The paper presents a methodology to enhance the stiffness analysis of parallel manipulators with parallelogram-based linkage. It directly takes into account the influence of the external loading and allows computing both the non-linear ``load-deflection" relation and relevant rank-deficient stiffness matrix. An equivalent bar-type pseudo-rigid model is also proposed to describe the parallelogram stiffness by means of five mutually coupled virtual springs. The contributions of this paper are highlighted with a parallelogram-type linkage used in a manipulator from the Orthoglide family.
Institut de Recherches en Communications et Cybernétique de Nantes（南特通信与控制研究所）；Ecole des Mines de Nantes（南特矿业学院）
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 fo…
Laboratoire des Sciences du Numérique de Nantes (LS2N)（南特数字科学实验室）；Innopolis University（因诺波利斯大学）；IMT Atlantique Nantes（大西洋矿业电信学院南特校区）；Centre National de la Recherche Scientifique (CNRS)（法国国家科学研究中心）
The paper focuses on the stiffness analysis of multi-link serial planar manipulators, which may demonstrate nonlinear stiffness behavior under the compressive loading. Two important cases are considered, where the manipulator has either a straight or non-straight initial configuration. It was proved that in the first case the loading may cause the buckling if it exceeds some critical value, and the manipulator suddenly changes its straight shape and stiffness properties. For computing this critical force, a general eigenvalue-based technique was proposed that can be applied to any multi-link s…
Ecole des Mines de Nantes（南特矿业学院）；Institut de Recherches en Communications et en Cybernetique de Nantes（南特通信与控制研究所）
The paper presents a methodology to enhance the stiffness analysis of serial and parallel manipulators with passive joints. It directly takes into account the loading influence on the manipulator configuration and, consequently, on its Jacobians and Hessians. The main contributions of this paper are the introduction of a non-linear stiffness model for the manipulators with passive joints, a relevant numerical technique for its linearization and computing of the Cartesian stiffness matrix which allows rank-deficiency. Within the developed technique, the manipulator elements are presented as pse…
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 modeli…
Ecole des Mines de Nantes（南特矿业学院）；Institut de Recherches en Communications et en Cybernetique de Nantes（南特通信与控制研究所）
The paper focuses on stiffness matrix computation for manipulators with passive joints. It proposes both explicit analytical expressions and an efficient recursive procedure that are applicable in general case and allow obtaining the desired matrix either in analytical or numerical form. Advantages of the developed technique and its ability to produce both singular and non-singular stiffness matrices are illustrated by application examples that deal with stiffness modeling of two Stewart-Gough platforms.
Institut de Recherches en Communications et Cybernetique de Nantes（南特通信与控制研究所）；Ecole des Mines de Nantes（南特矿业学院）
The paper focuses on the accuracy improvement of stiffness models for parallel manipulators, which are employed in high-speed precision machining. It is based on the integrated methodology that combines analytical and numerical techniques and deals with multidimensional lumped-parameter models of the links. The latter replace the link flexibility by localized 6-dof virtual springs describing both translational/rotational compliance and the coupling between them. There is presented detailed accuracy analysis of the stiffness identification procedures employed in the commercial CAD systems (incl…
Ecole des Mines de Nantes（南特矿业学院）；National Center for Scientific Research（国家科学研究中心）；University of Nantes（南特大学）
The paper focuses on the stiffness modeling of robotic manipulators with gravity compensators. The main attention is paid to the development of the stiffness model of a spring-based compensator located between sequential links of a serial structure. The derived model allows us to describe the compensator as an equivalent non-linear virtual spring integrated in the corresponding actuated joint. The obtained results have been efficiently applied to the stiffness modeling of a heavy industrial robot of the Kuka family.
Ecole des Mines de Nantes（南特高等矿业学院）；Institut de Recherches en Communications et en Cybernetique de Nantes (IRCCyN)（南特通信与控制研究所）
The 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 obtaining the desired matrix either in analytical or numerical form. Advantages of the developed technique and its ability to produce both singular and non-singular stiffness matrices are illustrated by application examples that deal with stiffness modeling of two Stewart-Gough platforms.
The present project deals with the elastostatic modeling and calibration experiment of spacial industrial manipulators using an optimal selection of measurements pose, for the calibration procedure, the optimal pose selection aims to the efficiency improvement of identification procedure for serial manipulators which reduces noise impact on the parameters identification precision, it is usually used for planar manipulators, our work is mainly to extend the approach for a more complicated manipulator in 3D space using a wise decomposition of the spacial manipulator into a set of serial sub-chai…
Laboratoire des Sciences du Numérique de Nantes (LS2N)（南特数字科学实验室）；IMT Atlantique（大西洋国立高等矿业电信学校）；Centre National de la Recherche Scientifique (CNRS)（法国国家科学研究中心）
The paper focuses on the stiffness modeling of a new type of compliant manipulator and its non-linear behavior while interacting with the environment. The manipulator under study is a serial mechanical structure composed of dualtriangle segments. The main attention is paid to the initial straight configuration which may suddenly change its shape under the loading. It was discovered that under the external loading such manipulator may have six equilibrium configurations but only two of them are stable. In the neighborhood of these configurations, the manipulator behavior was analyzed using the …
The paper focuses on the enhanced stiffness modeling of robotic manipulators by taking into account influence of the external force/torque acting upon the end point. It implements the virtual joint technique that describes the compliance of manipulator elements by a set of localized six-dimensional springs separated by rigid links and perfect joints. In contrast to the conventional formulation, which is valid for the unloaded mode and small displacements, the proposed approach implicitly assumes that the loading leads to the non-negligible changes of the manipulator posture and corresponding a…
Innopolis University（因诺波利斯大学）；Centre National de la Recherche Scientifique (CNRS)（法国国家科学研究中心）；Le Laboratoire des Sciences du Numérique de Nantes (LS2N)（南特数字科学实验室）；IMT Atlantique（大西洋国立高等工业技术与矿业学校）
The paper presents advancement of the matrix structural analysis technique (MSA) for stiffness modeling of robotic manipulators. In contrast to the classical MSA, it can be applied to both parallel and serial manipulators composed of flexible and rigid links connected by rigid, passive or elastic joints with multiple external loadings. The manipulator stiffness model is presented as a set of basic equations describing the link elasticities that are supplemented by a set of constraints describing connections between links. These equations are aggregated straightforwardly in a common linear syst…
Institut de Recherche en Communications et en Cybernétique de Nantes（南特通信与控制研究院）；École des Mines de Nantes（南特矿业学院）
The paper presents a methodology for the enhanced stiffness analysis of parallel manipulators with internal preloading in passive joints. It also takes into account influence of the external loading and allows computing both the non-linear "load-deflection" relation and the stiffness matrices for any given location of the end-platform or actuating drives. Using this methodology, it is proposed the kinetostatic control algorithm that allows to improve accuracy of the classical kinematic control and to compensate position errors caused by elastic deformations in links/joints due to the external/…
Saratoga High School（萨拉托加高中）；University of Michigan（密歇根大学）
We propose a mechanically simple and cheap design for a series elastic actuator with controllable stiffness. Such characteristics are necessary for animals for running, jumping, throwing, and manipulation, yet in robots, variable stiffness actuators are either complicated or mimicked at low bandwidth through feedback controllers. A robust and simple design is needed to build reliable and cheap robots with animal capabilities. The key insight of our design is attaching torsional springs to timing belts to create a variable stiffness linear spring. In an antagonistic pair, varying the distance b…
Ecole des Mines de Nantes（南特矿业学院）；Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制论研究所）
The paper focuses on the calibration of elastostatic parameters of spatial anthropomorphic robots. It proposes a new strategy for optimal selection of the measurement configurations that essentially increases the efficiency of robot calibration. This strategy is based on the concept of the robot test-pose and ensures the best compliance error compensation for the test configuration. The advantages of the proposed approach and its suitability for practical applications are illustrated by numerical examples, which deal with calibration of elastostatic parameters of a 3 degrees of freedom anthrop…
IRCCyN (UMR CNRS 6597)（法国南特中央理工学院）；École des Mines de Nantes（南特矿业学院）
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…
Institut de Recherches en Communications et Cybernetique de Nantes（南特通信与控制研究所）；Ecole des Mines de Nantes（南特矿业学院）
This paper focuses on the performance evaluation of the parallel manipulators for milling of composite materials. For this application the most significant performance measurements, which denote the ability of the manipulator for the machining are defined. In this case, optimal synthesis task is solved as a multicriterion optimization problem with respect to the geometric, kinematic, kinetostatic, elastostostatic, dynamic properties. It is shown that stiffness is an important performance factor. Previous models operate with links approximation and calculate stiffness matrix in the neighborhood…
The Stiffness of 3-PRS PM Across Parasitic and Orientational Workspace
School of Mechanical Engineering, Zhejiang University（浙江大学机械工程学院）；Robotics Research Center of Yuyao (Robotics Institute of Zhejiang University)（余姚机器人研究中心（浙江大学机器人研究院））；xR Lab（xR实验室）
A Modular, Tendon Driven Variable Stiffness Manipulator with Internal Routing for Improved Stability and Increased Payload Capacity
National Robotarium（国家机器人研究院）；Heriot Watt University（赫瑞瓦特大学）；Institute for Integrated Micro and Nano Systems（集成微纳系统研究所）；University of Edinburgh（爱丁堡大学）；Tough Cyberphysical AI Research Center (TCPAI)（硬核赛博物理人工智能研究中心）；Tohoku University（东北大学）；Senai Cimatec（塞奈西马泰克）
Ecole des Mines de Nantes（南特矿业学院）；Institut de Recherches en Communications et Cybernétique de Nantes（南特通信与控制研究所）
The paper presents a new stiffness modelling method for multi-chain parallel robotic manipulators with flexible links and compliant actuating joints. In contrast to other works, the method involves a FEA-based link stiffness evaluation and employs a new solution strategy of the kinetostatic equations, which allows computing the stiffness matrix for singular postures and to take into account influence of the external forces. The advantages of the developed technique are confirmed by application examples, which deal with stiffness analysis of a parallel manipulator of the Orthoglide family
Ecole des Mines de Nantes（南特高等矿业学校）；Institut de Recherches en Communications et en Cybernetique de Nantes（南特通信与控制论研究所）
The paper presents an approach for the identification of elasto-static parameters of a robotic manipulator using the virtual experiments in a CAD environment. It is based on the numerical processing of the data extracted from the finite element analysis results, which are obtained for isolated manipulator links. This approach allows to obtain the desired stiffness matrices taking into account the complex shape of the links, couplings between rotational/translational deflections and particularities of the joints connecting adjacent links. These matrices are integral parts of the manipulator lum…
Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）
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…
Laboratoire des Sciences du Numérique de Nantes (LS2N), UMR CNRS 6004（南特数字科学实验室（法国国家科学研究中心UMR 6004））；Ecole Centrale Nantes（南特中央理工学院）；IMT Atlantique（大西洋电信学院）；Innopolis University（因诺波利斯大学）；Centre National de la Recherche Scientifique (CNRS)（法国国家科学研究中心）
The paper focuses on the mechanics of a compliant serial manipulator composed of new type of dual-triangle elastic segments. Both the analytical and numerical methods were used to find the manipulator stable and unstable equilibrium configurations, as well as to predict corresponding manipulator shapes. The stiffness analysis was carried on for both loaded and unloaded modes, the stiffness matrices were computed using the Virtual Joint Method (VJM). The results demonstrate that either buckling or quasi-buckling phenomenon may occur under the loading, if the manipulator corresponding initial co…
Most aerial manipulators use serial rigid-link designs, which results in large forces when initiating contacts during manipulation and could cause flight stability difficulty. This limitation could potentially be improved by the compliance of continuum manipulators. To achieve this goal, we present the novel design of a compact, lightweight, and modular cable-driven continuum manipulator for aerial drones. We then derive a complete modeling framework for its kinematics, statics, and stiffness (compliance). The modeling framework can guide the control and design problems to integrate the manipu…
ATDM:An Anthropomorphic Aerial Tendon-driven Manipulator with Low-Inertia and High-Stiffness
Research Institute of Intelligent Control and Systems, Harbin Institute of Technology（哈尔滨工业大学智能控制与系统研究所）；Peng Cheng Laboratory（鹏城实验室）；Ningbo Institute of Intelligent Equipment Technology Co., Ltd.（宁波智能装备技术研究院有限公司）
Ecole des Mines de Nantes（南特高等矿业学院）；Institut de Recherches en Communications et Cybernétique de Nantes（南特通信与控制研究所）
The paper presents a new stiffness modelling method for multi-chain parallel robotic manipulators with flexible links and compliant actuating joints. In contrast to other works, the method involves a FEA-based link stiffness evaluation and employs a new solution strategy of the kinetostatic equations, which allows computing the stiffness matrix for singular postures and to take into account influence of the internal forces. The advantages of the developed technique are confirmed by application examples, which deal with stiffness analysis of the Orthoglide manipulator.
Institut de Recherches en Communications et Cybernétique de Nantes（南特通信与控制研究院）
This paper presents a parametric stiffness analysis of the Orthoglide. A compliant modeling and a symbolic expression of the stiffness matrix are conducted. This allows a simple systematic analysis of the influence of the geometric design parameters and to quickly identify the critical link parameters. Our symbolic model is used to display the stiffest areas of the workspace for a specific machining task. Our approach can be applied to any parallel manipulator for which stiffness is a critical issue.
Institut de Recherche en Communications et Cybernetique de Nantes（南特通信与控制论研究所）；Ecole des Mines de Nantes（南特国立高等矿业学校）；University of Agder（阿格德大学）
The paper is devoted to the compliance errors compensation for parallel manipulators under external loading. Proposed approach is based on the non-linear stiffness modeling and reduces to a proper adjusting of a target trajectory. In contrast to previous works, in addition to compliance errors caused by machining forces, the problem of assembling errors caused by inaccuracy in the kinematic chains is considered. The advantages and practical significance of the proposed approach are illustrated by examples that deal with groove milling with Orthoglide manipulator.
Institut de Recherche en Cybernétique de Nantes（南特控制论研究所）
The aim of this paper is to characterize the moveability of fully-parallel manipulators in the presence of obstacles. Fully parallel manipulators are used in applications where accuracy, stiffness or high speeds and accelerations are required \cite{Merlet:97}. However, one of its main drawbacks is a relatively small workspace compared to the one of serial manipulators. This is due mainly to the existence of potential internal collisions, and the existence of singularities. In this paper, the notion of free aspect is defined which permits to exhibit domains of the workspace and the joint space …
University of Texas at Austin（德克萨斯大学奥斯汀分校）；Cornerstone Robotics Limited（基石机器人有限公司）；The Chinese University of Hong Kong（香港中文大学）；Johns Hopkins University（约翰斯·霍普金斯大学）
This paper addresses the problem of controlling a continuum manipulator (CM) in free or obstructed environments with no prior knowledge about the deformation behavior of the CM and the stiffness and geometry of the interacting obstructed environment. We propose a versatile data-driven priori-model-independent (PMI) control framework, in which various control paradigms (e.g. CM's position or shape control) can be defined based on the provided feedback. This optimal iterative algorithm learns the deformation behavior of the CM in interaction with an unknown environment, in real time, and then ac…
Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）；CNRS（法国国家科学研究中心）
This paper deals with the comparison of planar parallel manipulator architectures based on a multi-objective design optimization approach. The manipulator architectures are compared with regard to their mass in motion and their regular workspace size, i.e., the objective functions. The optimization problem is subject to constraints on the manipulator dexterity and stiffness. For a given external wrench, the displacements of the moving platform have to be smaller than given values throughout the obtained maximum regular dexterous workspace. The contributions of the paper are highlighted with th…
Ecole des Mines de Nantes（南特高等矿业学院）；Institut de Recherches en Communications et Cybernétique de Nantes（南特通信与控制研究所）
The paper proposes an integrated approach to the design optimization of parallel manipulators, which is based on the concept of the workspace grid and utilizes the goal-attainment formulation for the global optimization. To combine the non-homogenous design specification, the developed optimization technique transforms all constraints and objectives into similar performance indices related to the maximum size of the prescribed shape workspace. This transformation is based on the dedicated dynamic programming procedures that satisfy computational requirements of modern CAD. Efficiency of the de…
Institut de Recherches en Communications et Cybernétique de Nantes（南特通信与控制研究所）；École Centrale de Nantes（南特中央理工学院）；École des Mines de Nantes（南特矿业学院）；Université de Nantes（南特大学）；Université Laval（拉瓦尔大学）
This paper presents a parametric stiffness analysis of the Orthoglide, a 3-DOF translational Parallel Kinematic Machine. First, a compliant modeling of the Orthoglide is conducted based on an existing method. Then stiffness matrix is symbolically computed. This allows one to easily study the influence of the geometric design parameters on the matrix elements. Critical links are displayed. Cutting forces are then modeled so that static displacements of the Orthoglide tool during slot milling are symbolically computed. Influence of the geometric design parameters on the static displacements is c…
Institut de Recherche en Cybernétique de Nantes (IRCyN)（南特控制论研究所）；McGill University（麦吉尔大学）
This paper focuses on the kinematic properties of a new three-degree-of-freedom hybrid manipulator. This manipulator is obtained by adding in series to a five-bar planar mechanism (similar to the one studied by Bajpai and Roth) a third revolute passing through the line of centers of the two actuated revolute joints of the above linkage. The resulting architecture is hybrid in that it has both serial and parallel links. Fully-parallel manipulators are known for the existence of particularly undesirable singularities (referred to as parallel singularities) where control is lost [4] and [6]. On t…
Ultra-slender Coaxial Antagonistic Tubular Robot for Ambidextrous Manipulation
West China Hospital of Medicine, Sichuan University（四川大学华西医学院）；Shien-Ming Wu School of Intelligent Engineering, South China University of Technology（华南理工大学伍舜明智能工程学院）；School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China（电子科技大学机械与电气工程学院）；School of Mechanical Engineering, Sichuan University（四川大学机械工程学院）；Centre for Artificial Intelligence and Robotics (CAIR) Hong Kong Institute of Science and Innovation, Chinese Academy of Sciences（中国科学院香港创新研究院人工智能与机器人中心）
Belarusian State University of Informatics and Radioelectronics（白俄罗斯信息与无线电电子大学）；Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）；CNRS（法国国家科学研究中心）
The Orthoglide is a Delta-type PKM dedicated to 3-axis rapid machining applications that was originally developed at IRCCyN in 2000-2001 to meet the advantages of both serial 3-axis machines (regular workspace and homogeneous performances) and parallel kinematic architectures (good dynamic performances and stiffness). This machine has three fixed parallel linear joints that are mounted orthogonally. The geometric parameters of the Orthoglide were defined as function of the size of a prescribed cubic Cartesian workspace that is free of singularities and internal collision. The interesting featu…
Institut de Recherches en Communications et Cybernétique de Nantes (IRCCyN)（南特通信与控制研究所）；Ecole des Mines de Nantes（南特矿业学院）
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 l…
Belarusian State University of Informatics and Radioelectronics（白俄罗斯信息与无线电电子大学）；Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制研究所）；CNRS（法国国家科学研究中心）；École Centrale de Nantes（南特中央理工学院）；Université de Nantes（南特大学）；École des Mines de Nantes（南特矿业学院）
The paper addresses the geometric synthesis of Orthoglide-type mechanism, a family of 3-DOF parallel manipulators for rapid machining applications, which combine advantages of both serial mechanisms and parallel kinematic architectures. These manipulators possess quasi-isotropic kinematic performances and are made up of three actuated fixed prismatic joints, which are mutually orthogonal and connected to a mobile platform via three parallelogram chains. The platform moves in the Cartesian space with fixed orientation, similar to conventional XYZ-machine. Three strategies have been proposed to …
College of Engineering, University of Massachusetts Amherst（工程学院，马萨诸塞大学阿姆赫斯特分校）；College of Information and Computer Sciences, University of Massachusetts Amherst（信息与计算机科学学院，马萨诸塞大学阿姆赫斯特分校）
Ecole des Mines de Nantes（南特矿业学院）；Institut de Recherches en Communications et en Cybernétique de Nantes（南特通信与控制论研究所）；University of Agder（阿格德大学）
The paper presents the compliance errors compensation technique for over-constrained parallel manipulators under external and internal loadings. This technique is based on the non-linear stiffness modeling which is able to take into account the influence of non-perfect geometry of serial chains caused by manufacturing errors. Within the developed technique, the deviation compensation reduces to an adjustment of a target trajectory that is modified in the off-line mode. The advantages and practical significance of the proposed technique are illustrated by an example that deals with groove milli…
