A Geometric Approach to the Design of Serial and Parallel Manipulators with Passive Joints (original) (raw)
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Enhanced stiffness modeling of serial manipulators with passive joints
Advances in Robot Manipulators, 2010
The chapter focuses on the enhanced stiffness modeling and analysis of serial kinematic chains with passive joints, which are widely used in parallel robotic systems. In contrast to previous works, the stiffness is evaluated for the loaded working mode corresponding to the static equilibrium of the elastic forces and the external wrench acting upon the manipulator end point. It is assumed that the manipulator elasticity is described by a multidimensional lumped-parameter model, which consists of a chain of rigid bodies connected by 6-dof virtual springs. Each of these springs characterize flexibility of the corresponding link or actuating joint and takes into account both their translational/rotational compliance and the coupling between them. The proposed technique allows finding the full-scale "loaddeflection" relation for any given workspace point and to linearise it taking into account variation of the manipulator Jacobian due to the external load. These enable evaluating critical forces that may provoke non-linear behavior of the manipulator, such as sudden failure due to elastic instability (buckling). The advantages of the developed technique are illustrated by several examples that deal with kinematic chains employed in typical parallel manipulators.
Stability of manipulator configuration under external loading
ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis, ESDA 2012, 2012
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Study of the passive compliance of parallel manipulators
Mechanism and Machine Theory, 1999
The paper studies the mechanical characteristic stiffness or compliance by means of which the interaction of a manipulator with the environment is controlled. A mechanical model of manipulators with parallel structure is presented in which compliance is determined by the shaft stiffnesses in the joints and by the antagonistically acting driving forces. An optimization procedure of the stiffness of a manipulator with a variable structure is proposed. Computer experiments on the compliance of a parallel manipulator have been performed. The results are visualized by means of the compliance ellipses and ellipsoids.
Stiffness Analysis of Parallel Manipulators with Preloaded Passive Joints
Advances in Robot Kinematics: Motion in Man and Machine, 2010
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/internal loading. The results are illustrated by an example that deals with a parallel manipulator of the Orthoglide family where the internal preloading allows to eliminate the undesired buckling phenomena and to improve the stiffness in the neighborhood of its kinematic singularities.
The paper presents an advanced stiffness modeling technique for perfect and non-perfect parallel manipulators under internal and external loadings. Particular attention is paid to the manipulators composed of non-perfect serial chains, whose geometrical parameters differ from the nominal ones and do not allow to assemble manipulator without internal stresses that considerably affect the stiffness properties and also change the end-effector location. In contrast to other works, several types of loadings are considered simultaneously: an external force applied to the end-effector, internal loadings generated by the assembling of non-perfect serial chains and external loadings applied to the intermediate points (auxiliary loading due to the gravity forces and relevant compensator mechanisms, etc.). For this type of manipulators, a non-linear stiffness modeling technique is proposed that allows 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 the compliance errors caused by the considered factors are illustrated by an example that deals with parallel manipulators of the Orthoglide family. Stiffness modeling for perfect and non-perfect parallel manipulators under internal and external loadings 2 2 Related works on the stiffness modeling of robotic manipulator
Cartesian stiffness matrix of manipulators with passive joints: Analytical approach
IEEE International Conference on Intelligent Robots and Systems, 2011
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. K aggregates the stiffness coefficients of all elastic joints, and θ J is the corresponding kinematic Jacobian. Further, this result was extended by Gosselin for the case of parallel manipulators taking into account elasticity of other mechanical elements [2]. More recent publications present VJM-based stiffness analysis for particular case studies, such as various variants of the Stewart-Gough platform, manipulators with US/UPS legs, CaPAMan, Orthoglide, H4 etc. .
Design and Control of a Compliant Parallel Manipulator
Journal of Mechanical Design, 2002
We describe a novel design for a compliant arm that can be mounted on a mobile robot. Because the arm is compliant, a mobile robot can manipulate or interact with objects that are not precisely positioned in the environment. The main features of the arm are the in-parallel architecture and a novel control scheme that allows us to easily control the Cartesian stiffness or impedance in the plane. Springs are added in series to the limbs of the parallel manipulator. We analyze one limb and the manipulator to determine its performance when either controlling the force applied to an object or controlling its stiffness. Further, we present experimental results that show the performance of the compliant arm.
Mobility and Accuracy Analysis of a Class of Overconstrained Parallel Mechanisms
2017
The paper contributes to the mechanics of a class of overconstrained parallel manipulators. It presents an analytical approach to studying the mobility and accuracy of a special type of parallel manipulator, which has found broad industrial application in semiconductor automation. This is a three-degree-of-freedom closed loop mechanism, which exhibits local mobility in close vicinity of specific (singular) configurations. A distinctive feature of this mechanism when in a specific singular configuration is its ability to “use” the inherent elasticity and backlash of its components in order to perform finite small rotations, instead of using additional kinematic joints. The paper provides a formal description of the motion of the mechanism and its accuracy characteristics by analyzing the equations of constraints imposed on its links. The theoretical results are validated by computer simulations and 3D modeling with SolidWorks.
Design and analysis of a hybrid serial-parallel manipulator
Mechanism and Machine Theory, 1999
This work presents a novel design of a hybrid serial±parallel Stewart like mechanism (HS-PM). This design presents a compromise between high rigidity of fully parallel manipulators and extended workspace of serial manipulators. This mechanism is made of a base and two platforms in series. The ®rst platform, called the mid platform is linked to the base by three legs in parallel. Its motion is restricted to only three translations using three successive prismatic joints linking the mid platform to the base. The second platform, called the top platform, has a spherical joint with the mid platform and three legs in parallel are used to impart the relative motion between these two platforms. Therefore, the top platform has 6 degrees of freedom with respect to the base. The nature of this design presents several advantages. Firstly, a closed-form solution is obtained for this type of mechanism allowing the determination of all possible solutions of the forward analysis problem. This characteristic is a great help in investigating the capabilities of this type of platforms and it is a valuable tool for the engineer to derive its controller. It is also shown that for the lower platform, formed by the base and the mid platform, a maximum of two solutions exist, whereas eight solutions were found for the upper platform, which is made from the mid platform and the top platform. This second result con®rms the numerical solution of the upper platform found in recent literature. Secondly, this design presents the particularity of having the size of the orientation workspace independent of the position of the top platform, unlike the fully parallel mechanisms. This characteristic is achieved by separating the actuators responsible for each type of motion. Indeed, the three legs of the lower platform are responsible of the linear displacement of the top platform, whereas the three legs of the upper platform cause the change of orientation of the top platform. Finally, a numerical example is treated to demonstrate our analysis and to determine the range of permissible extension of the legs. #