platform type parallel structure robot (NASA's Dynamic Docking Test System) were modeled using the method of kinematic influence coefficients (KIC) and isomorphic transformations of system dependence from one set of generalized coordinates to another. By specifying the end-effector (platform) time trajectory, the required generalized input forces which would theoretically yield the desired motion were determined. It was found that the relationship between the platform motion and the actuators motion was nonlinear. In addition, the contribution to the total generalized forces, required at the actuators, from the acceleration related terms were found to be more significant than the velocity related terms. Hence, the curve representing the total required actuator force generally resembled the curve for the acceleration related force. Another observation revealed that the acceleration related effective inertia matrix I sub dd had the tendency to decouple, with the elements on the main diagonal of I sub dd being larger than the off-diagonal elements, while the velocity related inertia power array P sub ddd did not show such tendency. This tendency results in the acceleration related force curve of a given actuator resembling the acceleration profile of that particular actuator. Furthermore, it was indicated that the effective inertia matrix for the legs is more decoupled than that for the platform. These observations provide essential information for further research to develop an effective control strategy for real-time control of the Dynamic Docking Test System

Static force capabilities and dynamic capabilities of parallel mechanisms equipped with safety clutches

Cette thèse étudie les forces potentielles des mécanismes parallèles plans à deux degrés de liberté équipés d'embrayages de sécurité (limiteur de couple). Les forces potentielles sont étudiées sur la base des matrices jacobienne. La force maximale qui peut être appliquée à l'effecteur en fonction des limiteurs de couple ainsi que la force maximale isotrope sont déterminées. Le rapport entre ces deux forces est appelé l'efficacité de la force et peut être considéré ; comme un indice de performance. Enfin, les résultats numériques proposés donnent un aperçu sur la conception de robots coopératifs reposant sur des architectures parallèles. En isolant chaque lien, les modèles dynamiques approximatifs sont obtenus à partir de l'approche Newton-Euler et des équations de Lagrange pour du tripteron et du quadrupteron. La plage de l'accélération de l'effecteur et de la force externe autorisée peut être trouvée pour une plage donnée de forces d'actionnement.This thesis investigates the force capabilities of two-degree-of-freedom planar parallel mechanisms that are equipped with safety clutches (torque limiters). The force capabilities are studied based on the Jacobian matrices. The maximum force that can be applied at the end-effector for given torque limits (safety index) is determined together with the maximum isotropic force that can be produced. The ratio between these two forces, referred to as the force effectiveness, can be considered as a performance index. Finally, some numerical results are proposed which can provide insight into the design of cooperation robots based on parallel architectures. Considering each link and slider system as a single body, approximate dynamic models are derived based on the Newton-Euler approach and Lagrange equations for the tripteron and the quadrupteron. The acceleration range or the external force range of the end-effector are determined and given as a safety consideration with the dynamic models

Stiffness modeling of non-perfect parallel manipulators

The paper focuses on the stiffness modeling of parallel manipulators composed of non-perfect serial chains, whose geometrical parameters differ from the nominal ones. In these manipulators, there usually exist essential internal forces/torques that considerably affect the stiffness properties and also change the end-effector location. These internal load-ings are caused by elastic deformations of the manipulator ele-ments during assembling, while the geometrical errors in the chains are compensated for by applying appropriate forces. For this type of manipulators, a non-linear stiffness modeling tech-nique is proposed that allows us to take into account inaccuracy in the chains and to aggregate their stiffness models for the case of both small and large deflections. Advantages of the developed technique and its ability to compute and compensate for the compliance errors caused by different factors are illustrated by an example that deals with parallel manipulators of the Or-thoglide famil

Optimal Reconfiguration of a Parallel Robot for Forward Singularities Avoidance in Rehabilitation Therapies. A Comparison via Different Optimization Methods

[EN] This paper presents an efficient algorithm for the reconfiguration of a parallel kinematic manipulator with four degrees of freedom. The reconfiguration of the parallel manipulator is posed as a nonlinear optimization problem where the design variables correspond to the anchoring points of the limbs of the robot on the fixed platform. The penalty function minimizes the forces applied by the actuators during a specific trajectory. Some constraints are imposed to avoid forward singularities and guarantee the feasibility of the active generalized coordinates for a certain trajectory. The results are compared with different optimization approaches with the aim of avoiding getting trapped into a local minimum and undergoing forward singularities. The comparison covers evolutionary algorithms, heuristics optimizers, multistrategy algorithms, and gradient-based optimizers. The proposed methodology has been successfully tested on an actual parallel robot for different trajectories.This research was funded by the Spanish Ministry of Education, Culture and Sports, grant number DPI2017-84201-R.Llopis-Albert, C.; Valero Chuliá, FJ.; Mata Amela, V.; Pulloquinga-Zapata, J.; Zamora-Ortiz, P.; Escarabajal-Sánchez, RJ. (2020). Optimal Reconfiguration of a Parallel Robot for Forward Singularities Avoidance in Rehabilitation Therapies. A Comparison via Different Optimization Methods. Sustainability. 12(14):1-18. https://doi.org/10.3390/su12145803S1181214Rubio, F., Valero, F., & Llopis-Albert, C. (2019). A review of mobile robots: Concepts, methods, theoretical framework, and applications. International Journal of Advanced Robotic Systems, 16(2), 172988141983959. doi:10.1177/1729881419839596Jamwal, P. K., Xie, S. Q., Hussain, S., & Parsons, J. G. (2014). An Adaptive Wearable Parallel Robot for the Treatment of Ankle Injuries. 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(2019). Modeling Parallel Robot Kinematics for 3T2R and 3T3R Tasks Using Reciprocal Sets of Euler Angles. Robotics, 8(3), 68. doi:10.3390/robotics8030068Chen, Z., Xu, L., Zhang, W., & Li, Q. (2019). Closed-form dynamic modeling and performance analysis of an over-constrained 2PUR-PSR parallel manipulator with parasitic motions. Nonlinear Dynamics, 96(1), 517-534. doi:10.1007/s11071-019-04803-2Zhang, D., & Wei, B. (2017). Interactions and Optimizations Analysis between Stiffness and Workspace of 3-UPU Robotic Mechanism. Measurement Science Review, 17(2), 83-92. doi:10.1515/msr-2017-0011Wu, G., & Zou, P. (2016). Comparison of 3-DOF asymmetrical spherical parallel manipulators with respect to motion/force transmission and stiffness. Mechanism and Machine Theory, 105, 369-387. doi:10.1016/j.mechmachtheory.2016.07.017Meng, W., Xie, S. Q., Liu, Q., Lu, C. Z., & Ai, Q. (2017). Robust Iterative Feedback Tuning Control of a Compliant Rehabilitation Robot for Repetitive Ankle Training. 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A method for the mechatronico analysis of parallel kinematics manipulators based on decoupling the dynamics of actuators and mechanism

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